Search

In this paper, we analyze and provide innovative soliton solutions for a (2+1)-dimensional generalized Korteweg-de Vries (gKdV) problem. We obtain phase shifts and dispersion relations by using the generalized Arnous technique and the Riccati equation approach, thus allowing different soliton solutions to be developed. Several precise solutions with special structural properties, including kink and solitary soliton solutions, are included in our study. This detailed examination demonstrates the complex behavior of the model and its capability to explain a large scale of nonlinear wave occurrences in many physical settings. Thus, in scientific domains such as fluid mechanics, plasma physics, and wave propagation in media ranging from ocean surfaces to optical fibers, our results are crucial to comprehend the principles behind the production and propagation of many complicated phenomena. Finally, we provide 2D and 3D graphs for various solutions that have been obtained using Maple.

The COVID-19 pandemic has impacted many aspects of life, including immunization services. As a result of disruptions in these services, tens of millions of children worldwide are at risk of contracting diphtheria, hundreds of thousands of infants did not receive complete DPT immunization, and more than a million infants missed BCG vaccination at birth. Over the past three years, there has been an increase in mortality rates, reaching 10.6% in 2022. Additionally, the number of diphtheria cases in 2022 was more than twice that of 2021. To address the re-emerging of diphtheria, various studies have been conducted, one of which is through mathematical modeling, which can be useful in predicting the dynamics of disease spread and devising strategies to control it. This study developed a mathematical model to describe the dynamics of diphtheria spread with the influence of vaccination completeness. The dynamical analysis method used is by analyzing the eigenvalues and numerical calculation, while numerical simulations employ Fourth Order Runge-Kutta Method. Results from the dynamical analysis and numerical simulations indicate that the disease-free equilibrium point is stable if basic reproduction number , and the endemic equilibrium point is feasible and stable if . Moreover, increasing the vaccination completeness factor within a given population can aid in efforts to prevent the spread of diphtheria. Based on the simulation of the scenarios developed in this study, diphtheria will not become endemic when the vaccination completeness factor reaches 90% and the treatment rate reaches 30%.

In this study, we investigate the qualitative properties of solutions to a general model of difference equations (DEs), which includes the flour beetle model as a particular case. We investigate local and global stability and boundedness, as well as the periodic behavior of the solutions to this model. Moreover, we present some general theorems that help study the periodicity of solutions to the DEs. The presented numerical examples support the finding and illustrate the behavior of the solutions for the studied model. A significant agricultural pest that is extremely resistant to insecticides is the flour beetle. Therefore, studying the qualitative characteristics of the solutions in this model greatly helps in understanding the behavior of this pest and how to resist it or benefit from it. By applying the general results to the flour beetle model, we clarify the conditions of global stability, boundedness, and periodicity.

Collective migration underlies key developmental and disease processes in vertebrates. Mathematical models describing collective migration can shed light on emergent patterns arising from simple mechanisms. In this paper, a mathematical model for collective migration is given for arbitrary numbers and types of individuals using principles outlined as a set of assumptions, such as the assumed preference for individuals to be “close but not too close" to others. The model is then specified to the case of two species with arbitrary numbers of individuals in each species. A particular form of signal response is used that may be parameterized based on experiments involving two or three agents. In its simplest form, the model describes two species of individuals that emit distinct signals, distinguishes between them, and exhibits responses unique to the type by moving according to signal gradients in various planar regions, a situation described as "mixotaxis". Beyond this simple form, initial conditions and boundary conditions are altered to simulate specific, additional in vitro as well as in vivo dynamics. The behaviors that were specifically accounted for include motility, directed migration, and a functional response to a signal. Ultimately, the paper’s results highlight the ability of a single framework for signal and response to account for patterns seen in multi-species systems, in particular the emergent self-organization seen in the embryonic development of placodal cells, which display chase-and-run behavior, flocking behavior, herding behavior, and the splitting of a herd, depending on initial conditions. Numerical experiments focus around the primary example of neural crest and placodal cell “chase-and-run” and “flocking” behaviors; the model reproduces the separation of placodal cells into distinct clumps, as described in the literature for neural crest and placodal cell development. This model was developed to describe a heterogeneous environment and can be expanded to capture other biological systems with one or more distinct species.

In this article, we investigate the behavior of weak solutions for the three-dimensional Navier-Stokes-Voigt-Brinkman-Forchheimer fluid model with memory and Tresca friction law within a thin domain. We analyze the asymptotic behavior as one dimension of the fluid domain approaches zero. We derive the limit problem and obtain the specific Reynolds equation, while also establishing the uniqueness of the limit velocity and pressure distributions.

Algal blooms pose a significant threat to the ecological integrity and biodiversity in aquatic ecosystems. In lakes, enriched with nutrients, these blooms result in overgrowth of periphyton, leading to biological clogging, oxygen depletion, and ultimately a decline in ecosystem's health and water quality. In this article, we presented a mathematical model centered around the role of aquatic species (specifically fish population) to alleviate algal blooms. The model analysis revealed significant shifts in dynamics, shedding light on the effectiveness of fish-mediated sustainability strategies to control algal proliferation. Notably, our study identified critical thresholds and regime transitions through the observation of saddle-node bifurcation within the proposed mathematical model. To validate our analytical findings, we have conducted numerical simulations, which provided robust evidence for the resilience of the ecosystem under different scenarios.

We propose and analyze a simple modification to the Rosenzweig-MacArthur predator (zooplankton)-prey (phytoplankton) model to account for the interference of the predators with the impacts of nanoparticles. We have taken into account the influence of predators by quantifying the impact of nanoparticles in actual environments. It is shown that the influence of the nanoparticles may reduce the prey's maximum physiological per-capita growth rate. An elementary Lotka-Volterra uptake term is taken into consideration in order to investigate the nanoparticle dynamics or interactions. Most importantly, our research shows that phytoplankton growth suppression caused by nanoparticles can destabilize the system and cause periodic oscillation. Additionally, it was demonstrated that a decrease in the equilibrium densities of both phytoplankton and zooplankton might occur from an increase in the rate of interaction between the nanoparticles and phytoplankton. Additionally, the study shows that the stable coexistence of the system dynamics depends critically on the aquatic system's nanoparticles being depleted. We also looked into the system using different kinds of functional reactions. Compared to other commonly used ecology, The complex relationship that exists between phytoplankton and nanoparticles in the natural environment is better described by the Monod-Haldane functional response.

