In this paper, we establish the global asymptotic stability of an endemic equilibrium for an SIRS epidemic model with distributed time delays. It is shown that the global stability holds for any rate of immunity loss, if the basic reproduction number is greater than 1 and less than or equals to a critical value. Otherwise, there is a maximal rate of immunity loss which guarantees the global sta...

We analyse SIS epidemics amongst populations partitioned into households. The analysis considers both the stochastic and deterministic model and unlike previous analysis, we consider general infectious period distributions. For the deterministic model, we prove the existence of an endemic equilibrium for the epidemic if and only if the threshold parameter, R∗ > 1. Furthermore, by utilising Mark...

We analyse here the equilibria of an infinite system of partial differential equations modelling the dynamics of a population infected by macroparasites. We find that it is possible to define a reproduction number R(0) that satisfies the intuitive definition, and yields a sharp threshold in the behaviour of the system: if R(0) < 1, the parasite-free equilibrium (PFE) is asymptotically stable an...

We study an SV IR model of disease transmission with immigration into all four classes. Vaccinated individuals may only receive partial immunity to the disease, giving a leaky vaccine. The incidence function permits a nonlinear response to the number of infectives, so that mass action and saturating incidence are included as special cases. Because of the immigration of infected individuals, the...

This paper proves a First Welfare Theorem for Games it shows that asynchronous dynamic games with voluntary one period ahead transfers have a unique optimal equilibrium. The equilibrium coincides with the Utilitarian Pareto Optimum and hence can be computed from a (simpler) programming problem (rather than as a fixed point). Whilst it is commonly thought that Folk Theorems are endemic in dynami...

We investigate the stability of an SIR epidemic model with stage structure and time delay. By analyzing the eigenvalues of the corresponding characteristic equation, the local stability of each feasible equilibrium of the model is established. By using comparison arguments, it is proved when the basic reproduction number is less than unity, the disease free equilibrium is globally asymptoticall...

A new SEIR model with distributed infinite delay is derived when the infectivity depends on the age of infection. The basic reproduction number R0, which is a threshold quantity for the stability of equilibria, is calculated. If R0 < 1, then the disease-free equilibrium is globally asymptotically stable and this is the only equilibrium. On the contrary, if R0 > 1, then an endemic equilibrium ap...

An SEIR model with vaccination strategy that incorporates distinct incidence rates for the exposed and the infected populations is studied. By means of Lyapunov function and LaSalle's invariant set theorem, we proved the global asymptotical stable results of the disease-free equilibrium. The sufficient conditions for the global stability of the endemic equilibrium are obtained using the compoun...

We study the SIR epidemic model with varying total population size and constant immigration rate. We derive the sufficient conditions on parameters of the system to guarantee that the equilibrium points of the system are locally asymptotically stable or globally asymptotically stable. If the disease-free equilibrium point is stable, then the disease will not affect the population in the system....

In this paper, an SIR epidemic model involving information-related vaccination, non-linear incidence rate and the information variable is studied. We get a critical value 0  . When 1 < ) (1 0 0  p  , the disease-free Equilibrium is stable, on the contrary, if 1 > ) (1 0 0  p  , the disease-free equilibrium is unstable and an endemic equilibrium appears. We study the local stability and glo...