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Malaria is a fever condition that results from Plasmodium parasites, which are transferred to humans by the attacks of infected female Anopheles mosquitos. The deterministic compartmental model was examined using stability theory of differential equations. The reproduction number was obtained to be asymptotically stable conditions for the disease-free, and the endemic equilibria were determined. More so, the qualitatively evaluated model incorporates time-dependent variable controls which was aimed at reducing the proliferation of malaria disease. The reproduction number R o was determined to be an asymptotically stable condition for disease free and endemic equilibria. In this paper, we used various schemes such as Runge-Kutta order 4 (RK-4) and non-standard finite difference (NSFD). All of the schemes produce different results, but the most appropriate scheme is NSFD. This is true for all step sizes. Various criteria are used in the NSFD scheme to assess the local and global stability of disease-free and endemic equilibrium points. The Routh-Hurwitz condition is used to validate the local stability and Lyapunov stability theorem is used to prove the global asymptotic stability. Global asymptotic stability is proven for the disease-free equilibrium when R 0 ≤ 1 . The endemic equilibrium is investigated for stability when R 0 ≥ 1 . All of the aforementioned schemes and their effects are also numerically demonstrated. The comparative analysis demonstrates that NSFD is superior in every way for the analysis of deterministic epidemic models. The theoretical effects and numerical simulations provided in this text may be used to predict the spread of infectious diseases.

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During any infectious disease outbreak, effective and timely quarantine of infected individuals, along with preventive measures by the population, is vital for controlling the spread of infection in society. Therefore, this study attempts to provide a mathematically validated approach for managing the epidemic spread by incorporating the Monod-Haldane incidence rate, which accounts for psychological effects, and a saturated quarantine rate as Holling functional type III that considers the limitation in quarantining of infected individuals into the standard Susceptible-Exposed-Infected-Quarantine-Recovered (SEIQR) model. The rate of change of each subpopulation is considered as the Caputo form of fractional derivative where the order of derivative represents the memory effects in epidemic transmission dynamics and can enhance the accuracy of disease prediction by considering the experience of individuals with previously encountered. The mathematical study of the model reveals that the solutions are well-posed, ensuring nonnegativity and boundedness within an attractive region. Further, the study identifies two equilibria, namely, disease-free (DFE) and endemic (EE); and stability analysis of equilibria is performed for local as well as global behaviours for the same. The stability behaviours of equilibria mainly depend on the basic reproduction number R0 and its alternative threshold T0 which is computed using the Next-generation matrix method. It is investigated that DFE is locally and globally asymptotic stable when R0<1. Furthermore, we show the existence of EE and investigate that it is locally and globally asymptotic stable using the Routh-Hurwitz criterion and the Lyapunov stability theorem for fractional order systems with R0>1 under certain conditions. This study also addresses a fractional optimal control problem (FOCP) using Pontryagin's maximum principle aiming to minimize the spread of infection with minimal expenditure. This approach involves introducing a time-dependent control measure, u(t), representing the behavioural response of susceptible individuals. Finally, numerical simulations are presented to support the analytical findings using the Adams Bashforth Moulton scheme in MATLAB, providing a comprehensive understanding of the proposed SEIQR model.

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The SARSCoV-2 virus, also known as the coronavirus-2, is the consequence of COVID-19, a severe acute respiratory syndrome. Droplets from an infectious individual are how the pathogen is transmitted from one individual to another and occasionally, these particles can contain toxic textures that could also serve as an entry point for the pathogen. We formed a discrete fractional-order COVID-19 framework for this investigation using information and inferences from Thailand. To combat the illnesses, the region has implemented mandatory vaccination, interpersonal stratification and mask distribution programs. As a result, we divided the vulnerable people into two groups: those who support the initiatives and those who do not take the influence regulations seriously. We analyze endemic problems and common data while demonstrating the threshold evolution defined by the fundamental reproductive quantity R 0 . Employing the mean general interval, we have evaluated the configuration value systems in our framework. Such a framework has been shown to be adaptable to changing pathogen populations over time. The Picard Lindelöf technique is applied to determine the existence-uniqueness of the solution for the proposed scheme. In light of the relationship between the R 0 and the consistency of the fixed points in this framework, several theoretical conclusions are made. Numerous numerical simulations are conducted to validate the outcome.