The COVID-19 pandemic has had a significant impact on public health worldwide.. Mathematical modeling is considered an alternative tool for understanding real-life problems, including the dynamics of COVID-19 spread. This is an applied research that purpose adds vaccination to Zeb et al. (2020) SEIQR model of COVID-19 spread and examines the dynamic of COVID-19 spread in Mataram City. First, we construct the new model by making assumptions. The fixed point and basic reproduction number (R_0 ) are then used to analyze the model using the next-generation matrix method. The next-generation matrix method is utilized to estimate the R_0 in a compartmental disease model. Two fixed points are acquired, specifically the disease-free fixed point, which is locally asymptotically stable under the condition R_01 indicated by Lyapunov function. The population dynamics when R_01 can also be observed through numerical simulation. The results of a numerical simulation indicate that giving the proportion of number vaccinated 62 per cent is effective in suppressing the number of infections.

Tuberculosis (TB) remains one of deadly infectious diseases worldwide. Smoking habits are a significant factor that can increase TB transmission rates, as smokers are more susceptible to contracting TB than nonsmokers. Therefore, a control strategy that focused on minimizing TB transmission among smokers was essential. The control of TB transmission was evaluated based on the case detection rate. Undetected TB cases often resulted from economic challenges, low awareness, negative stigma toward TB patients, and health system delay (HSD). In this study, we developed a mathematical model that captured the dynamics of TB transmission specifically among smokers, incorporating the effects of case detection. Our innovative approach lied in the integration of smoking behavior as a key factor in TB transmission dynamics, which has been underexplored in previous models. We analyzed the existence and stability of the TB model equilibrium based on the basic reproduction number. Additionally, parameter sensitivity analysis was conducted to identify the most influential factors in the spread of the disease. Furthermore, this study investigated the effectiveness of various control strategies, including social distancing for smokers, TB screening in high-risk populations, and TB treatment in low-income communities. By employing the Pontryagin maximum principle, we solved optimal control problems to determine the most effective combination of interventions. Simulation results demonstrated that a targeted combination of control measures can effectively reduce the number of TB-infected individuals.

Mathematical modeling and analysis of a crop-pest interacting system helps us to understand the dynamical properties of the system such as stability, bifurcations and chaos. In this article, a predator-prey type mathematical model for pest control using bio-pesticides has been analysed to study the global stability property of the interior equilibrium point. Moreover, the occurrence and orbital stability of Hopf bifurcating limit cycle solutions have been studied using ref30's conditions. Analytical and numerical results show that the interior equilibrium of the pest control model is globally asymptotically stable. Also, Hopf bifurcating occurs when the bifurcation parameter crosses the critical value, and the bifurcating periodic solution is found to be stable.

Background. The purpose of this study is to develop an effective non-invasive method for determining the properties of the object under consideration. Material and methods. For these purposes, the inverse diffraction problem is solved using combined or generalized computational grids. The paper presents a description of the direct and inverse problems. Results and conclusions. The result of solving the direct problem is obtained as a solution to the corresponding volume integral equation. To solve the inverse problem, a two-step method is used. A detailed description of the numerical method is presented. Numerical results are obtained and solutions to the problem with noisy and non-noisy input data are compared.

This research seeks to propose an innovative mathematical approach for measuring students’ performance in engineering education. The numerical solutions to this mathematical model and a thorough analysis are included in this study. Four categories – average candidates, poor candidates, below average candidates, and good candidates – are used to build the mathematical model that was built. To solve the differential system based on the migration rate and average student rate moving to weak and above average, the Adams numerical scheme is applied to the numerical results of the designed nonlinear mathematical model. Moreover, an artificial neural network is also applied to get the stochastic results of ANNs-LMB, also known as the Levenberg-Marquardt training algorithm. The ANNs-LMB procedures have been implemented with three samples of data scales using the authentication, testing and training, which are chosen as 75%, 15% and 10%, respectively. According to the findings, when the rate of students leaving engineering studies increased, good students performed better, and when the rate of students below average moved, it was due to an increase in the rate of migration above average, the performance of the good students was only impacted in this way. This research material can be used in different designs and models to improve the students’ performance.

Numerous novel concepts in fractional mathematics have been created to provide numerical models for a variety of real-world, engineering, and scientific challenges because of the kernel's memory and non-local effects. In this post, we have looked at a deadly illness known as rabies. For our analysis, we employed the Atangana–Baleanu fractional derivative in Caputo sense. Additionally, the mathematical answer was obtained by applying the Laplace transform. Our approach is distinct, and we illustrated the vital role immunizations play in limiting the spread of the illness using graphical data. Furthermore, in this article, we have shown that fractional order systems are preferable to integer order systems.

An ordinary differential equation (ODE) which models human muscular movement is considered. A functional form of the model parameter is specified through the Lie symmetry approach, yielding a different expression from the one derived in the previous study (Kosugi et al., 2019). The Lie point symmetries corresponding to the model parameter are employed for derivation of exact solution.

In this paper, we construct an age-structured epidemic model to analyze the optimal vaccine allocation strategy in an epidemic. We focus on two topics: the first one is the optimal vaccination interval between the first and second doses, and the second one is the optimal vaccine allocation ratio between young and elderly people. On the first topic, we show that the optimal interval tends to become longer as the relative efficacy of the first dose to the second dose (RE) increases. On the second topic, we show that the heterogeneity in the age-dependent susceptibility (HS) affects the optimal allocation ratio between young and elderly people, whereas the heterogeneity in the contact frequency among different age groups (HC) tends to affect the effectiveness of the vaccination campaign. A counterfactual simulation suggests that the epidemic wave in the summer of 2021 in Japan could have been greatly mitigated if the optimal vaccine allocation strategy had been taken.

