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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.

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.

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.

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.

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]

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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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.

The study establishes two mathematical formulations to predict the pressure drop in a solid–liquid slurry flowing through a straight pipe. Employing the Eulerian–Eulerian RNG k-ε model, the computational investigation uses water as the carrier fluid and glass beads as solid particles. The analysis spans various particle sizes (d50 = 75–175 μm), volumetric concentrations (Cvf = 10–50%), and velocities (Vm = 1–5 m/s). The first model, developed using the MATLAB curve-fitting tool, is complemented by a second empirical equation derived through non-polynomial mathematical formulation. Results from both models are validated against existing experimental and computational data, demonstrating accurate predictions for d50 = 75–175 µm particles within a Reynolds number range of 20,000 ≤ Re ≤ 320,000.

The Zika virus has been shown to infect glioblastoma stem cells via the membrane receptor αvβ5, which is activated by the stem-specific transcription factor SOX2. Since the expression level of SOX2 is an important predictive marker for successful virotherapy, it is important to understand the fundamental mechanisms of the role of SOX2 in the dynamics of cancer stem cells and Zika viruses. In this paper, we develop a mathematical ODE model to investigate the effects of SOX2 expression levels on Zika virotherapy against glioblastoma stem cells. Our study aimed to identify the conditions under which SOX2 expression level, viral infection, and replication can reduce or eradicate the glioblastoma stem cells. Analytic work on the existence and stability conditions of equilibrium points with respect to the basic reproduction number are provided. Numerical results were in good agreement with analytic solutions. Our results show that critical threshold levels of both SOX2 and viral replication, which change the stability of equilibrium points through population dynamics such as transcritical and Hopf bifurcations, were observed. These critical thresholds provide the optimal conditions for SOX2 expression levels and viral bursting sizes to enhance therapeutic efficacy of Zika virotherapy against glioblastoma stem cells. This study provides critical insights into optimizing Zika virus-based treatment for glioblastoma by highlighting the essential role of SOX2 in viral infection and replication.

Middle East Respiratory Syndrome (MERS) is a human coronavirus subtype that poses a significant public health concern due to its ability to spread between individuals. This research aims to develop a fractional-order mathematical model to investigate the MERS pandemic and to subsequently develop two numerical methods to solve this model numerically to evaluate and comprehend the analysis results. The fixed-point theorem has been used to demonstrate the existence and uniqueness of the solution to the suggested model. We approximate the solutions of the proposed model using two numerical methods: the mean value theorem and the implicit trapezoidal method. The stability of these numerical methods is studied using various results and primary lemmas. Finally, we compare the results of our methods to demonstrate their efficiency and conduct a numerical simulation of the obtained results. A comparative study based on real data from Riyadh, Saudi Arabia is provided. The study’s conclusions demonstrate the computational efficiency of our approaches in studying nonlinear fractional differential equations that arise in daily life problems.

In this article, a diffusion component in an SIR model is introduced, and its impact is analyzed using fractional calculus. We have included the diffusion component in the SIR model. in order to illustrate the variations. Here, we have applied the general fractional derivative to analyze the impact. The Laplace decomposition technique is employed to obtain the numerical outcomes of the model. In order to observe the effect of the diffusion component in the SIR model, graphical solutions are also displayed.

Hospital Pneumatic Systems, specializing in pneumatic systems, are among the most essential components for hospitals. It offers efficient and cost-effective solutions to problems related to the transportation of various materials in hospitals. However, in existing systems, the need for compressed air is met without worrying about cost control and without depending on the sample transported, and this not only makes the system inefficient but also may cause sample degradation. The main purpose of this study is to provide speed/pressure control according to the type of material transported to eliminate the disadvantages of existing systems such as energy use and sample degradation. In this study, a new mathematical model is presented that can be used to make more energy-efficient hospital pneumatic systems. Although there are many studies on various pneumatic systems in the literature, there is not enough for the control of hospital pneumatic systems. According to the results obtained in this study, the system parameters were determined and the mathematical model of the system was obtained by using the Multivariate nonlinear regression method. A genetic algorithm was used to test the validity of the obtained mathematical model and to optimize the coefficient of the input parameters of the model. It is expected that this proposed model will contribute to the use of hospital pneumatic systems and provide a scientific and practical solution to the proposed mathematical model. The proposed mathematical model provides up to %43 more efficient transportation over the currently used system that has been tested.

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.