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Though overfishing and climate change are the primary reasons for a regime shift in the fishery, we demonstrate here a different reason for the regime shift, not reported earlier to the best of our knowledge. We show that high demand for fish may cause a regime shift in a fishery in a shorter time. For this, a four-dimensional bioeconomic fishery model is considered and analyzed to explore the system's dynamic behavior. The objective is to demonstrate how increasing demand may cause a catastrophic change in the fish and fishery. We provide the local and global stabilities of different equilibrium points, guaranteeing the stable coexistence of ecological and economic states. Our bifurcation analysis revealed that the demand parameter might play positive and negative roles in the system dynamics. Demand can make an unstable fishery stable. It can also help remove the infection from the system. On the flip side, high demand may cause a regime shift from a harvested state to a non-harvested state, making the price unbounded. Using Pontryagin's maximum principle, we further discussed optimal revenue generation.

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In this paper, a mathematical analysis of the HIV/AIDS deterministic model studied in the paper called Mathematical Model of HIV/AIDS Considering Sexual Preferences Under Antiretroviral Therapy, a case study in the previous works preformed by Espitia is performed. The objective is to gain insight into the qualitative dynamics of the model determining the conditions for the persistence or effective control of the disease in the community through the study of basic properties such as positiveness and boundedness; the calculus of the basic reproduction number; stationary points such as disease-free equilibrium (DFE), boundary equilibrium (BE) and endemic equilibrium (EE); and the local stability (LAS) of disease-free equilibrium. The findings allow us to conclude that the best way to reduce contagion and consequently reach a DFE is thought to be the reduction in the rate of homosexual partners, as they are the most affected population by the virus and are therefore the most likely to become infected and spread it. Increasing the departure rate of infected individuals leads to a decrease in untreated infected heterosexual men and untreated infected women.

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In this article, a novel susceptible-infected-recovered epidemic model with nonmonotonic incidence and treatment rates is proposed and analyzed mathematically. The Monod-Haldane functional response is considered for nonmonotonic behavior of both incidence rate and treatment rate. The model analysis shows that the model has two equilibria which are named as disease-free equilibrium (DFE) and endemic equilibrium (EE). The stability analysis has been performed for the local and global behavior of the DFE and EE. With the help of the basic reproduction number R 0 , we investigate that DFE is locally asymptotically stable when R 0 < 1 and unstable when R 0 > 1 . The local stability of DFE at R 0 = 1 has been analyzed, and it is obtained that DFE exhibits a forward transcritical bifurcation. Further, we identify conditions for the existence of EE and show the local stability of EE under certain conditions. Moreover, the global stability behavior of DFE and EE has been investigated. Lastly, numerical simulations have been done in the support of our theoretical findings.

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In this study, we developed and analyzed a mathematical model for explaining the transmission dynamics of COVID-19 in India. The proposed SI u I k R model is a modified version of the existing SIR model. Our model divides the infected class I of SIR model into two classes: I u (unknown infected class) and I k (known infected class). In addition, we consider R a recovered and reserved class, where susceptible people can hide them due to fear of the COVID-19 infection. Furthermore, a non-monotonic incidence function is deemed to incorporate the psychological effect of the novel coronavirus diseases on India's community. The epidemiological threshold parameter, namely the basic reproduction number, has been formulated and presented graphically. With this threshold parameter, the local and global stability analysis of the disease-free equilibrium and the endemic proportion equilibrium based on disease persistence have been analyzed. Lastly, numerical results of long-run prediction using MATLAB show that the fate of this situation is very harmful if people are not following the guidelines issued by the authority.