Recently, max-min fuzzy relation inequalities (FRIs) have been used to model a (peer-to-peer) P2P network system. Any feasible scheme in the P2P network system is reflected by a solution of the max-min FRIs. One of the objectives of system managers is to decrease network congestion. To satisfy this objective, we attempt to minimize a weighted minimax function motivated by existing research. As a consequence, we establish a weighted minimax programming model in which the constraint is the max-min FRIs. Our goal in this work is to develop an effective algorithm to obtain the optimal solution of the optimization model. The so-called SCP-based algorithm is proposed to find the optimal solution. A numerical example shows the efficiency of our proposed SCP-based algorithm.

The threat posed by the COVID-19 pandemic has been accompanied by an epidemic of misinformation, causing confusion and mistrust among the public. Misinformation about COVID-19 whether intentional or unintentional takes many forms, including conspiracy theories, false treatments, and inaccurate information about the origins and spread of the virus. Though the pandemic has brought to light the significant impact of misinformation on public health, mathematical modeling emerged as a valuable tool for understanding the spread of COVID-19 and the impact of public health interventions. However, there has been limited research on the mathematical modeling of the spread of misinformation related to COVID-19. In this paper, we present a mathematical model of the spread of misinformation related to COVID-19. The model highlights the challenges posed by misinformation, in that rather than focusing only on the reproduction number that drives new infections, there is an additional threshold parameter that drives the spread of misinformation. The equilibria of the model are analyzed for both local and global stability, and numerical simulations are presented. We also discuss the model’s potential to develop effective strategies for combating misinformation related to COVID-19.

This paper introduces a novel framework for modeling nonlocal fractional system with a p-Laplacian operator under power nonlocal fractional derivatives (PFDs), a generalization encompassing established derivatives like Caputo–Fabrizio, Atangana–Baleanu, weighted Atangana–Baleanu, and weighted Hattaf. The core methodology involves employing a PFD with a tunable power parameter within a non-singular kernel, enabling a nuanced representation of memory effects not achievable with traditional fixed-kernel derivatives. This flexible framework is analyzed using fixed-point theory, rigorously establishing the existence and uniqueness of solutions for four symmetric cases under specific conditions. Furthermore, we demonstrate the Hyers–Ulam stability, confirming the robustness of these solutions against small perturbations. The versatility and generalizability of this framework is underscored by its application to an epidemiological model of transmission of Hepatitis B Virus (HBV) and numerical simulations for all four symmetric cases. This study presents findings in both theoretical and applied aspects of fractional calculus, introducing an alternative framework for modeling complex systems with memory processes, offering opportunities for more sophisticated and accurate models and new avenues for research in fractional calculus and its applications.

This work presents an in-depth study on the system identification of a servo-valve controlled hydraulic cylinder operating under variable load. This research addresses the growing demand for improved control systems (enhancing time response, settling time, and precision) in variable load hydraulic actuators, such as those used in blade pitching systems of wind turbines. The paper begins by detailing the experimental setup, followed by the development of the system’s mathematical model, a fourth-order transfer function (TF). The experimental data collected by a proposed data acquisition system are used for the dynamic identification of the hydraulic setup using periodical signals as commands. All possible combinations of TFs up to order 8 are identified. After an initial visual preselection of the 15 most accurate ones, analyses comparing quality indicators between the measured (experimental) and the TF (simulated) step and sinusoidal responses are conducted to determine the most accurate TF. The paper concludes with the presentation and analysis of the dynamic model, identified as being a fourth-order TF, which replicates the system dynamics with the greatest fidelity. It provides an identification methodology with significant potential for industry practitioners aiming to improve, optimize, and enhance control strategies for variable load hydraulic actuators.

Since private cars and vans accounted for more than 25% of global oil consumption and about 10% of energy-related CO2 emissions in 2022, increasing the share of electric vehicle (EV) ownership is considered an important solution for reducing CO2 emissions. At the same time, reducing emissions entails certain economic losses for those countries whose exports are largely covered by the oil trade. The explosive growth of the EV segment over the past 15 years has given rise to overly optimistic forecasts for global EV penetration by 2050. One of the major obstacles to such a development scenario is the limited availability of resources, especially critical materials. This paper proposes a mathematical model to predict the global EV fleet based on the limited availability of critical materials such as lithium, one of the key elements for battery production. The proposed model has three distinctive features. First, it shows that the classical logistic function, due to the specificity of its structure, cannot correctly describe market saturation in the case of using resources with limited serves. Second, even the use of a special multiplier that describes the market saturation process taking into account the depletion (finiteness) of the used resource does not obtain satisfactory economic results because of the “high speed” depletion of this resource. Third, the analytical solution of the final model indicates the point in time at which changes in saturation rate occur. The latter situation allows us to determine the tracking of market saturation, which is more similar to the process that is actually occurring. We believe that this model can also be validated to estimate the production of wind turbines that use rare earth elements such as neodymium and dysprosium (for the production of powerful and permanent magnets for wind turbines). These results also suggest the need for oil-exporting countries to technologically diversify their economies to minimize losses in the transition to a low-carbon economy.

