*Correspondence: [email protected] 1Department of Applied Mathematics, Xi’an Jiaotong University, Xi’an, 710049, China Full list of author information is available at the end of the article Abstract The basic reproductive number R0 of a discrete SIR epidemic model is defined and the dynamical behavior of the model is studied. It is proved that the disease free equilibrium is globally asympto...

In this paper, we propose a multi-patch model to study the effects of population dispersal on the spatial spread of malaria between patches. The basic reproduction number [Formula: see text] is derived and it is shown that the disease-free equilibrium is locally asymptotically stable if [Formula: see text] and unstable if [Formula: see text]. Bounds on the disease-free equilibrium and [Formula:...

The conceptual difference between equilibrium and non-equilibrium steady state (NESS) is well established in physics and chemistry. This distinction, however, is not widely appreciated in dynamical descriptions of biological populations in terms of differential equations in which fixed point, steady state, and equilibrium are all synonymous. We study NESS in a stochastic SIS (susceptible-infect...

A deterministic model for the transmission dynamics of a communicable disease is developed and rigorously analysed. The model, consisting of five mutually exclusive compartments representing the human dynamics, has a globally asymptotically stable disease-free equilibrium (DFE) whenever a certain epidemiological threshold, known as the basic reproduction number (ℛ₀), is less than unity; in such...

In this paper, a metapopulation model is formulated as a system of ordinary differential equations to study the impact of vaccination on the spread of measles. The disease-free equilibrium is computed and proved to be locally and globally asymptotically stable if 1 C R < and unstable if 1 C R > . We show that when there are no movements between the two patches, there exists at least one endemic...

This paper studies the dynamics of a network-based SIRS epidemic model with vaccination and a nonmonotone incidence rate. This type of nonlinear incidence can be used to describe the psychological or inhibitory effect from the behavioral change of the susceptible individuals when the number of infective individuals on heterogeneous networks is getting larger. Using the analytical method, epidem...

Abstract. A model is developed for the spread of an infectious disease in a population with constant recruitment of new susceptibles and the fundamental properties of its solutions are analyzed. The model allows for arbitrarily many stages of infection all of which have general length distributions and disease mortalities. Existence and uniqueness of solutions to the model equations are establi...

We study a population model for an infectious disease that spreads in the host population through both horizontal and vertical transmission. The total host population is assumed to have constant density and the incidence term is of the bilinear mass-action form. We prove that the global dynamics are completely determined by the basic reproduction number R0(p, q), where p and q are fractions of ...

We analyze the global dynamics of a mathematical model for infectious diseases that progress through distinct stages within infected hosts with possibility of amelioration. An example of such diseases is HIV/AIDS that progresses through several stages with varying degrees of infectivity; amelioration can result from a host's immune action or more commonly from antiretroviral therapies, such as ...

In this paper, an SIS patch model with non-constant transmission coefficients is formulated to investigate the effect of media coverage and human movement on the spread of infectious diseases among patches. The basic reproduction number R(0) is determined. It is shown that the disease-free equilibrium is globally asymptotically stable if R(0)≤1, and the disease is uniformly persistent and there...