In this paper, a mathematical model is developed to simulate the activation of regulatory T lymphocytes dynamics. The model considers the adaptive immune response and consists of epithelial cells, infected cells, free virus particles, helper and cytotoxic T lymphocytes, B lymphocytes, and regulatory T lymphocytes. A mathematical analysis was carried out to discuss the conditions of existence and stability of equilibrium solutions in terms of the basic reproductive number. In addition, the definitions and properties necessary to preserve the positivity and stability of the model are shown. The precision of these mathematical models can be affected by numerous sources of uncertainty, partly due to the balance between the complexity of the model and its predictive capacity to depict the biological process accurately. Nevertheless, these models can provide remarkably perspectives on the dynamics of infection and assist in identification specific immunological traits that improve our comprehension of immune mechanisms. The theoretical results are validated by numerical simulations using data reported in the literature. The construction, analysis, and simulation of the developed models demonstrate that the increased induced regulatory T lymphocytes effectively suppress the inflammatory response in contrast to similar cells at lower contents, playing a key role in maintaining self-tolerance and immune homeostasis.

This paper presents an innovative mathematical model of solid fuel gasification, which is not described in the available literature. The calculation of the components of the heterogeneous phase (including both solid and gaseous phases) as well as the calculation of the homogeneous phase (only gaseous components) is based on the balance of the total amounts of carbon, oxygen, hydrogen, and nitrogen entering the reactor space. Additionally, this paper introduces a new method for calculating the composition of the gaseous phase, based on reducing the heterogeneous mixture (composed of solid and gaseous phases) to a homogeneous gaseous phase. This approach to calculating the gaseous phase composition in the solid fuel gasification process has not been found by the authors in the cited literature. This paper also presents a model for calculating the heterogeneous and gaseous phases using the number of moles that participate in the assumed chemical reactions of the solid fuel gasification process. This approach to calculating the composition of the heterogeneous and gaseous phases of the solid fuel gasification process is also not represented in the cited literature. For comparison with the literature data, municipal solid waste (MSW) and cashew nut shell (Cashew Shell Char (CNSC)) were used as fuels in the calculation of gasification composition. The results of the calculation of the gaseous phase composition using the model presented in the paper show good agreement with the data from the literature. The calculation of the composition of the heterogeneous mixture during the steam gasification of MSW (α = 0.4) shows the presence of a solid phase (carbon) up to approximately 735 °C. At that temperature, the synthetic gas contains only gaseous components: CO = 33.10%, H2 = 52.70%, CH4 = 2.54%, CO2 = 4.97, H2O = 5.93% and N2 = 0.76%. Increasing the temperature above 735 °C eliminates the solid phase from the equilibrium mixture. The literature data on solid fuel gasification generally do not consider the proportion of the solid phase (carbon) in the equilibrium mixture. To satisfy the material balance at the input and output of the gasification reactor, it is necessary to determine the proportion of the solid phase (carbon) in the equilibrium mixture. Since the proportion of the solid phase (carbon) in the heterogeneous equilibrium mixture can only be determined through measurement, the development and application of a mathematical model in engineering practice is of great importance, so this developed model can be considered a useful tool for simulating the influence of process parameters on gas characteristics.

This study introduces the KdV–Caudrey–Dodd–Gibbon (KdV-CDGE) equation to describe long water waves, acoustic waves, plasma waves, and nonlinear optics. Employing a generalized new auxiliary equation scheme, we derive exact analytical wave solutions, revealing rational, exponential, trigonometric, and hyperbolic trigonometric structures. The model also produces periodic, dark, bright, singular, and other soliton wave profiles. We compute classical and translational symmetries to develop abelian algebra, and visualize our results using selected parameters.

This paper investigates the behavior of a fluid queue driven by a non-truncated Erlangian service queue, focusing on the symmetrical properties within the system. This study determines the formulations of the steady-state distribution of both the buffer content and stationary state probabilities of a background queueing system. The efficient generating function technique is employed, utilizing a new generalization of the modified Bessel function of the second kind. Performance metrics such as mean buffer content and throughput are calculated, and server utilization is examined. The results contribute to the understanding of fluid queueing systems and offer insights into their performance in various applications, including telecommunications, manufacturing systems, healthcare operations, and ecological models, where symmetry plays a critical role in optimizing performance.