The COVID-19 pandemic has highlighted the need to use infection testing databases to rapidly estimate effectiveness of prior infection in preventing reinfection (⁠|$P{E}_S$|⁠) by novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants. Mathematical modeling was used to demonstrate a theoretical foundation for applicability of the test-negative, case–control study design to derive |$P{E}_S$|⁠. Apart from the very early phase of an epidemic, the difference between the test-negative estimate for |$P{E}_S$| and true value of |$P{E}_S$| was minimal and became negligible as the epidemic progressed. The test-negative design provided robust estimation of |$P{E}_S$| and its waning. Assuming that only 25% of prior infections are documented, misclassification of prior infection status underestimated |$P{E}_S$|⁠ , but the underestimate was considerable only when > 50% of the population was ever infected. Misclassification of latent infection, misclassification of current active infection, and scale-up of vaccination all resulted in negligible bias in estimated |$P{E}_S$|⁠. The test-negative design was applied to national-level testing data in Qatar to estimate |$P{E}_S$| for SARS-CoV-2. |$P{E}_S$| against SARS-CoV-2 Alpha and Beta variants was estimated at 97.0% (95% CI, 93.6-98.6) and 85.5% (95% CI, 82.4-88.1), respectively. These estimates were validated using a cohort study design. The test-negative design offers a feasible, robust method to estimate protection from prior infection in preventing reinfection. [ABSTRACT FROM AUTHOR]

This paper is devoted to solving the inverse problem (determining the parameters of a system of ordinary differential equations based on additional information determined at discrete points in time) and analyzing its solution for a mathematical model describing the dynamics of changes in the population and capital of two regions of the world. The inverse problem is reduced to the problem of minimizing the target functional and is solved by the method of differential evolution. A numerical method for solving direct and inverse problems is implemented. The developed method was tested on model and real data for countries such as Russia, China, India and the USA.

Our goal of this study is to prevent marijuana smoking in the human population. In this manuscript, an updated mathematical model was established by incorporating two additional compartments: The hospitalized class and the prisoner's class. The updated model was validated, and it was shown to be novel compared to the non-user, experimental, recreational, and addicted (NERA) users' model. This distinction was crucial as it was challenging to prevent marijuana usage without these realistic classes. The entire population was split into six primary groups, including these new classes: non-users, experimental, recreational, addicted, hospitalized, and prisoners' class. Additionally, control techniques for marijuana prevention in the population were addressed with the aid of sensitivity analysis. The important point at which we may have determined the preliminary transmission rate of marijuana smoking was the basic reproductive number R0. Utilizing MATLAB, the Runge-Kutta method of order four was employed for the numerical simulation of the updated model to investigate the impact of control measures on marijuana smoking prevention.

In recent years, the coverage path planning (CPP) of unmanned aerial vehicles (UAVs) has attracted attention in reconnaissance, patrol, and search and rescue efforts, aiming to plan the paths for UAVs to cover a specified area as efficiently as possible. This paper proposes a UAV path fast coverage model to prioritize important targets with domain composition based on the starting point and location of the targets, combined with the domain decomposition strategy of important targets. Considering the constraints of the number of UAVs, the number of operators, and the flight time, the parallel search strategy can plan the coverage scheme with the shortest search time for the search range, and further obtain the coordinate points and path coordinates of the UAV turning. Finally, through multiple simulation experiments in four maps of various islands, the proposed method is verified to have an improved performance compare to the two track path coverage algorithms methods in terms of the coverage efficiency and the time complexity, thus providing a more scientific basis for the path coverage research of multi-target searches.

The objective of the present study was to improve our understanding of the complex biological process of bone mineralization by performing mathematical modeling with the Caputo-Fabrizio fractional operator. To obtain a better understanding of Komarova's bone mineralization process, we have thoroughly examined the boundedness, existence, and uniqueness of solutions and stability analysis within this framework. To determine how model parameters affect the behavior of the system, sensitivity analysis was carried out. Furthermore, the fractional Adams-Bashforth method has been used to carry out numerical and graphical simulations. Our work is significant owing to its comparison of fractional- and integer-order models, which provides novel insight into the effectiveness of fractional operators in representing the complex dynamics of bone mineralization.

This study examines an epidemiological model known as the susceptible-exposed-infected-hospitalized-recovered (SEIHR) model, with and without impulsive vaccination strategies. First, the model was analyzed without impulsive vaccination in the presence of a reinfection effect. Subsequently, it was studied as part of a periodic impulsive vaccination strategy targeting the susceptible population. These vaccination impulses were administered in very brief intervals at specific time instants, with a fixed time gap between each impulse. The two approaches can be modified to respond to different amounts of susceptibility, with control efforts intensifying as susceptibility levels rise. The model's analysis includes crucial aspects such as the non-negativity of solutions, the existence of steady states, and the stability corresponding to the basic reproduction number. We demonstrate that when vaccination measures are taken into account, the basic reproduction number remains as less than one. Therefore, the disease-free equilibrium in the case of vaccination could still be asymptotically stable at the higher disease transmission rate, as compared to the case of no vaccination in which the disease-free equilibrium may no longer be asymptotically stable. Furthermore, we show that when the disease-free equilibrium is stable, the endemic equilibrium cannot be attained, and that when the reproduction number rises above unity, the disease-free equilibrium becomes unstable while the endemic equilibrium becomes stable. We have also derived conditions for the global stability of both equilibriums. To support our theoretical results, we have constructed a time series of numerical simulations and compared them with real-world data from the ongoing SARS-CoV-2 (COVID-19) pandemic.

Bortezomib and oncolytic virotherapy are two emerging targeted cancer therapies. Bortezomib, a proteasome inhibitor, disrupts protein degradation in cells, leading to the accumulation of unfolded proteins that induce apoptosis. On the other hand, virotherapy uses genetically modified oncolytic viruses (OVs) to infect cancer cells, trigger cell lysis, and activate anti-tumor response. Despite progress in cancer treatment, identifying administration protocols for therapeutic agents remains a significant concern, aiming to strike a balance between efficacy, minimizing toxicity, and administrative costs. In this work, optimal control theory was employed to design a cost-effective and efficient co-administration protocols for bortezomib and OVs that could significantly diminish the population of cancer cells via the cell death program with the NFKB-BAX-RIP1 signaling network. Both linear and quadratic control strategies were explored to obtain practical treatment approaches by adapting necroptosis protocols to efficient cell death programs. Our findings demonstrated that a combination therapy commencing with the administration of OVs followed by bortezomib infusions yields an effective tumor-killing outcome. These results could provide valuable guidance for the development of clinical administration protocols in cancer treatment.

