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In this paper we consider the ultimate dynamics of one 4D cancer model which was created for studying the immune response to the two-phenotype tumors. Our approach is based on the localization method of compact invariant sets. The existence of a positively invariant polytope is shown and its size is calculated depending on the parameters of this cancer model. Various convergence conditions to the tumor free equilibrium point were proposed. This property has the biological meaning of global asymptotic tumor eradication (GATE). Further, the case in which local asymptotic tumor eradication (LATE) conditions entail GATE conditions was found. Our theoretical studies of ultimate dynamics are complemented by numerical simulation results. [ABSTRACT FROM AUTHOR]

In this paper, we establish and study a novel predator–prey model that incorporates: (i) the migration of prey between breeding and non-breeding regions; (ii) the refuge effect of prey; and (iii) the reduction in prey pulse birth rate, in the form of a fear effect, in the presence of predators. Applying the Floquet theory and the comparison theorem of impulsive differential equations, we obtain the sufficient conditions for the stability of the prey-extinction periodic solution and the permanence of the system. Furthermore, we also study the case where the prey population does not migrate. Sufficient conditions for the stability of the prey-extinction periodic solution and the permanence are also established, and the threshold for extinction and permanence of the prey population is obtained. Finally, some numerical simulations are provided to verify the theoretical results. These results provide a theoretical foundation for the conservation of biodiversity. [ABSTRACT FROM AUTHOR]

This paper presents and analyzes two mathematical models for the human immunodeficiency virus type-1 (HIV-1) infection with Cytotoxic T Lymphocyte cell (CTL) immune impairment. These models describe the interactions between healthy CD 4 + T cells, latently and actively infected cells, HIV-1 particles, and CTLs. The healthy CD 4 + T cells might be infected when they make contact with: (i) HIV-1 particles due to virus-to-cell (VTC) contact; (ii) latently infected cells due to latent cell-to-cell (CTC) contact; and (iii) actively infected cells due to active CTC contact. Distributed time delays are considered in the second model. We show the nonnegativity and boundedness of the solutions of the systems. Further, we derive basic reproduction numbers ℜ 0 and ℜ ˜ 0 , that determine the existence and stability of equilibria of our proposed systems. We establish the global asymptotic stability of all equilibria by using the Lyapunov method together with LaSalle's invariance principle. We confirm the theoretical results by numerical simulations. The effect of immune impairment, time delay and CTC transmission on the HIV-1 dynamics are discussed. It is found that weak immunity contributes significantly to the development of the disease. Further, we have established that the presence of time delay can significantly decrease the basic reproduction number and then suppress the HIV-1 replication. On the other hand, the presence of latent CTC spread increases the basic reproduction number and then enhances the viral progression. Thus, neglecting the latent CTC spread in the HIV-1 infection model will lead to an underestimation of the basic reproduction number. Consequently, the designed drug therapies will not be accurate or sufficient to eradicate the viruses from the body. These findings may help to improve the understanding of the dynamics of HIV-1 within a host. [ABSTRACT FROM AUTHOR]

This paper presents two viral infection models that describe dynamics of the virus under the effect of two distinct types of antibodies. The first model considers the population of five compartments, target cells, infected cells, free virus particles, antibodies type-1 and antibodies type-2. The presence of two types of antibodies can be a result of secondary viral infection. In the second model, we incorporate the latently infected cells. We assume that the antibody responsiveness is given by a combination of the self-regulating antibody response and the predator–prey-like antibody response. For both models, we verify the nonnegativity and boundedness of their solutions, then we outline all possible equilibria and prove the global stability by constructing proper Lyapunov functions. The stability of the uninfected equilibrium EQ 0 and infected equilibrium EQ * is determined by the basic reproduction number R 0 . The theoretical findings are verified through numerical simulations. According to the outcomes, the trajectories of the solutions approach EQ 0 and EQ * when R 0 ≤ 1 and R 0 > 1 , respectively. We study the sensitivity analysis to show how the values of all the parameters of the suggested model affect R 0 under the given data. The impact of including the self-regulating antibody response and latently infected cells in the viral infection model is discussed. We showed that the presence of the self-regulating antibody response reduces R 0 and makes the system more stabilizable around EQ 0 . Moreover, we established that neglecting the latently infected cells in the viral infection modeling leads to the design of an overflow of antiviral drug therapy. [ABSTRACT FROM AUTHOR]

Reaction–diffusion systems have a broad variety of applications, particularly in biology, and it is well known that fractional calculus has been successfully used with this type of system. However, analyzing these systems using discrete fractional calculus is novel and requires significant research in a diversity of disciplines. Thus, in this paper, we investigate the discrete-time fractional-order Lengyel–Epstein system as a model of the chlorite iodide malonic acid (CIMA) chemical reaction. With the help of the second order difference operator, we describe the fractional discrete model. Furthermore, using the linearization approach, we established acceptable requirements for the local asymptotic stability of the system's unique equilibrium. Moreover, we employ a Lyapunov functional to show that when the iodide feeding rate is moderate, the constant equilibrium solution is globally asymptotically stable. Finally, numerical models are presented to validate the theoretical conclusions and demonstrate the impact of discretization and fractional-order on system dynamics. The continuous version of the fractional-order Lengyel–Epstein reaction–diffusion system is compared to the discrete-time system under consideration. [ABSTRACT FROM AUTHOR]