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Sequential infections with different dengue serotypes (DENV-1, 4) significantly increase the risk of a severe disease outcome (fever, shock, and hemorrhagic disorders). Two hypotheses have been proposed to explain the severity of the disease: (1) antibody-dependent enhancement (ADE) and (2) original T cell antigenic sin. In this work, we explored the first hypothesis through mathematical modeling. The proposed model reproduces the dynamic of susceptible and infected target cells and dengue virus in scenarios of infection-neutralizing and infection-enhancing antibody competition induced by two distinct serotypes of the dengue virus during secondary infection. The enhancement and neutralization functions are derived from basic concepts of chemical reactions and used to mimic binding to the virus by two distinct populations of antibodies. The analytic study of the model showed the existence of two equilibriums: a disease-free equilibrium and an endemic one. Using the concept of the basic reproduction number [Formula: see text], we performed the asymptotic stability analysis for the two equilibriums. To measure the severity of the disease, we considered the maximum value of infected cells as well as the time when this maximum is reached. We observed that it corresponds to the time when the maximum enhancing activity for the infection occurs. This critical time was calculated from the model to be a few days after the occurrence of the infection, which corresponds to what is observed in the literature. Finally, using as output [Formula: see text], we were able to rank the contribution of each parameter of the model. In particular, we highlighted that the cross-reactive antibody responses may be responsible for the disease enhancement during secondary heterologous dengue infection.

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This current work studies a new mathematical model for SARS-CoV-2. We show how immigration, protection, death rate, exposure, cure rate and interaction of infected people with healthy people affect the population. Our model is SIR model, which has three classes including susceptible, infected and recovered respectively. Here, we find the basic reproduction number and local stability through jacobean matrix. Lyapunvo function theory is used to calculate the global stability for the problem under investigation. Also a nonstandard finite difference sachem (NSFDS) is used to simulate the results.

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The fact that no there exists yet an absolute treatment or vaccine for COVID-19, which was declared as a pandemic by the World Health Organization (WHO) in 2020, makes very important spread out over time of the epidemic in order to burden less on hospitals and prevent collapsing of the health care system. This case is a consequence of limited resources and is valid for all countries in the world facing with this serious threat. Slowing the speed of spread will probably make that the outbreak last longer, but it will cause lower total death count. In this study, a new SEIR epidemic model formed by taking into account the impact of health care capacity has been examined and local and global stability of the model has been analyzed. In addition, the model has been also supported by some numerical simulations.

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Dengue hemorrhagic fever (DHF) can occur in primary dengue virus infection of infants [Formula: see text] year of age. To understand the presumed role of maternal dengue-specific antibodies received until birth in the development of this primary DHF in infants, we investigated a mathematical model based on a system of nonlinear ordinary differential equations that mimics cells, virus and antibodies interactions. The neutralization and enhancement activities of maternal antibodies against the virus are represented by a function derived from experimental data and knowledge from the medical literature. The analytic study of the model shows the existence of two equilibriums, a disease-free equilibrium and an endemic one. We performed the asymptotic stability analysis for these two equilibriums. The local asymptotic stability of the endemic equilibrium (DHF equilibrium) corresponds to the occurrence of DHF. Numerical results are also presented in order to illustrate the mathematical analysis performed, highlighting the most important parameters that drive model dynamics. We defined the age at which DHF occurs as the time when the infection takes off that means at the inflection point of the curve of infected cell population. We showed that this age corresponds to the one at which maximum enhancing activity for dengue infection appears. This critical time for the occurrence of DHF is calculated from the model to be approximately 2 months after the time for maternal dengue neutralizing antibodies to degrade below a protective level, which corresponds to what is observed in the experimental data from the literature.