Hepatitis B is a liver disease caused by the human hepatitis B virus (HBV). Mathematical models help further the understanding of the processes involved and help make predictions. The basic reproduction number, R0, is an index that predicts whether the disease will be chronic or not. This is the single most-important information that a mathematical model can give. Within-host virus processes involve delays. We study two within-host hepatitis B virus infection models without and with delay. One is a standard one, and the other considering additional processes and with two delays is new. We analyze the basic reproduction number and alternative threshold indices. The values of R0 and the alternative indices change depending on the model. All these indices predict whether the infection will persist or not, but they do not give the same rate of growth of the infection when it is starting. Therefore, the choice of the model is very important in establishing whether the infection is chronic or not and how fast it initially grows. We analyze these indices to see how to decrease their value. We study the effect of adding delays and how the threshold indices depend on how the delays are included. We do this by studying the local asymptotic stability of the disease-free equilibrium or by using an equivalent method. We show that, for some models, the indices do not change by introducing delays, but they change when the delays are introduced differently. Numerical simulations are presented to confirm the results. Finally, some conclusions are presented.

Radiotherapy can differentially affect the phases of the cell cycle, possibly enhancing suppression of tumor growth, if cells are synchronized in a specific phase. A model is designed to replicate experiments that synchronize cells in the S phase using gemcitabine before radiation at various doses, with the goal of quantifying this effect. The model is used to simulate a clinical trial with a cohort of 100 individuals receiving only radiation and another cohort of 100 individuals receiving radiation after cell synchronization. The simulations offered in this study support the statement that, at suitably high levels of radiation, synchronizing melanoma cells with gemcitabine before treatment substantially reduces the final tumor size. The improvement is statistically significant, and the effect size is noticeable, with the near suppression of growth at 8 Gray and 92% synchronization.

At the end of 2022, a total of 20,003 diagnoses of human immunodeficiency virus (HIV) infection and 8,983 cases of acquired immunodeficiency syndrome (AIDS) among Japanese nationals, and 3,860 HIV diagnoses and 1,575 AIDS cases among foreign residents, had been notified to the government in Japan. This study updates the estimate of HIV incidence, including during the COVID-19 pandemic. It aimed to reconstruct the incidence of HIV and understand how the disruption caused by COVID-19 affected the epidemiology of HIV. Using a median incubation period of 10.0 years, the number of undiagnosed HIV infections was estimated to be 3,209 (95% confidence interval (CI): 2,642, 3,710) at the end of 2022. This figure has declined steadily over the past 10 years. Assuming that the median incubation period was 10.0 years, the proportion of diagnosed HIV infections, including surviving AIDS cases, was 89.3% (95% CI: 87.8%, 91.0%). When AIDS cases were excluded, the proportion was 86.2% (95% CI: 84.3%, 88.3%). During the COVID-19 pandemic, the estimated annual diagnosis rate was slightly lower than during earlier time intervals, at around 16.5% (95% CI: 14.9%, 18.1%). Japan may already have achieved diagnostic coverage of 90%, given its 9% increment in the diagnosed proportion during the past 5 years. The incidence of HIV infection continued to decrease even during the COVID-19 pandemic from 2020 to 2022, and the annual rate of diagnosis decreased slightly to 16.5%. Monitoring the recovery of diagnosis along with the effective reproduction number is vital in the future.

The prevention and control of the spread of Cystic Echinococcosis is an important public health issue. Health education has been supported by many governments because it can increase public awareness of echinococcosis, promote the development of personal hygiene habits, and subsequently reduce the transmission of echinococcosis. In this paper, a dynamic model of echinococcosis is used to integrate all aspects of health education. Theoretical analysis and numerical model fitting were used to quantitatively analysed by the impact of health education on the spread of echinococcosis. Theoretical findings indicate that the basic reproduction number is crucial in determining the prevalence of echinococcosis within a given geographical area. The parameters of the model were estimated and fitted by using data from the Ningxia Hui Autonomous Region in China, and the sensitivity of the basic reproduction number was analysed by using the partial rank correlation coefficient method. These findings illustrate that all aspects of health education demonstrate a negative correlation with the basic reproduction number, suggesting the effectiveness of health education in reducing the basic reproduction number and mitigating the transmission of echinococcosis, which is consistent with reality. Particularly, the basic reproduction number showed a strong negative correlation with the burial rate of infected livestock ($ b $) and the incidence of infected livestock viscera that is not fed to dogs ($ q $). This paper further analyzes the implementation plan for canine deworming rates and sheep immunity rates, as well as the transmission of infected hosts over time under different parameters $ b $ and $ q $. According to the findings, emphasizing the management of infected livestock in health education has the potential to significantly reduce the risk of echinococcosis transmission. This study will provide scientific support for the creation of higher quality health education initiatives.

The article is devoted to the study of economic cycles and crises, which are studied within the framework of the theory of N.D. Kondratiev long waves (K-waves). The object of the study is the fractional mathematical models of S. V. Dubovsky, consisting of two nonlinear differential equations of fractional order and describing the dynamics of the efficiency of new technologies and the efficiency of capital productivity, taking into account constant and variable heredity. Fractional mathematical models also take into account the dependence of the rate of accumulation on capital productivity and the influx of external investment and new technological solutions. The effects of heredity lead to a delayed effect of the response of the system in question to the impact. The property of heredity in mathematical models is taken into account using fractional derivatives of constant and variable orders in the sense of Gerasimov–Caputo. The fractional mathematical models of S. V. Dubovsky are further studied numerically using the Adams–Bashforth–Moulton algorithm. Using a numerical algorithm, oscillograms and phase trajectories were constructed for various values and model parameters. It is shown that the fractional mathematical models of S. V. Dubovsky may have limit cycles, which are not always stable.