The stability of traveling waves for the Lotka–Volterra competition system with three species is investigated in this paper. Specifically, we first show the asymptotic behavior of traveling wave solutions and then establish the local stability and the global stability under the weighted functional space. For local stability, the spectrum approach is used, while for global stability, the comparison principle and squeezing theorem are combined. [ABSTRACT FROM AUTHOR]

The paper mainly investigates a stochastic SIRS epidemic model with Logistic birth and nonlinear incidence. We obtain a new threshold value ( R 0 m ) through the Stratonovich stochastic differential equation, different from the usual basic reproduction number. If R 0 m < 1 , the disease-free equilibrium of the illness is globally asymptotically stable in probability one. If R 0 m > 1 , the disease is permanent in the mean with probability one and has an endemic stationary distribution. Numerical simulations are given to illustrate the theoretical results. Interestingly, we discovered that random fluctuations can suppress outbreaks and control the disease. [ABSTRACT FROM AUTHOR]

In several publications, the dynamical system of HIV and HTLV mono-infections taking into account diffusion, as well as latently infected cells in cellular transmission has been mathematically analyzed. However, no work has been conducted on HTLV/HIV co-infection dynamics taking both factors into consideration. In this paper, a partial differential equations (PDEs) model of HTLV/HIV dual infection was developed and analyzed, considering the cells' and viruses' spatial mobility. CD 4 + T cells are the primary target of both HTLV and HIV. For HIV, there are three routes of transmission: free-to-cell (FTC), latent infected-to-cell (ITC), and active ITC. In contrast, HTLV transmits horizontally through ITC contact and vertically through the mitosis of active HTLV-infected cells. In the beginning, the well-posedness of the model was investigated by proving the existence of global solutions and the boundedness. Eight threshold parameters that determine the existence and stability of the eight equilibria of the model were obtained. Lyapunov functions together with the Lyapunov–LaSalle asymptotic stability theorem were used to investigate the global stability of all equilibria. Finally, the theoretical results were verified utilizing numerical simulations. [ABSTRACT FROM AUTHOR]

The coronavirus disease 2019 (COVID-19) is a respiratory disease that appeared in 2019 caused by a virus called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). COVID-19 is still spreading and causing deaths around the world. There is a real concern of SARS-CoV-2 coinfection with other infectious diseases. Tuberculosis (TB) is a bacterial disease caused by Mycobacterium tuberculosis (Mtb). SARS-CoV-2 coinfection with TB has been recorded in many countries. It has been suggested that the coinfection is associated with severe disease and death. Mathematical modeling is an effective tool that can help understand the dynamics of coinfection between new diseases and well-known diseases. In this paper, we develop an in-host TB and SARS-CoV-2 coinfection model with cytotoxic T lymphocytes (CTLs). The model investigates the interactions between healthy epithelial cells (ECs), latent Mtb-infected ECs, active Mtb-infected ECs, SARS-CoV-2-infected ECs, free Mtb, free SARS-CoV-2, and CTLs. The model's solutions are proved to be nonnegative and bounded. All equilibria with their existence conditions are calculated. Proper Lyapunov functions are selected to examine the global stability of equilibria. Numerical simulations are implemented to verify the theoretical results. It is found that the model has six equilibrium points. These points reflect two states: the mono-infection state where SARS-CoV-2 or TB occurs as a single infection, and the coinfection state where the two infections occur simultaneously. The parameters that control the movement between these states should be tested in order to develop better treatments for TB and COVID-19 coinfected patients. Lymphopenia increases the concentration of SARS-CoV-2 particles and thus can worsen the health status of the coinfected patient. [ABSTRACT FROM AUTHOR]

