Related papers: Threshold dynamics in a within host infection mode…
In this paper, we first propose a diffusive pathogen infection model with general incidence rate which incorporates cell-to-cell transmission. By applying the theory of monotone dynamical systems, we prove that the model admits the global…
We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate and it is shown the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence.…
It is essential to understand the dynamics of epidemics in the presence of coexisting pathogens. There are various phenomenon that can effect the dynamics. In this paper, we formulate a mathematical model using different assumptions to…
In this paper, we study a reaction-diffusion vector-host epidemic model. We define the basic reproduction number $R_0$ and show that $R_0$ is a threshold parameter: if $R_0\le 1$ the disease free steady state is globally stable; if $R_0>1$…
In this paper, a mathematical analysis of the global dynamics of a viral infection model in vivo is carried out. We study the dynamics of a hepatitis C virus (HCV) model, under therapy, that considers both extracellular and intracellular…
This paper studies the spread dynamics of a stochastic SIRS epidemic model with nonlinear incidence and varying population size, which is formulated as a piecewise deterministic Markov process. A threshold dynamic determined by the basic…
We study the Suscectible-Infected-Recovered-Susceptible (SIRS) epidemic model on deterministic networks. For connected but otherwise general interaction patterns and heterogeneous recovery and loss-of-immunity rates, we identify a…
This research gives a thorough examination of an HIV infection model that includes quiescent cells and immune response dynamics in the host. The model, represented by a system of ordinary differential equations, captures the complex…
When an infectious disease propagates throughout society, the incidence function may rise at first due to an increase in pathogenicity and then decrease due to inhibitory effects until it reaches saturation. Effective vaccination and…
In this paper, we consider a compartmental SIRS epidemic model with asymptomatic infection and seasonal succession, which is a periodic discontinuous differential system. The basic reproduction number $\mathcal{R}_0$ is defined and valuated…
We study an SIR epidemic model with a seasonal contact rate and saturated treatment function. It is shown that the basic reproduction number $(\mathcal {R}_0)$ cannot be acted as a threshold that predicts the spread of an infection. Based…
The evolution and emergence of antibiotic resistance is a major public health concern. The understanding of the within-host microbial dynamics combining mutational processes, horizontal gene transfer and resource consumption, is one of the…
In this paper, we further investigate the global dynamics of a stochastic differential equation SIS (Susceptible-Infected-Susceptible) epidemic model recently proposed in [A. Gray et al., SIAM. J. Appl. Math., 71 (2011), 876-902]. We…
It has been known for some time that human autoimmune diseases can be triggered by viral infections. Several possible mechanisms of interactions between a virus and immune system have been analysed, with a prevailing opinion being that the…
We investigate the global dynamics of a general Kermack-McKendrick-type epidemic model formulated in terms of a system of renewal equations. Specifically, we consider a renewal model for which both the force of infection and the infected…
This paper is concerned with a nonlocal dispersal susceptible-infected-susceptible (SIS) epidemic model with Dirichlet boundary condition, where the rates of disease transmission and recovery are assumed to be spatially heterogeneous. We…
A current challenge for disease modeling and public health is understanding pathogen dynamics across scales since their ecology and evolution ultimately operate on several coupled scales. This is particularly true for vector-borne diseases,…
In this study, we investigate a stochastic SIR model with media effects. The uniqueness and the existence of a global positive solution are studied. The sufficient conditions of extinction and persistence of the disease are established. We…
A great issue of discussion of an infectious disease is its basic reproduction number R0, which provides an estimation of the contagiousness of the disease. When R0 > 1, the disease spread will potentially lead to an outbreak, such that of…
For a heterogeneous host population, the basic reproduction number of an infectious disease, $\cR_0$, is defined as the spectral radius of the next generation operator (NGO). The threshold properties of the basic reproduction number are…