In this paper, we present a new result that allows for studying the global stability of disease-free equilibrium point when basic reproduction number is less than 1, in fractional calculus context. The method only involves linear algebra and can be easily applied to study asymptotic stability. After proving some auxiliary lemmas involving Mittag–Leffler function, main paper. Under assumptions, ...

This paper considers a non-linear mathematical model for HIV epidemic that spreads in a variable size population through both horizontal and vertical transmission. The equilibrium points of the model system are found and their stability is investigated. The model exhibits two equilibria namely, the disease-free and the endemic equilibrium. It is found that if the basic reproduction number R0 < ...

Various mathematical models have been developed to describe the transmission of malaria disease. The purpose this study was modify an existing model disease by using a CTMC stochastic model. investigation focused on transition probability, basic reproduction number (R0), outbreak expected time required reach disease-free equilibrium, and quasi-stationary probability distribution. population sys...

A discrete-time susceptible and infected (SI) epidemic model, with less than 100% vertical disease transmission, for the spread of a fungal disease in a structured amphibian host population, is analysed. Criteria for persistence of the population as well as the disease are established. Stability results for host extinction and for the disease-free equilibrium are presented. Bifurcation theory i...

In this paper, with the assumptions that an infectious disease in a population has a fixed latent period and the latent individuals of the population may disperse, we formulate an SIR model with a simple demographic structure for the population living in an n-patch environment (cities, towns, or countries, etc.). The model is given by a system of delay differential equations with a fixed delay ...

This paper is concerned with global analysis of a delay SVEIR epidemiological model in a population of varying size. By using Lyapunov stability method and LaSalle’s invariance principle for delay systems, we prove that when there is no endemic equilibrium, the disease free equilibrium is globally asymptotically stable, otherwise the endemic equilibrium is globally stable.

We have proposed an unprecedented deterministic model of Lassa Hemorrhagic fever (LHF) with nonlinear force LHF infection to capture the transmission dynamics and long-term effects disease. The Qualitative analyses we conveyed on this using well-established methods viz: Cauchy's differential theorem, Birkhoff & Rota's theorems verify reveal well-posedness respectively. established that LHF-free...

We study an S-I type epidemic model in an age-structured population, with mortality due to the disease. A threshold quantity is found that controls the stability of the disease-free equilibrium and guarantees the existence of an endemic equilibrium. We obtain conditions on the age-dependence of the susceptibility to infection that imply the uniqueness of the endemic equilibrium. An example with...

A SIR epidemic model with delay, saturated contact rate and vertical transmission is considered. The basic reproduction number 0 R is calculated. It is shown that this number characterizes the disease transmission dynamics: if 0 1 R , there only exists the disease-free equilibrium which is globally asymptotically stable; if 0 1 R , there is a unique endemic equilibrium and the disease persists,...

The dynamics of many epidemic models for infectious diseases that spread in a single host population demonstrate a threshold phenomenon If the basic reproduction number R is below unity the disease free equilibrium P is globally stable in the feasible region and the disease always dies out If R a unique endemic equilibrium P is globally asymptotically stable in the interior of the feasible regi...