In this paper, we propose and study a Middle East respiratory syndrome coronavirus (MERS-CoV) infection model with cytotoxic T lymphocyte (CTL) immune response and intracellular delay. This model includes five compartments: uninfected cells, infected cells, viruses, dipeptidyl peptidase 4 (DPP4), and CTL immune cells. We obtained an immunity-inactivated reproduction number R 0 and an immunity-activated reproduction number R 1 . By analyzing the distributions of roots of the corresponding characteristic equations, the local stability results of the infection-free equilibrium, the immunity-inactivated equilibrium, and the immunity-activated equilibrium were obtained. Moreover, by constructing suitable Lyapunov functionals and combining LaSalle's invariance principle and Barbalat's lemma, some sufficient conditions for the global stability of the three types of equilibria were obtained. It was found that the infection-free equilibrium is globally asymptotically stable if R 0 ≤ 1 and unstable if R 0 > 1 ; the immunity-inactivated equilibrium is locally asymptotically stable if R 0 > 1 > R 1 and globally asymptotically stable if R 0 > 1 > R 1 and condition (H1) holds, but unstable if R 1 > 1 ; and the immunity-activated equilibrium is locally asymptotically stable if R 1 > 1 and is globally asymptotically stable if R 1 > 1 and condition (H1) holds. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to formulate two new mathematical models to describe the co-dynamics of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and human T-cell lymphotropic virus type-I (HTLV-I) in a host. The models characterizes the interplaying between seven compartments, uninfected ECs, latently SARS-CoV-2-infected ECs, actively SARS-CoV-2-infected ECs, free SARS-CoV-2 particles, uninfected CD4 + T cells, latently HTLV-I-infected CD4 + T cells and actively HTLV-I-infected CD4 + T cells. The models incorporate five intracellular time delays: (i) two delays in the formation of latently SARS-CoV-2-infected ECs and latently HTLV-I-infected CD4 + T cells, (ii) two delays in the reactivation of latently SARS-CoV-2-infected ECs and latently HTLV-I-infected CD4 + T cells, and (iii) maturation delay of new SARS-CoV-2 virions. We consider discrete-time delays and distributed-time delays in the first and second models, respectively. We first investigate the properties of the model's solutions, then we calculate all equilibria and study their global stability. The global asymptotic stability is examined by constructing Lyapunov functionals. The analytical findings are supported via numerical simulation. The impact of time delays on the coinfection progression is discussed. We found that, increasing time delays values can have an antiviral treatment-like impact. Our developed coinfection model can contribute to understand the SARS-CoV-2 and HTLV-I co-dynamics and help to select suitable treatment strategies for COVID-19 patients with HTLV-I. [ABSTRACT FROM AUTHOR]

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a new virus which infects the respiratory system and causes the coronavirus disease 2019 (COVID-19). The coinfection between malaria and COVID-19 has been registered in many countries. This has risen an urgent need to understand the dynamics of coinfection. In this paper, we construct a reaction–diffusion in-host malaria/COVID-19 model. The model includes seven-dimensional partial differential equations that explore the interactions between seven compartments, healthy red blood cells (RBCs), infected RBCs, free merozoites, healthy epithelial cells (ECs), infected ECs, free SARS-CoV-2 particles, and antibodies. The biological validation of the model is confirmed by establishing the nonnegativity and boundedness of the model's solutions. All equilibrium points with the corresponding existence conditions are calculated. The global stability of all equilibria is proved by picking up appropriate Lyapunov functionals. Numerical simulations are used to enhance and visualize the theoretical results. We found that the equilibrium points show the different cases when malaria and SARS-CoV-2 infections occur as mono-infection or coinfection. The shared antibody immune response decreases the concentrations of SARS-CoV-2 and malaria merozoites. This can have an important role in reducing the severity of SARS-CoV-2 if the immune response works effectively. [ABSTRACT FROM AUTHOR]

Studies have reported several cases with respiratory viruses coinfection in hospitalized patients. Influenza A virus (IAV) mimics the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) with respect to seasonal occurrence, transmission routes, clinical manifestations and related immune responses. The present paper aimed to develop and investigate a mathematical model to study the dynamics of IAV/SARS-CoV-2 coinfection within the host. The influence of SARS-CoV-2-specific and IAV-specific antibody immunities is incorporated. The model simulates the interaction between seven compartments, uninfected epithelial cells, SARS-CoV-2-infected cells, IAV-infected cells, free SARS-CoV-2 particles, free IAV particles, SARS-CoV-2-specific antibodies and IAV-specific antibodies. The regrowth and death of the uninfected epithelial cells are considered. We study the basic qualitative properties of the model, calculate all equilibria and investigate the global stability of all equilibria. The global stability of equilibria is established using the Lyapunov method. We perform numerical simulations and demonstrate that they are in good agreement with the theoretical results. The importance of including the antibody immunity into the coinfection dynamics model is discussed. We have found that without modeling the antibody immunity, the case of IAV and SARS-CoV-2 coexistence is not observed. Finally, we discuss the influence of IAV infection on the dynamics of SARS-CoV-2 single-infection and vice versa. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic continues to be a problem in South Africa. Individuals affected and infected by the disease suffer from stigma resulting in increased COVID-19 infections. In this paper, we developed a mathematical model to assess the effects of stigma on COVID-19 in South Africa, using low, moderate, and high stigma regimes in the population. The mathematical model was analysed and the basic reproduction number, R0, of the COVID-19 model with stigma was determined. The model was then fitted to data of the four COVID-19 waves for the new daily infected cases, and the estimated parameter values from different waves are presented. The effects of stigma on COVID-19 waves were examined using the four stigma regimes (high, moderate, low, and stigma-free regimes). Our results revealed that stigma is instrumental in the increase in the number of COVID-19 infections. It is also a significant contributor to sustaining COVID-19 in the population and probably in other infectious diseases such as HIV/AIDS and sexually transmitted diseases. The results obtained can influence policy directions with respect to stigma and its impact on the transmission dynamics of diseases. [ABSTRACT FROM AUTHOR]

