A class of global Lyapunov functions is revisited and used to resolve a long-standing open problem on the uniqueness and global stability of the endemic equilibrium of a class of multi-group models in mathematical epidemiology. We show how the group structure of the models, as manifested in the derivatives of the Lyapunov function, can be completely described using graph theory.

An SEI model with distributed delay is proposed where the transmission and the death rates depend on the age of infection. The basic reproduction number R0 is identified as a threshold quantity for the stability of equilibria. If R0 < 1, then the disease-free equilibrium is globally asymptotically stable and the disease dies out. On the contrary, ifR0 > 1, then a locally asymptotically stable e...

ABSTRACT. For a class of multigroup SIR epidemic models with varying subpopulation sizes, we establish that the global dynamics are completely determined by the basic reproduction number R0. More specifically, we prove that, if R0 ≤ 1, then the disease-free equilibrium is globally asymptotically stable; if R0 > 1, then there exists a unique endemic equilibrium and it is globally asymptotically ...

In this paper we propose an age-structured malaria within-host model taking into account multi-strains interaction. We provide a global analysis of the model depending upon some threshold T0. When T0 ≤ 1, then the disease free equilibrium is globally asymptotically stable and the parasites are cleared. On the contrary if T0 > 1, the model exhibits the competition exclusion principle. Roughly sp...

We study a model of disease transmission with continuous age-structure for latently infected individuals and for infectious individuals. The model is very appropriate for tuberculosis. Key theorems, including asymptotic smoothness and uniform persistence, are proven by reformulating the system as a system of Volterra integral equations. The basic reproduction number R0 is calculated. For R0 < 1...

An SIS/SAS model of gonorrhea transmission in a men-seeking-men (MSM) system is presented in this paper to study the impact of education on the dynamics of gonorrhea prevalence. Education affects behaviors that may fall into two categories– prevention and disease status awareness. Stability conditions for the disease free equilibrium and endemic equilibrium are determined along with an analytic...

To curb the impact and transmission of worms and virus for simple mass action incidence rate in computer networks, SI1I2RS (Susceptible, Infectious due to worm, Infectious due to virus, Recovered and Susceptible) model have been formed. Basic reproduction number, endemic equilibrium state and their stability are discussed for the simple mass action incidence. For locally and globally asymptotic...