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The aim of this work is to study the impact of sex and gender disparity on the overall dynamics of influenza A virus infection and to explore the direct and indirect effect of influenza A mass vaccination. To this end, a deterministic SIR model has been formulated and throughly analysed, where the equilibrium and stability analyses have been explored. The impact of sex disparity (i.e., disparity in susceptibility and in recovery rate between females and males) on the disease outcome (i.e., the basic reproduction number R0 and the endemic prevalence of influenza in females and males) has been investigated. Mathematical and numerical analyses show that sex and gender disparities affect on the severity as well as the endemic prevalence of infection in both sexes. The analysis shows further that the efficacy of the vaccine for both sexes (e1&e2) and the response of the gender to mass-vaccination campaigns Ψ play a crucial role in influenza A containment and elimination process, where they impact significantly on the protection ratio as well as on the direct, indirect and total effect of vaccination on the burden of infection.

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In this paper, we are concerned with an epidemic model of susceptible, infected and recovered (SIR) population dynamic by considering an age-structured phase of protection with limited duration, for instance due to vaccination or drugs with temporary immunity. The model is reduced to a delay differential-difference system, where the delay is the duration of the protection phase. We investigate the local asymptotic stability of the two steady states: disease-free and endemic. We also establish when the endemic steady state exists, the uniform persistence of the disease. We construct quadratic and logarithmic Lyapunov functions to establish the global asymptotic stability of the two steady states. We prove that the global stability is completely determined by the basic reproduction number.

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It is recently known that parasites provide a better picture of an ecosystem, gaining attention in theoretical ecology. Parasitic fungi belong to a food chain between zooplankton and inedible phytoplankton, called mycoloop. We consider a chemostat model that incorporates a single mycoloop, and analyze the limiting behavior of solutions, adding to previous work on steady-state analysis. By way of persistence theory, we establish that a given species survives depending on the food web configuration and the nutrient level. Moreover, we conclude that the model predicts coexistence under bounded nutrient levels.

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This study proposes a mathematical model of Anthroponotic visceral leishmaniasis epidemic with saturated infection rate and recommends different control strategies to manage the spread of this disease in the community. To do this, first, a model formulation is presented to support these strategies, with quantifications of transmission and intervention parameters. To understand the nature of the initial transmission of the disease, the reproduction number [Formula: see text] is obtained by using the next-generation method. On the basis of sensitivity analysis of the reproduction number [Formula: see text], four different control strategies are proposed for managing disease transmission. For quantification of the prevalence period of the disease, a numerical simulation for each strategy is performed and a detailed summary is presented. Disease-free state is obtained with the help of control strategies. The threshold condition for globally asymptotic stability of the disease-free state is found, and it is ascertained that the state is globally stable. On the basis of sensitivity analysis of the reproduction number, it is shown that the disease can be eradicated by using the proposed strategies.

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A new modelling framework is proposed to study the within-host and between-host dynamics of cholera, a severe intestinal infection caused by the bacterium Vibrio cholerae. The within-host dynamics are characterized by the growth of highly infectious vibrios inside the human body. These vibrios shed from humans contribute to the environmental bacterial growth and the transmission of the disease among humans, providing a link from the within-host dynamics at the individual level to the between-host dynamics at the population and environmental level. A fast-slow analysis is conducted based on the two different time scales in our model. In particular, a bifurcation study is performed, and sufficient and necessary conditions are derived that lead to a backward bifurcation in cholera epidemics. Our result regarding the backward bifurcation highlights the challenges in the prevention and control of cholera.

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In this paper, a discrete-time analog of a viral infection model with nonlinear incidence and CTL immune response is established by using the Micken non-standard finite difference scheme. The two basic reproduction numbers R 0 and R 1 are defined. The basic properties on the positivity and boundedness of solutions and the existence of the virus-free, the no-immune, and the infected equilibria are established. By using the Lyapunov functions and linearization methods, the global stability of the equilibria for the model is established. That is, when R 0 ≤ 1 then the virus-free equilibrium is globally asymptotically stable, and under the additional assumption ( A 4 ) when R 0 > 1 and R 1 ≤ 1 then the no-immune equilibrium is globally asymptotically stable and when R 0 > 1 and R 1 > 1 then the infected equilibrium is globally asymptotically stable. Furthermore, the numerical simulations show that even if assumption ( A 4 ) does not hold, the no-immune equilibrium and the infected equilibrium also may be globally asymptotically stable.