The mathematical modeling and analysis of within-host or between-host coronavirus disease 2019 (COVID-19) dynamics are considered robust tools to support scientific research. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the cause of COVID-19. This paper proposes and investigates a within-host COVID-19 dynamics model with latent infection, the logistic growth of healthy epithelial cells and the humoral (antibody) immune response. Time delays can affect the dynamics of SARS-CoV-2 infection predicted by mathematical models. Therefore, we incorporate four time delays into the model: (i) delay in the formation of latent infected epithelial cells, (ii) delay in the formation of active infected epithelial cells, (iii) delay in the activation of latent infected epithelial cells, and (iv) maturation delay of new SARS-CoV-2 particles. We establish that the model's solutions are non-negative and ultimately bounded. This confirms that the concentrations of the virus and cells should not become negative or unbounded. We deduce that the model has three steady states and their existence and stability are perfectly determined by two threshold parameters. We use Lyapunov functionals to confirm the global stability of the model's steady states. The analytical results are enhanced by numerical simulations. The effect of time delays on the SARS-CoV-2 dynamics is investigated. We observe that increasing time delay values can have the same impact as drug therapies in suppressing viral progression. This offers some insight useful to develop a new class of treatment that causes an increase in the delay periods and then may control SARS-CoV-2 replication. [ABSTRACT FROM AUTHOR]

The effect of vaccination on the dengue fever epidemic described by an age structured modified SIR (Susceptible-Infected-Retired) model is studied using standard stability analysis. The chimeric yellow fever dengue tetravalent dengue vaccine (CYD-TDV™) is a vaccine recently developed to control this epidemic in several Southeast Asian countries. The dengue vaccination program requires a total of three injections, 6 months apart at 0, 6, and 12 months. The ages of the recipients are nine years and above. In this paper, we analyze the mathematical dynamics SIR transmission model of the epidemic. The stability of the model is established using Routh–Hurwitz criteria to see if a Hopf Bifurcation occurs and see when the equilibrium states are local asymptotically stable or global asymptotically stable. We have determined the efficiency of CYD-TDV by simulating the optimal numerical solution for each age range for this model. The numerical results showed the optimal age for vaccination and significantly reduced the severity and severity of the disease. [ABSTRACT FROM AUTHOR]

The world has been fighting against the COVID-19 Coronavirus which seems to be constantly mutating. The present wave of COVID-19 illness is caused by the Omicron variant of the coronavirus. The vaccines against the five variants (α, β, γ, δ, and ω) have been quickly developed using mRNA technology. The efficacy of the vaccine developed for one of the strains is not the same as the efficacy of the vaccine developed for the other strains. In this study, a mathematical model of the spread of COVID-19 was made by considering asymptomatic population, symptomatic population, two infected populations and quarantined population. An analysis of basic reproduction numbers was made using the next-generation matrix method. Global asymptotic stability analysis was made using the Lyapunov theory to measure stability, showing an equilibrium point's stability, and examining the model with the fact of COVID-19 spread in Thailand. Moreover, an analysis of the sensitivity values of the basic reproduction numbers was made to verify the parameters affecting the spread. It was found that the most common parameter affecting the spread was the initial number in the population. Optimal control problems and social distancing strategies in conjunction with mask-wearing and vaccination control strategies were determined to find strategies to give better control of the spread of disease. Lagrangian and Hamiltonian functions were employed to determine the objective function. Pontryagin's maximum principle was employed to verify the existence of the optimal control. According to the study, the use of social distancing in conjunction with mask-wearing and vaccination control strategies was able to achieve optimal control rather than controlling just one or another. [ABSTRACT FROM AUTHOR]

Based on the graph theory and stability theory of dynamical system, this paper studies the stability of the trivial solution of a coupled fractional-order system. Some sufficient conditions are obtained to guarantee the global stability of the trivial solution. Finally, a comparison between fractional-order system and integer-order system ends the paper. [ABSTRACT FROM AUTHOR]

The present paper proposes a five-dimensional mathematical model for studying the labor market, focusing on unemployment, migration, fixed term contractors, full time employment and the number of available vacancies. The distributed time delay is considered in the rate of change of available vacancies that depends on the past regular employment levels. The non-dimensional mathematical model is introduced and the existence of the equilibrium points is analyzed. The positivity and boundedness of solutions are provided and global asymptotic stability findings are presented both for the employment free equilibrium and the positive equilibrium. The numerical simulations support the theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the global stability analysis of the SEIRS epidemic model with a nonlinear incidence rate function according to the Lyapunov functions and Volterra-Lyapunov matrices. By creating special conditions and using the properties of Volterra-Lyapunov matrices, it is possible to recognize the stability of the endemic equilibrium ( E 1 ) for the SEIRS model. Numerical results are used to verify the presented analysis. [ABSTRACT FROM AUTHOR]

Mathematical models play a crucial role in predicting disease dynamics and estimating key quantities. Non-autonomous models offer the advantage of capturing temporal variations and changes in the system. In this study, we analyzed the transmission of typhoid fever in a population using a compartmental model that accounted for dynamic changes occurring periodically in the environment. First, we determined the basic reproduction number, R 0 , for the periodic model and derived the time-average reproduction rate, [ R 0 ] , for the non-autonomous model as well as the basic reproduction number, R 0 A , for the autonomous model. We conducted an analysis to examine the global stability of the disease-free solution and endemic periodic solutions. Our findings demonstrated that when R 0 < 1 , the disease-free solution was globally asymptotically stable, indicating the extinction of typhoid fever. Conversely, when R 0 > 1 , the disease became endemic in the population, confirming the existence of positive periodic solutions. We also presented numerical simulations that supported these theoretical results. Furthermore, we conducted a sensitivity analysis of R 0 A , [ R 0 ] and the infected compartments, aiming to assess the impact of model parameters on these quantities. Our results showed that the human-to-human infection rate has a significant impact on the reproduction number, while the environment-to-human infection rate and the bacteria excretion rate affect long-cycle infections. Moreover, we examined the effects of parameter modifications and how they impact the implementing of efficient control strategies to combat TyF. Although our model is limited by the lack of precise parameter values, the qualitative results remain consistent even with alternative parameter settings. [ABSTRACT FROM AUTHOR]