We derive a one-dimensional macroscopic model for biofilm formation in a porous medium reactor to investigate the role of longitudinal diffusion of substrate and suspended bacteria on reactor performance. By comparing an existing base model—one without longitudinal diffusion, which was the point of departure for our work, to the new model—we noticed significant changes in system dynamics. Our results suggest that neglecting it can lead to underestimation of quenching length and biofilm accumulation downstream, even in the advection-dominated regime. The effects of attachment and detachment of suspended bacteria on biofilm formation and substrate degradation were also examined. In the one-dimensional model, it was found that attachment has a stronger influence on substrate depletion, which becomes more pronounced as diffusion in the pore space increases.

In this article, the modified α equation is solved using the direct algebraic approach. As a result, numerous new and more generalized exact solutions for such equations have been found, taking into account the wide range of travelling structures. The rational, trigonometric, hyperbolic, and exponential functions with a couple of licentious parameters are thus included in these exact answers. Analytical solutions feature a variety of physical structures, which are visually studied to demonstrate their dynamic behavior in 2D and 3D. Considering the parameters, all feasible phase portraits are shown. Furthermore, we used numerical approaches to determine the nonlinear periodic structures of the mentioned model, and the data are graphically displayed. Additionally, we employed numerical approaches to determine the nonlinear conditions that contribute to the presented model, and the data are graphically displayed. After evaluating the influence of frequency following the application of an external periodic factor, sensitivity exploration is used to study quasi-periodic and chaotic behavior for several starting value problems. Furthermore, the function of physical characteristics is investigated using an external periodic force. Quasi-periodic and quasi-periodic-chaotic patterns are described with the inclusion of a perturbation term. The direct algebraic methodology would be used to derive the soliton solution of modified α equation, from which the Galilean transformation derives traveling wave solutions of the considered and a bifurcation behavior is reported. Analytical and numerical methods have been used to have the condition of the travelling wave phase transformation. The well-judged values of parameters are enhanced well with a graphically formal analysis of such specific solutions to illustrate their propagation. Then a planer dynamical system is introduced, and a bifurcation analysis is utilized to identify the bifurcation structures of the dynamical model’s nonlinear wave propagation solutions. Additionally, the periodic and quasi-periodic behavior of the discussed equation is analyzed using sensitivity analysis for a range of beginning values. To further comprehend the dynamical behaviors of the resultant solutions, a graphic analysis is conducted.

Platooning technology, which reduces fuel consumption by decreasing aerodynamic drag, is emerging as a key solution for enhancing road efficiency and environmental sustainability in logistics. Conventional vehicle-to-vehicle communication has limitations when forming platoons across multiple trucking companies. To overcome these limitations, a hub-based platooning system has been proposed, enabling coordinated vehicle platoons through hubs distributed along highways. This study develops a mathematical model to optimize platoon formation at hubs, considering the reality that uncertainty in vehicle arrival times can be resolved as vehicles approach the hub and use vehicle-to-hub communication. The model applies robust optimization techniques to consider worst-case vehicle arrival scenarios and examine how the range of data exchange points—where exact arrival times become known—affects platoon efficiency. Numerical experiments demonstrate that if the range of data exchange points is sufficiently wide, optimal efficiency can be achieved even under uncertainty. Sensitivity analysis also confirms that reducing uncertainty enhances energy savings efficiency. This study provides practical insights into forming vehicle platoons in uncertain environments, contributing to the economic and environmental benefits of the logistics industry. Future studies could extend the model to multiple hubs and consider stochastic disruptions, such as communication failures.

This paper proposes and analyzes a mathematical model of tuberculosis and HIV co-infection that specifies for Russian Federation regions, based on mass balance law and described by eight ordinary differential equations. A sensitivity-based identifiability analysis of this mathematical model was performed, which revealed the sensitivity of the averaged parameters of the models to statistical real data of infectious individuals based on the Sobol method. The problem of identifying the sensitive epidemiological parameters (contagiousness, the rate of tuberculosis activation, additional mortality rate, etc.) for the model was reduced to the problem of minimization of the quadratic misfit function. The numerical results of the modeling of the number of people expected to be infected with tuberculosis and HIV were shown and discussed for the Sverdlovsk and Moscow regions of the Russian Federation. It has been shown that increasing the capacity of the medical system by 10% will make it possible to reduce the number of diagnosed cases of active tuberculosis by 2 times over the next 3 years in some regions of Russian Federation.

The fourth-order nonlinear Boussinesq water wave equation, which describes the propagation of long waves in the intertidal zone, is investigated in this study. The exact wave patterns of the equation were computed using the tanh method. As stability decreased, soliton wave structures were derived using similarity transformations. Numerical simulations supported these findings. The tanh method introduced a Galilean modification, leading to the discovery of several new exact solutions. Subsequently, the fourth-order nonlinear Boussinesq wave equation was transformed into a planar dynamical system using the travelling wave transformation. The quasi-periodic, cyclical, and nonlinear behaviors of the analyzed equation were particularly examined. Numerical simulations revealed that varying the physical parameters impacts the system’s nonlinear behavior. Graphs represent all possible examples of phase portraits in terms of these parameters. Furthermore, the study was proven to be highly beneficial for addressing issues such as shock waves and highly active travelling wave processes. Sensitivity analysis theory and the Lyapunov exponent were employed, offering a wide variety of linear periodic and first-frequency periodic characteristics. Sensitivity analysis and multistability analysis of the Boussinesq water wave equation were thoroughly investigated.

Hashimoto’s thyroiditis (HT) is a prevalent autoimmune disorder marked by chronic inflammation of the thyroid gland, predominantly affecting children and adolescents. In a previous study, we developed a “maximal” mathematical model of thyroid physiology to simulate the complex interactions within the thyroid gland. The present research introduces an enhanced version of the “maximal” model, integrating the pathophysiological impacts of HT. It specifically models the adverse effects of thyroid peroxidase (TPO) and thyroglobulin (Tg) antibodies (TPOAb and TgAb) on TPO, Tg, sodium iodide symporter (NIS), albeit indirectly, and thyroid volume. Additionally, we present a new “minimal” model offering a streamlined interpretation of thyroid physiology and pathophysiology, designed for faster computational analysis while maintaining essential physiological interactions. Both models were fitted against longitudinal clinical data from patients with HT, assessing the concentrations of Thyroid Stimulating Hormone (TSH), Thyroxine (T4), and thyroid volume over 36 months, in both untreated patients and those receiving levothyroxine (LT4) treatment. The adaptation of the models to data shows that both of them accurately reproduce the available observed clinical outcomes, with the “maximal” model providing more detailed physiological insights but requiring extensive data and longer computation times. In contrast, the “minimal” model, despite exhibiting less realistic TSH oscillations, offers rapid parameter estimation and may be more feasible in clinical settings. These models hold significant potential as tools for detailed study and management of HT, enabling simulations of disease progression and therapeutic responses, thus paving the way for personalized treatment strategies.

