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We investigate a malaria transmission model with SEIR (susceptible-exposed-infected-recovered) classes for the human population, SEI (susceptible-exposed-infected) classes for the wild mosquitoes and an additional class for the sterile mosquitoes. The basic reproduction number of the disease transmission is obtained, and a release threshold of the sterile mosquitoes is provided. We formulate an optimal control problem in which the goal is to minimize both the infected human populations and the cost to implement two control strategies: the release of sterile mosquitoes and the usage of insecticide-treated nets to reduce the malaria transmission. Adjoint equations are derived, and the characterization of the optimal controls is established. Finally, we quantify the effectiveness of the two interventions aimed at limiting the spread of malaria transmission. A combination of both strategies leads to more rapid elimination of the wild mosquito population that can suppress malaria transmission. Numerical simulations are provided to illustrate the results. [ABSTRACT FROM AUTHOR]

Coronavirus disease 2019 (COVID‐19) is a viral disease which is declared as a pandemic by WHO. This disease is posing a global threat, and almost every country in the world is now affected by this disease. Currently, there is no vaccine for this disease, and because of this, containing COVID‐19 is not an easy task. It is noticed that elderly people got severely affected by this disease specially in Europe. In the present paper, we propose and analyze a mathematical model for COVID‐19 virus transmission by dividing whole population in old and young groups. We find disease‐free equilibrium and the basic reproduction number (R0). We estimate the parameter corresponding to rate of transmission and rate of detection of COVID‐19 using real data from Italy and Spain by least square method. We also perform sensitivity analysis to identify the key parameters which influence the basic reproduction number and hence regulate the transmission dynamics of COVID‐19. Finally, we extend our proposed model to optimal control problem to explore the best cost‐effective and time‐dependent control strategies that can reduce the number of infectives in a specified interval of time. [ABSTRACT FROM AUTHOR]

• A multi-scale novel model for cholera is proposed. • The epidemiological dynamics for cholera are further shown. • The connection between the within-host and between-host dynamics for cholera is discovered. • The new suggestions on possible mechanisms of the cholera prevalence are given. In this paper, a multi-scale mathematical model for environmentally transmitted diseases is proposed which couples the pathogen-immune interaction inside the human body with the disease transmission at the population level. The model is based on the nested approach that incorporates the infection-age-structured immunological dynamics into an epidemiological system structured by the chronological time, the infection age and the vaccination age. We conduct detailed analysis for both the within-host and between-host disease dynamics. Particularly, we derive the basic reproduction number R 0 for the between-host model and prove the uniform persistence of the system. Furthermore, using carefully constructed Lyapunov functions, we establish threshold-type results regarding the global dynamics of the between-host system: the disease-free equilibrium is globally asymptotically stable when R 0 < 1, and the endemic equilibrium is globally asymptotically stable when R 0 > 1. We explore the connection between the within-host and between-host dynamics through both mathematical analysis and numerical simulation. We show that the pathogen load and immune strength at the individual level contribute to the disease transmission and spread at the population level. We also find that, although the between-host transmission risk correlates positively with the within-host pathogen load, there is no simple monotonic relationship between the disease prevalence and the individual pathogen load. [ABSTRACT FROM AUTHOR]

Malaria is one of the most common mosquito-borne diseases widespread in the tropical and subtropical regions. Few models coupling the within-host malaria dynamics with the between-host mosquito-human dynamics have been developed. In this paper, by adopting the nested approach, a malaria transmission model with immune response of the host is formulated. Applying age-structured partial differential equations for the between-host dynamics, we describe the asymptomatic and symptomatic infectious host population for malaria transmission. The basic reproduction numbers for the within-host model and for the coupled system are derived, respectively. The existence and stability of the equilibria of the coupled model are analyzed. We show numerically that the within-host model can exhibit complex dynamical behavior, possibly even chaos. In contrast, equilibria in the immuno-epidemiological model are globally stable and their stabilities are determined by the reproduction number. Increasing the activation rate of the within-host immune response 'dampens' the sensitivity of the population level reproduction number and prevalence to the increase of the within-host reproduction of the pathogen. From public health perspective this means that treatment in a population with higher immunity has less impact on the population-level reproduction number and prevalence than in a population with less immunity. [ABSTRACT FROM AUTHOR]

Abstract: As drug treatment allows more and more people with HIV/AIDS to live longer, the trade-off between benefits to drug treatment and potential threat infectivity individuals needs to be carefully evaluated. In this paper, we shall extend and investigate an HIV/AIDS treatment model (Cai et al., 2009) [14]. The infection force of the extended model is assumed to be of density dependent form. The resulting incidence term contains, the bilinear and the standard incidence. Mathematical analysis establishes that the global dynamics of the HIV infectious disease is completely determined by the basic reproduction number . If , the disease always dies out and the disease-free equilibrium is globally stable. If , the disease persists and the unique endemic equilibrium is globally asymptotically stable in the interior of the feasible region. [Copyright &y& Elsevier]

Abstract: In this paper, a mathematical model for HILV-I infection of CD4+ T-cells is investigated. The force of infection is assumed be of a function in general form, and the resulting incidence term contains, as special cases, the bilinear and the saturation incidences. The model can be seen as an extension of the model [Wang et al. Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression, Math. Biosci. 179 (2002) 207-217; Song, Li, Global stability and periodic solution of a model for HTLV-I infection and ATL progression, Appl. Math. Comput. 180(1) (2006) 401-410]. Mathematical analysis establishes that the global dynamics of T-cells infection is completely determined by a basic reproduction number . If , the infection-free equilibrium is globally stable; if , the unique infected equilibrium is globally stable in the interior of the feasible region. [Copyright &y& Elsevier]

Abstract: An HIV/AIDS epidemic model with treatment is investigated. The model allows for some infected individuals to move from the symptomatic phase to the asymptomatic phase by all sorts of treatment methods. We first establish the ODE treatment model with two infective stages. Mathematical analyses establish that the global dynamics of the spread of the HIV infectious disease are completely determined by the basic reproduction number . If , the disease-free equilibrium is globally stable, whereas the unique infected equilibrium is globally asymptotically stable if . Then, we introduce a discrete time delay to the model to describe the time from the start of treatment in the symptomatic stage until treatment effects become visible. The effect of the time delay on the stability of the endemically infected equilibrium is investigated. Moreover, the delay model exhibits Hopf bifurcations by using the delay as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the results. [Copyright &y& Elsevier]