We present a nonautonomous compartmental model that incorporates vaccination and accounts for the seasonal transmission of typhoid fever. The dynamics of the system are governed by the basic reproductive number R 0 . This demonstrates the global stability of the disease-free solution if R 0 < 1 . On the contrary, if R 0 > 1 , the disease persists and positive periodic solutions exist. Numerical simulations validate our theoretical findings. To accurately fit typhoid fever data in Taiwan from 2008 to 2023, we use the model and estimate its parameters using Latin hypercube sampling and least squares techniques. A sensitivity analysis reveals the significant influence of parameters such as infection rates on the reproduction number. Increasing vaccination coverage, despite challenges in developing countries, reduces typhoid cases. Accessible and highly effective vaccines play a critical role in suppressing the epidemic, outweighing concerns about the efficacy of the vaccine. Investigating possible parameter changes in Taiwan highlights the importance of monitoring and managing transmission rates to prevent recurring annual epidemics. [ABSTRACT FROM AUTHOR]

Plankton occupy a vital place in the marine ecosystem due to their essential role. However small or microscopic, their absence can bring the entire life process to a standstill. In this work, we have proposed a prey–predator ecological model consisting of phytoplankton, zooplankton, and fish, incorporating the cannibalistic nature of zooplankton harvesting the fish population. Due to differences in their feeding habits, zooplankton are divided into two sub-classes: herbivorous and carnivorous. The dynamic behavior of the model is examined for each of the possible steady states. The stability criteria of the model have been analyzed from both local and global perspectives. Hopf bifurcation analysis has been accomplished with the growth rate of carnivorous zooplankton using cannibalism as a bifurcation parameter. To characterize the optimal control, we have used Pontryagin's maximum principle. Subsequently, the optimal system has been derived and solved numerically using an iterative method with Runge–Kutta fourth-order scheme. Finally, to facilitate the interpretation of our mathematical results, we have proceeded to investigate it using numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we study possibilities of eradication of populations at an early stage of a patient's infection in the framework of the seven-order Stengel model with 11 model parameters and four treatment parameters describing the interactions of wild-type and mutant HIV particles with various immune cells. We compute ultimate upper bounds for all model variables that define a polytope containing the attracting set. The theoretical possibility of eradicating HIV-infected populations has been investigated in the case of a therapy aimed only at eliminating wild-type HIV particles. Eradication conditions are expressed via algebraic inequalities imposed on parameters. Under these conditions, the concentrations of wild-type HIV particles, mutant HIV particles, and infected cells asymptotically tend to zero with increasing time. Our study covers the scope of acceptable therapies with constant concentrations and values of model parameters where eradication of infected particles/cells populations is observed. Sets of parameter values for which Stengel performed his research do not satisfy our local asymptotic stability conditions. Therefore, our exploration develops the Stengel results where he investigated using the optimal control theory and numerical dynamics of his model and came to a negative health prognosis for a patient. The biological interpretation of these results is that after a sufficiently long time, the concentrations of wild-type and mutant HIV particles, as well as infected cells will be maintained at a sufficiently low level, which means that the viral load and the concentration of infected cells will be minimized. Thus, our study theoretically confirms the possibility of efficient treatment beginning at the earliest stage of infection. Our approach is based on a combination of the localization method of compact invariant sets and the LaSalle theorem. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamics of a fractional-order epidemic model with general nonlinear incidence rate functionals and time-delay. We investigate the local and global stability of the steady-states. We deduce the basic reproductive threshold parameter, so that if R 0 < 1 , the disease-free steady-state is locally and globally asymptotically stable. However, for R 0 > 1 , there exists a positive (endemic) steady-state which is locally and globally asymptotically stable. A Holling type III response function is considered in the numerical simulations to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

We investigate global dynamics of the following second order rational difference equation xn+1... where the parameters α, β, a, b are positive real numbers and initial conditions x-1 and x0 are arbitrary positive real numbers. The map associated to the right-hand side of this equation is always decreasing in the second variable and can be either increasing or decreasing in the first variable depending on the corresponding parametric space. In most cases, we prove that local asymptotic stability of the unique equilibrium point implies global asymptotic stability. [ABSTRACT FROM AUTHOR]