This research paper attempts to describe the transmission dynamic of zoonotic visceral leishmaniasis with the aid of a mathematical model by considering the asymptomatic stages in humans and animals. The disease is endemic in several countries. Data used in the research are obtained from the literature while some are assumed based on the disease dynamic. The consideration of both asymptomatic and the symptomatic infected individuals is incorporated in both humans and animals (reservoir), as well as lines of treatment for the human population. It is found that the model has two fixed points; the VL-free fixed point and the VL-endemic fixed point. Stability analysis of the fixed points shows that the VL-free fixed point is globally asymptotically stable whenever the basic reproduction number is less than one and the VL-endemic fixed point is globally asymptotically stable whenever the basic reproduction number is greater than one. Sensitivity analysis is conducted for the parameters in the basic reproduction number, and the profile of each state variable is also depicted using the data obtained from the literature and those assumed. The transmission probability from infected sandflies to animals, transmission probability from infected animals to sandflies, per capita biting rate of sandflies of animals, and rate of transfer from symptomatic infected animals to the recovered class are among the most sensitive parameters that have the greatest influence on the basic reproduction number. Moreover, the value of the basic reproduction number is obtained to be 0.98951, which may require further study, as the margin between potential disease control and outbreak is thin.

This paper aims to investigate appropriate mathematical models devoted to the optimization of some cleaning processes related to pharmaceutical contaminant removal. In our recent works, we found the rehabilitation of the existing cleaning plants as a viable solution for the removal of this type of micropollutants from waters by introducing efficient techniques such as adsorption on granulated active carbon filters and micro-, nano-, or ultrafiltration. To have these processes under better control and to assure the transfer from small- to large-scale treatment stations, specific mathematical models are necessary. Starting from Navier–Stokes equations and imposing proper boundary conditions, some mathematical physics problems are obtained for which adequate solving methods via variational methods and surjectivity results are proposed. The importance of these solution characterizations consists in their continuation in adequate numerical methods and the possibility to visualize the result by using a CFD program.

To facilitate a direct comparison of the differences in network resources among countries worldwide, this paper proposes a method for quantifying the relationship between autonomous systems and territorial networks from the perspective of network topology. Using global router-level network topology data as the foundational data for the network resources of various countries, we abstract the dual mapping information of router geographic distribution and operational ownership into a matrix-form mathematical model. By employing relevant indicators from both network scale and border connectivity, we compare matrix model data from different periods to quantitatively assess changes in the network structures of countries globally. The study results show that internet resources are concentrated in the United States, which owns 38.04% of the global routers, distributed across 87.88% of the countries, significantly impacting the global network. Compared to the average quantitative indicators of each country, 67.00% of the countries exhibit higher deployment consistency, 37.30% show higher border connection consistency, 23.81% perform prominently in terms of impact, and 46.20% have outstanding border node degrees. From a continental perspective, the analysis indicates that Asian and African countries have a closer relationship between AS and territorial networks, while Europe’s connections are relatively sparse. Over time, we observe a slight decline in deployment consistency in Asia, Africa, and Europe, a slight increase in border connection consistency in Asia, Africa, and North America, and enhanced impact in Asia, Africa, Europe, and South America. These trends suggest that the integration between AS and territorial networks is intensifying in most countries.

ABSTRACTThis work proposes a new mathematical model describing the dynamics of growing bacterial cultures. The model, described by a first order non-linear differential equation, as a generalization of the logistic equation, was compared with the most studied mathematical models. All models were numerically implemented and fitted to the experimental data, collected from the incubation of a bacterial strain of Pseudomonas fluorescens, to obtain the growth parameters. The experimental data showed the lowest fit error for both the Baranyi–Roberts and new models, which turned out to be equivalent. Simulations of the fitting algorithm were also implemented and repeated for a large number of initial guesses of the parameters, chosen in order to test the fitting and convergence performances. The innovative feature that makes the new model easier to use than Baranyi–Roberts model is definitely its simple and manageable analytical form and its good performance in terms of convergence time.

This study aims to develop a mathematical model for analyzing Lassa fever transmission dynamics and proposing effective control measures. The stability of the Lassa fever-free equilibrium point is examined and the model's accuracy is assessed using real-world data. Additionally, the parameter values and the basic reproduction number are estimated. A sensitivity analysis is also conducted, which identifies the key drivers influencing transmission dynamics. Moreover, the impact of model parameters on basic reproduction numbers is investigated. Multiple control methodologies including use of Ribavirin, implementing mobile health technology and incorporating natural predators are devised and analyzed using optimal control theory to curtail virus transmission.

Production control of cashew nuts greatly affects the profits earned by the company. When cashew nut raw materials exceed production needs, it results in storing cashews for an extended period, causing the cashew products to lose freshness, and the quality of processed cashews deteriorates. If the raw materials are damaged, the manufacturer must acquire additional costs to procure raw materials again. Another issue is that cashew nut raw materials are seasonal products and are not always available. To solve these problems, a calculation method is needed to control optimal production inventory to minimize the company's expenditures. The method used is to formulate the problem into a Fuzzy Linear Programming mathematical model using a combination of methods: the Simplex algorithm and Duality Theory. The case implementation focuses on the uncertainty of cashew nut production quantities outside the harvest season. Moreover, the calculation of an optimal production quantity to minimize resulting losses is needed. The output generated is an optimal production prediction using the combination of the Simplex Algorithm and Duality Theory in solving Fuzzy Linear Programming.

