The final epidemic size (R∞) remains one of the fundamental outcomes of an epidemic, and
measures the total number of individuals infected during a “free-fall” epidemic when no …

In this paper, we propose and analyze an epidemic problem which can be controlled by
vaccination as well as treatment. In the first part of our analysis we study the dynamical …

HIV/AIDS model for sexual transmission with explicit incubation period is proposed as a
system of discrete time delay differential equations. The threshold and equilibrium for the …

In this paper, we describe the dynamics of an SEIR epidemic model with saturated
incidence, treatment function, and optimal control. Rigorous mathematical results have been …

BACKGROUND: Mathematical models of disease transmission and vaccination typically
assume that protective vaccine efficacy (ie the relative reduction in the transmission rate …

This paper describes a traditional SIR type epidemic model with saturated infection rate and
treatment function. The dynamics of the model is studied from the point of view of stability …

The control of some childhood diseases has proved to be difficult even in countries that
maintain high vaccination coverage. This may be due to the use of imperfect vaccines, and …

Anti-retroviral treatments (ART) such as HAART have been used to control the replication of
HIV virus in HIV-positive patients. In this paper, we study an in-host model of HIV infection …

This paper aims to improve the analysis of a stochastic SIVR epidemic model with an
imperfect vaccination process, taking into consideration the fact that a fraction of vaccinated …

An epidemic model with distributed time delay is derived to describe the dynamics of
infectious diseases with varying immunity. It is shown that solutions are always positive, and …