Malaria is a serious illness caused by a parasite, called Plasmodium, transmitted to humans through the bites of female Anopheles mosquitoes. The parasite infects and destroys the red blood cells in the human body leading to symptoms, such as fever, headache, and flu-like illness. Awareness campaigns that educate people about malaria prevention and control reduce transmission of the disease. In this research, a mathematical model is proposed to study the impact of awareness-based control measures on the transmission dynamics of malaria. Some basic properties of the proposed model, such as non-negativity and boundedness of the solutions, the existence of the equilibrium points, and their stability properties, have been studied using qualitative theory. Disease-free equilibrium is globally asymptotic when the basic reproduction number, R 0 , is less than the number of current cases. Finally, optimal control theory is applied to minimize the cost of disease control and solve the optimal control problem by applying Pontryagin's minimum principle. Numerical simulations have been provided for the confirmation of the analytical results. Endemic equilibrium exists for R 0 > 1 , and a forward transcritical bifurcation occurs at R 0 = 1 . The optimal profiles of the treatment process, organizing awareness campaigns, and insecticide uses are obtained for the cost-effectiveness of malaria management. This research concludes that awareness campaigns through social media with an optimal control approach are best for cost-effective malaria management. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated the global dynamics of a discrete-time middle east respiratory syndrome (MERS-Cov) model. The proposed discrete model was analyzed and the threshold conditions for the global attractivity of the disease-free equilibrium (DFE) and the endemic equilibrium are established. We proved that the DFE is globally asymptotically stable when R 0 ≤ 1 . Whenever R ˜ 0 > 1 , the proposed model has a unique endemic equilibrium that is globally asymptotically stable. The theoretical results are illustrated by a numerical simulation. [ABSTRACT FROM AUTHOR]

Human T-lymphotropic virus type I (HTLV-I) and human immunodeficiency virus (HIV) are two famous retroviruses that share similarities in their genomic organization, and differ in their life cycle as well. It is known that HTLV-I and HIV have in common a way of transmission via direct contact with certain body fluids related to infected patients. Thus, it is not surprising that a single-infected person with one of these viruses can be dually infected with the other virus. In the literature, many researchers have devoted significant efforts for modeling and analysis of HTLV or HIV single infection. However, the dynamics of HTLV/HIV dual infection has not been formulated. In the present paper, we formulate an HTLV/HIV dual infection model. The model includes the impact of the Cytotoxic T lymphocyte (CTLs) immune response, which is important to control the dual infection. The model describes the interaction between uninfected CD 4 + T cells, HIV-infected cells, HTLV-infected cells, free HIV particles, HIV-specific CTLs, and HTLV-specific CTLs. We establish that the solutions of the model are non-negative and bounded. We calculate all steady states of the model and deduce the threshold parameters which determine the existence and stability of the steady states. We prove the global asymptotic stability of all steady states by utilizing the Lyapunov function and Lyapunov–LaSalle asymptotic stability theorem. We solve the system numerically to illustrate the our main results. In addition, we compared between the dynamics of single and dual infections. [ABSTRACT FROM AUTHOR]

In this paper, the problem of robust stability for a class of linear switched positive time-varying delay systems with all unstable subsystems and interval uncertainties is investigated. By establishing suitable time-scheduled multiple copositive Lyapunov-Krasovskii functionals (MCLKF) and adopting a mode-dependent dwell time (MDDT) switching strategy, new delay-dependent sufficient conditions guaranteeing global uniform asymptotic stability of the considered systems are formulated. Apart from past studies that studied switched systems with at least one stable subsystem, in the present study, the MDDT switching technique has been applied to ensure robust stability of the considered systems with all unstable subsystems. Compared with the existing results, our results are more general and less conservative than some of the previous studies. Two numerical examples are provided to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Vaccination is an essential tool for the management of infectious diseases. However, many vaccines are imperfect, having only a partial protective effect in decreasing disease transmission and/or favouring recovery of infected individuals and possibly exhibiting a trade-off between these two properties. Furthermore, the success of vaccination also depends on the population turnover, and the rate of entry to and exit from the population. We here investigate by means of a mathematical model the interplay between these factors to predict optimal vaccination strategies. We first compute the basic reproduction number and study the global stability of the equilibria. We then assess the most influential parameters determining the total number of infected over time using a sensitivity analysis. We derive conditions for the vaccination coverage and efficiency to achieve disease eradication, assuming different intensities of population turnover (weak and strong), vaccine properties (transmission and/or recovery) and the trade-off between the latter. We show that the minimum vaccination coverage increases with lower population turnover decreases with higher vaccine efficiency (transmission or recovery) and is increased/decreased by up to 15% depending on the vaccine trade-off. We conclude that the coverage target for vaccination campaigns should be evaluated based on the interplay between these factors. [ABSTRACT FROM AUTHOR]

In this paper we deal with the problems of existence, boundedness and global stability of integral manifolds for impulsive Lasota–Wazewska equations of fractional order with time-varying delays and variable impulsive perturbations. The main results are obtained by employing the fractional Lyapunov method and comparison principle for impulsive fractional differential equations. With this research we generalize and improve some existing results on fractional-order models of cell production systems. These models and applied technique can be used in the investigation of integral manifolds in a wide range of biological and chemical processes. [ABSTRACT FROM AUTHOR]