In this work, a mathematical model of the transfer process in a layer under the condition of given experimental data on a part of the layer boundary is presented and investigated. Such research is important for the mathematical description of the objects and systems for which, based on physical considerations, it is impossible to correctly impose boundary or initial conditions, even in a sufficiently general form, but there are experimental data on the desired function or its derivative at the boundary of the body or at the initial time. The values of the desired function at the boundary are known at certain moments in time. The boundary condition is constructed by the experimental data and the initial-boundary value problem, with such a boundary condition, is formulated and solved. The influence of the statistical characteristics of the sample of experimental data on the solution to the initial-boundary value problem is analyzed, and a two-sided statistical estimation of the solution is determined. The confidence intervals for the coefficients of the regression equation and the corresponding confidence intervals for the sought function are established. The influence of the statistical characteristics of the sample on the sought function at the lower boundary of the layer is investigated. Numerical analysis of the solution to the initial-boundary value problem is carried out depending on the statistical characteristics of the sample. Various cases of samples by size and variance are considered. Numerical solutions are studied under the conditions of large and small time intervals of the considered process.

Diphtheria, a potentially life-threatening infectious disease, is primarily caused by the bacterium Corynebacterium diphtheriae. This pathogen induces a range of severe symptoms, including respiratory distress, cardiac arrhythmias, and, in extreme cases, fatal outcomes. This paper aim to unravel the transmission dynamics of diphtheria infection within the Caputo fractional derivatives framework, establishing the solutions’ existence and uniqueness. Through forward normalized sensitivity analysis, we scrutinize the key parameters influencing the basic reproduction number, a pivotal metric in understanding and controlling the spread of the disease. The results indicate that reducing the values of the interaction rate, transmission rate, and birth rate plays a key role in curtailing diphtheria transmission. Furthermore, employing an effective numerical tool, we present graphical representations that delineate the influence of various crucial model parameters on infection dynamics.

SARS-CoV-2 still presents a global threat to human health due to the continued emergence of new strains and waning immunity among vaccinated populations. Therefore, it is still relevant to investigate potential therapeutics, such as therapeutic interfering particles (TIPs). Mathematical and computational modeling are valuable tools to study viral infection dynamics for predictive analysis. Here, we expand on the previous work on SARS-CoV-2 intra-cellular replication dynamics to include defective interfering particles (DIPs) as potential therapeutic agents. We formulate a deterministic model that describes the replication of wild-type (WT) SARS-CoV-2 virus in the presence of DIPs. Sensitivity analysis of parameters to several model outputs is employed to inform us on those parameters to be carefully calibrated from experimental data. We then study the effects of co-infection on WT replication and how DIP dose perturbs the release of WT viral particles. Furthermore, we provide a stochastic formulation of the model that is compared to the deterministic one. These models could be further developed into population-level models or used to guide the development and dose of TIPs.

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.

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.

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.

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.

Type 1 diabetes (T1D) is a chronic autoimmune disease caused by the immune-mediated reduction of β cells, resulting in lifelong dependence on exogenous insulin administration. We studied the impact of M1/M2 macrophages on the β cell level. We obtained the healthy state (absence of T1D) and unhealthy state (presence of T1D). We found that in the unhealthy state, β cell levels are decreased with a continuous alternative switch between M1 and M2 macrophages. However, in the healthy state, the β cell levels increase with a high level of M2 macrophages.

To solve the problem that the current forecasting methods cannot describe the long-term correlation of traffic, which leads to low prediction accuracy, the author proposes a mathematical modeling, forecasting and analysis method for village nonlinear traffic. The original nonlinear traffic data collected from the village comes from each base station, the information contained is uneven, pre-processing the collected data, eliminating abnormal values and duplicate data, and supplementing the missing data. Nonlinear traffic contains limited information, so a random forest algorithm is used to extract traffic characteristics and reduce data processing dimensions. The nonlinear traffic characteristics of the village are convolved, and the cross entropy function is used as the loss function, the feature vector of the input prediction model is deeply learned, and the communication traffic prediction results are obtained. Taking the traffic data of the communication operation enterprise’s base station as the test data, the experiment results show that, in the test with 1 million pieces of data, the decision coefficient of the mathematical modeling, prediction and analysis method of village nonlinear flow designed by the author is 0.9599, which is 0.1267 and 0.1431 higher than the prediction and analysis method based on genetic algorithm and fuzzy clustering algorithm respectively. In the modeling and prediction of nonlinear flow, the determination coefficient of the method proposed by the author is closer to 1, the fitting degree of this method is better than that of the contrast method, and it is adaptive in the real scene with a large amount of data. It is proved that the mathematical modeling and prediction analysis method designed in this design can reduce NRMSE and MAPE, improve the determination coefficient of prediction results, and provide the basis for village analysis.