The dengue viruses (of which there are four strains) are the causes of three illnesses of increasing severity; dengue fever (DF), dengue hemorrhagic fever (DHF) and dengue shock syndrome (DSS). Recently, dengue fever has reached epidemic proportion in several countries. Strategies or preventative methods have to be developed to combat these epidemics. This can be done by development of vaccines or by preventing the transmission of the virus. The latter approach could involve the use of mosquito nets or insecticide spraying. To determine which strategy would work, we test the strategy using mathematical modeling to simulate the effects of the strategy on the dynamics of the transmission. We have chosen the Susceptible-Exposed-Infected-Recovered (SEIR) model and the SusceptibleExposed-Infected (SEI) model to describe the human and mosquito populations, repectively. We use the Pontryagin's maximum principle to find the optimal control conditions. A sensitivity analysis revealed that the transmission rate $ ({\gamma }_{h}, {\gamma }_{v}) $, the birth rate of human population ($ {\mu }_{h} $), the constant recruitment rate of the vector population ($ A $) and the total human population ($ {N}_{h} $) are the most influential factors affecting the disease transmission. Numerical simulations show that the optimal controlled infective responses, when implemented, cause the convergence to zero to be faster than that in uncontrolled cases.

This article discusses the mathematical model of the spread of COVID-19 by considering vaccination and population migration. The former model is analyzed by determining the equilibrium point, basic reproduction number, analyzing the stability of the equilibrium point, sensitivity analysis, and accompanied by numerical simulation. Analysis of the stability of disease-free and endemic equilibrium points using the Routh-Hurwitz Criteria and the Castillo-Chaves and Song theorems. The results of the analysis show that there are two equilibrium points, namely a disease-free equilibrium point (T1), which is locally asymptotically stable when R0 1, and an endemic equilibrium point (T2), which is locally asymptotically stable when R0 1. Furthermore, the sensitivity analysis showed that the most sensitive parameters to changes in the basic reproduction number were the emigration rate parameter (m2) and the infection probability parameter after contact between infected and susceptible individuals without vaccination (h). In addition, the numerical simulation results show that the sensitive parameter values, namely m2, h, zse, g, and # have a significant effect on the basic reproduction numbers. Suppressing the chance of infection in susceptible individuals and the rate of contact between susceptible and exposed individuals, as well as increasing the number of individuals who emigrate and who are vaccinated, can reduce the transmission of COVID-19.

We introduce a two-strain model with asymmetric temporary immunity periods and partial cross-immunity. We derive explicit conditions for competitive exclusion and coexistence of the strains depending on the strain-specific basic reproduction numbers, temporary immunity periods, and degree of cross-immunity. The results of our bifurcation analysis suggest that, even when two strains share similar basic reproduction numbers and other epidemiological parameters, a disparity in temporary immunity periods and partial or complete cross-immunity can provide a significant competitive advantage. To analyze the dynamics, we introduce a quasi-steady state reduced model which assumes the original strain remains at its endemic steady state. We completely analyze the resulting reduced planar hybrid switching system using linear stability analysis, planar phase-plane analysis, and the Bendixson-Dulac criterion. We validate both the full and reduced models with COVID-19 incidence data, focusing on the Delta (B.1.617.2), Omicron (B.1.1.529), and Kraken (XBB.1.5) variants. These numerical studies suggest that, while early novel strains of COVID-19 had a tendency toward dramatic takeovers and extinction of ancestral strains, more recent strains have the capacity for co-existence.

A mathematical model is developed for analysis of the spread of mosaic disease in plants, which account for incubation period and latency that are represented by time delays. Feasibility and stability of different equilibria are studied analytically and numerically. Conditions that determine the type of behavior exhibited by the system are found in terms of various parameters. We have derived the basic reproduction number and identify the conditions resulting in eradication of the disease, as well as those that lead to the emergence of stable oscillations in the population of infected plants, as a result of Hopf bifurcation of the endemic equilibrium. Numerical simulations are performed to verify the analytical results and also to illustrate different dynamical regimes that can be observed in the system. In this research, the stabilizing role of both the time delay has been established i.e. when delay time is large, disease will persist if the infection rate is higher. The results obtained here are useful for plant disease management.

A bivariate extension of a flexible univariate family is proposed. The new family is called bivariate q-extended Weibull Morgenstern family of distributions which can be constructed based on the Farlie-Gumbel-Morgenstern (FGM) copula technique. After introducing the new family, four sub-models are discussed in detail from the theoretical and numerical coefficient of correlation point of view with pointing to the effect of the $ q $ parameter.

The circadian clock is an autonomous timing system that regulates the physiological and behavioral activities of organisms. Dopamine (DA) is an important neurotransmitter that is associated with many biological activities such as mood and movement. Experimental studies have shown that the circadian clock influences the DA system and disorders in the circadian clock lead to DA-related diseases. However, the regulatory mechanism of the circadian clock on DA is far from clear. In this paper, we apply an existing circadian-dopamine mathematical model to explore the effects of the circadian clock on DA. Based on numerical simulations, we find the disturbance of the circadian clock, including clock gene mutations, jet lag and light pulses, leads to abnormal DA levels. The effects of mutations in some clock genes on the mood and behavior of mice are closely related to DA disruptions. By sensitivity analysis of DA levels to parameter perturbation, we identify key reactions that affect DA levels, which provides insights into modulating DA disorders. Sudden changes in external light influence the circadian clock, bringing about effects on the DA system. Jet lag causes transient DA rhythm desynchronization with the environment and the influence of jet lag in different directions on DA level and phase varies. Light pulses affect the amplitude and phase shift of DA, which provides a promising method for treating DA disorders through light exposure. This study helps to better understand the impact of the circadian clock on the DA system and provides theoretical support for the treatment of DA disorders.