The first purpose of this article was to establish and analyze system 4 with an abstract function incidence rate under homogeneous Neumann boundary conditions. The system models the dynamics of interactions between pathogens and the host immune system, which has important applications in HIV-1, HCV, flu etc. By the Lyapunov–LaSalle method, we obtained the globally asymptotic stability of the equilibria. Specifically speaking, by introducing the reproductive numbers R 0 and R 1 , we showed that if R 0 ≤ 1 , then the infection-free equilibrium E 0 is globally asymptotically stable, i.e., the virus is unable to sustain the infection and will become extinct; if R 1 ≤ 1 < R 0 , then the C T L -inactivated infection equilibrium E 1 is globally asymptotically stable, i.e., the infection becomes chronic but without persistent CTL response; if R 1 > 1 , the C T L -activated equilibrium E 2 is globally asymptotically stable, and the infection is chronic with persistent CTL response. Additionally, we also investigate the discretization of the model by using a non-standard finite difference scheme, and our results confirm that the global stability of the equilibria of the continuous model and the discrete model is consistent. Finally, numerical simulations are performed to illustrate the theoretical results. Our model and results are to a certain extent generalizations of and improvements upon the previous results given by Zhu, Wang. [ABSTRACT FROM AUTHOR]

This research manifesto has a comprehensive discussion of the global dynamics of an achievable discrete-time two predators and one prey Lotka–Volterra model in three dimensions, i.e., in the space R 3 . In some assertive parametric circumstances, the discrete-time model has eight equilibrium points among which one is a special or unique positive equilibrium point. We have also investigated the local and global behavior of equilibrium points of an achievable three-dimensional discrete-time two predators and one prey Lotka–Volterra model. The conversion of a continuous-type model into its discrete counterpart model has been completed by adopting a dynamically consistent nonstandard difference scheme with the end goal that the equilibrium points are conserved in twin cases. The difficulty lies in how to find all fixed points O , P , Q , R , S , T , U , V and the Jacobian matrix and its characteristic polynomial at the unique positive fixed point. For that purpose, we use Mathematica software to find the equilibrium points and all of the Jacobian matrices at those equilibrium points. Moreover, we discuss boundedness conditions for every solution and prove the existence of a unique positive equilibrium point. We discuss the local stability of the obtained system about all of its equilibrium points. The discrete Lotka–Volterra model in three dimensions is given by system (3), where parameters α , β , γ , δ , ζ , η , μ , ε , υ , ρ , σ , ω ∈ R + and initial conditions x 0 , y 0 , z 0 are positive real numbers. Additionally, the rate of convergence of a solution that converges to a unique positive equilibrium point is discussed. To represent theoretical perceptions, some numerical debates are introduced, including phase portraits. [ABSTRACT FROM AUTHOR]

In this work, we analyze a delayed rumor-propagation model. First, we analyze the existence and boundedness of the solution of the model. Then, we give the conditions for the existence of the rumor-endemic equilibrium. Regrading the delay as a bifurcating parameter, we explore the local asymptotic stability and Hopf bifurcation of the rumor-endemic equilibrium. By a Lyapunov functional technique, we examine the global asymptotically stability of the rumor-free and the rumor-endemic equilibria. We provide two control variables in the rumor-spreading model with time delay, and get the optimal solution via the optimal procedures. Finally, we present some numerical simulations to verify our theoretical predictions. They illustrate that the delay is a crucial issue for system, and it can lead to not just Hopf bifurcation but also chaos. [ABSTRACT FROM AUTHOR]

In this paper, we construct an Human immunodeficiency virus (HIV) dynamics model with impairment of B-cell functions and the general incidence rate. We incorporate three types of infected cells, (i) latently-infected cells, which contain the virus, but do not generate HIV particles, (ii) short-lived productively-infected cells, which live for a short time and generate large numbers of HIV particles, and (iii) long-lived productively-infected cells, which live for a long time and generate small numbers of HIV particles. The model considers five distributed time delays to characterize the time between the HIV contact of an uninfected CD4 + T-cell and the creation of mature HIV. The nonnegativity and boundedness of the solutions are proven. The model admits two equilibria, infection-free equilibrium E P 0 and endemic equilibrium E P 1 . We derive the basic reproduction number R 0 , which determines the existence and stability of the two equilibria. The global stability of each equilibrium is proven by utilizing the Lyapunov function and LaSalle's invariance principle. We prove that if R 0 < 1 , then E P 0 is globally asymptotically stable, and if R 0 > 1 , then E P 1 is globally asymptotically stable. These theoretical results are illustrated by numerical simulations. The effect of impairment of B-cell functions, time delays, and antiviral treatment on the HIV dynamics are studied. We show that if the functions of B-cells are impaired, then the concentration of HIV is increased in the plasma. Moreover, we observe that the time delay has a similar effect to drug efficacy. This gives some impression for developing a new class of treatments to increase the delay period and then suppress the HIV replication. [ABSTRACT FROM AUTHOR]