As speech recognition technology continues to advance in sophistication and computer processing power, more and more recognition technologies are being integrated into a variety of software platforms, enabling intelligent speech processing. We create a comprehensive processing platform for multilingual resources used in business and security fields based on speech recognition and distributed processing technology. Based on the federated learning model, this study develops speech recognition and its mathematical model for languages in South China. It also creates a speech dataset for dialects in South China, which at present includes three dialects of Mandarin and Cantonese, Chaoshan and Hakka that are widely spoken in the Guangdong region. Additionally, it uses two data enhancement techniques—audio enhancement and spectrogram enhancement—for speech signal characteristics in order to address the issue of unequal label distribution in the dataset. With a macro-average F-value of 91.54% and when compared to earlier work in the field, experimental results show that this structure is combined with hyperbolic tangent activation function and spatial domain attention to propose a dialect classification model based on hybrid domain attention.

The purpose of this work is to provide a stochastic framework based on the scale conjugate gradient neural networks (SCJGNNs) for solving the malaria disease model of pesticides and medication (MDMPM). The host and vector populations are divided in the mathematical form of the malaria through the pesticides and medication. The stochastic SCJGNNs procedure has been presented through the supervised neural networks based on the statics of validation (12%), testing (10%), and training (78%) for solving the MDMPM. The optimization is performed through the SCJGNN along with the log-sigmoid transfer function in the hidden layers along with fifteen numbers of neurons to solve the MDMPM. The accurateness and precision of the proposed SCJGNNs is observed through the comparison of obtained and source (Runge-Kutta) results, while the small calculated absolute error indicate the exactitude of designed framework based on the SCJGNNs. The reliability and consistency of the SCJGNNs is observed by using the process of correlation, histogram curves, regression, and function fitness.

Abstract The disease caused by the virus has caused a continuous pandemic worldwide since 2012. In order to slow down the rapid spread of the virus, many countries have taken recovery measures. This paper aims to analyze the trends of modeling pandemic cases in Scopus-indexed journals. The research method is a literature review using a bibliometric analysis approach starting from defining the keywords modeling' and ‘pandemic' in the Publish or Perish application with Google Scholar as the database. After narrowing the results by selecting the topic of modeling the pandemic problem it consisted of 200 articles in total. After that, the metadata was compiled using the Mendeley application, the VosViewer application was used to create a research trend visualization. The results obtained by bibliometric analysis show that the number of publications continues to increase. Which journals are published, which organizations and countries publish the most, how the evolution of perspective has changed since 2012, and which articles are most cited. We conclude that since the pandemic, there is a possibility of an evolution in the quality of publications. Keywords: bibliometric analysis; pandemic; mathematical model; Mendeley; Publish or Perish; Vosviewer. Abstrak Penyakit yang diakibatkan dari virus telah menyebabkan pandemi berkelanjutan di seluruh dunia sejak 2012. Untuk memperlambat penyebaran virus yang cepat, banyak negara telah mengambil langkah pemulihan. Tulisan ini bertujuan untuk menganalisis tren pemodelan kasus pandemi di jurnal terindeks Scopus. Metode penelitian adalah kajian pustaka dengan pendekatan analisis bibliometrik dimulai dari pendefinisian kata kunci ‘pemodelan’ dan 'pandemi' pada aplikasi Publish or Perish dengan database Google Scholar. Setelah dilakukan penyempitan hasil dengan pemilihan topik pemodelan masalah pandemi maka total artikel menjadi 200 artikel. Setelah itu dilakukan kompilasi metadata menggunakan aplikasi Mendeley, aplikasi VosViewer digunakan untuk membuat visualisasi trend penelitian. Hasil yang diperoleh dengan analisis bibliometrik menunjukkan bahwa jumlah publikasi terus meningkat. Jurnal mana yang diterbitkan, organisasi dan negara mana yang paling banyak menerbitkan, bagaimana evolusi perspektif telah berubah sejak 2012, dan artikel mana yang paling banyak dikutip. Kami menyimpulkan bahwa sejak pandemi, ada kemungkinan terjadi evolusi kualitas publikasi. Kata Kunci: analisis bibliometrik; pandemi; model matematika; Mendeley; Publish or Perish; Vosviewer. 2020MSC: 00A71, 92B05.

Diabetes mellitus is a global health problem, escalating at a disturbing rate due to unbalanced lifestyles and some underlying health issues. In this work, a system of first-order linear ordinary differential equations as well as numerical simulations were employed to gain insight into the dynamics of the disease. The theoretical outcomeof the analysis was derived in terms of the model parameters while computer simulation was used to assess the behavior of the model in terms of the parameter values. Both the theoretical and numerical studies of the model revealed lifestyles and effective treatment as the parameters to be targeted for effective reduction in both diabetes prevalence and mortality. It is therefore concluded that diabetes prevalence and mortality reduction is a function of adjustment in unbalanced lifestyles as well as improvement in diabetes treatment.