This paper deals with the study of an HIV dynamics model with two target cells, macrophages and CD4 + T cells and three categories of infected cells, short-lived, long-lived and latent in order to get better insights into HIV infection within the body. The model incorporates therapeutic modalities such as reverse transcriptase inhibitors (RTIs) and protease inhibitors (PIs). The model is incorporated with distributed time delays to characterize the time between an HIV contact of an uninfected target cell and the creation of mature HIV. The effect of antibody on HIV infection is analyzed. The production and removal rates of the ten compartments of the model are given by general nonlinear functions which satisfy reasonable conditions. Nonnegativity and ultimately boundedness of the solutions are proven. Using the Lyapunov method, the global stability of the equilibria of the model is proven. Numerical simulations of the system are provided to confirm the theoretical results. We have shown that the antibodies can play a significant role in controlling the HIV infection, but it cannot clear the HIV particles from the plasma. Moreover, we have demonstrated that the intracellular time delay plays a similar role as the Highly Active Antiretroviral Therapies (HAAT) drugs in eliminating the HIV particles. [ABSTRACT FROM AUTHOR]

The prime objective of the current study is to propose a novel mathematical framework under the fractional-order derivative, which describes the complex within-host behavior of SARS-CoV-2 by taking into account the effects of memory and carrier. To do this, we formulate a mathematical model of SARS-CoV-2 under the Caputo fractional-order derivative. We derived the conditions for the existence of equilibria of the model and computed the basic reproduction number R 0 . We used mathematical analysis to establish the proposed model's local and global stability results. Some numerical resolutions of our theoretical results are presented. The main result of this study is that as the fractional derivative order increases, the approach of the solution to the equilibrium points becomes faster. It is also observed that the value of R 0 increases as the value of β and π v increases. [ABSTRACT FROM AUTHOR]

Malignant tumor (cancer) is the leading cause of death globally and the annual cost of managing cancer is trillions of dollars. Although, there are established therapies including radiotherapy, chemotherapy and phototherapy for malignant tumors, the hypoxic environment of tumors and poor perfusion act as barriers to these therapies. Hyperthermia takes advantage of oxygen deficiency and irregular perfusion in the tumor environment to destroy malignant cells. Despite successes recorded with hyperthermia, there are concerns with the post-treatment condition of patients as well as the required thermal dose to prevent harm. The investigation of the dynamics of tumor-induced immune suppression with hyperthermia treatment using mathematical analysis and optimal control theory is potentially valuable in the development of hyperthermia treatment. The role of novel tumor-derived cytokines in counterattacking immune cells is considered in this study as a mechanism accounting for the aggressiveness of malignant tumors. Since biological processes are not instantaneous, a discrete time delay is used to model biological processes involved in tumor inhibitory mechanisms by secretion, the elaboration of suppressive cells, and effector cell differentiation to produce suppressive cells. Analytical results obtained using Lyapunov's function indicate the conditions required for global stability of the tumor-present steady-state. A thermal optimal control strategy is pursued based on optimal control theory, and the best strategy to avoid adverse outcomes is obtained. We validate the analytical results numerically and demonstrate the impact of both inadequate and excessive heat on the dynamics of interactive cell functioning. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability analysis of two within-host virus dynamics models with antibody immune response. We assume that the virus infects n classes of target cells. The second model considers two types of infected cells: (i) latently infected cells; and (ii) actively infected cells that produce the virus particles. For each model, we derive a biological threshold number R 0 . Using the method of Lyapunov function, we establish the global stability of the steady states of the models. The theoretical results are confirmed by numerical simulations. [ABSTRACT FROM AUTHOR]

By applying impulsive control, this work investigated the global stabilization of a single-species ecosystem with Markovian jumping, a time delay and a Neumann boundary condition. Variational methods, a fixed-point theorem, and Laplacian semigroup theory were employed to derive the unique existence of the global stable equilibrium point, which is a positive number. Numerical examples illuminate the feasibility of the proposed methods. [ABSTRACT FROM AUTHOR]

The sudden emergence of the COVID-19 pandemic has tested the strength of the public health system of the most developed nations and created a "new normal". Many nations are struggling to curb the epidemic in spite of expanding testing facilities. In this study, we consider the case of Bangladesh, and fit a simple compartmental model holding a feature to distinguish between identified infected and infectious with time series data using least square fitting as well as the likelihood approach; prior to which, dynamics of the model were analyzed mathematically and the identifiability of the parameters has also been confirmed. The performance of the likelihood approach was found to be more promising and was used for further analysis. We performed fitting for different lengths of time intervals starting from the beginning of the outbreak, and examined the evolution of the key parameters from Bangladesh's perspective. In addition, we deduced profile likelihood and 95 % confidence interval for each of the estimated parameters. Our study demonstrates that the parameters defining the infectious and quarantine rates change with time as a consequence of the change in lock-down strategies and expansion of testing facilities. As a result, the value of the basic reproduction number R 0 was shown to be between 1.5 and 12. The analysis reveals that the projected time and amplitude of the peak vary following the change in infectious and quarantine rates obtained through different lock-down strategies and expansion of testing facilities. The identification rate determines whether the observed peak shows the true prevalence. We find that by restricting the spread through quick identification and quarantine, or by implementing lock-down to reduce overall contact rate, the peak could be delayed, and the amplitude of the peak could be reduced. Another novelty of this study is that the model presented here can infer the unidentified COVID cases besides estimating the officially confirmed COVID cases. [ABSTRACT FROM AUTHOR]