Stability and bifurcations in a discrete-time epidemic model with vaccination and vital dynamics

BMC Bioinformatics
Mahmood ParsamaneshSaeed Mehrshad

Abstract

The spread of infectious diseases is so important that changes the demography of the population. Therefore, prevention and intervention measures are essential to control and eliminate the disease. Among the drug and non-drug interventions, vaccination is a powerful strategy to preserve the population from infection. Mathematical models are useful to study the behavior of an infection when it enters a population and to investigate under which conditions it will be wiped out or continued. A discrete-time SIS epidemic model is introduced that includes a vaccination program. Some basic properties of this model are obtained; such as the equilibria and the basic reproduction number [Formula: see text]. Then the stability of the equilibria is given in terms of [Formula: see text], and the bifurcations of the model are studied. By applying the forward Euler method on the continuous version of the model, a discretized model is obtained and analyzed. It is proven that the disease-free equilibrium and endemic equilibrium are stable if [Formula: see text] and [Formula: see text], respectively. Also, the disease-free equilibrium is globally stable when [Formula: see text]. The system has a transcritical bifurcation when [Formula: see text] ...Continue Reading

References

Nov 1, 1994·Mathematical Biosciences·L J Allen
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Jan 1, 2006·Mathematical Biosciences and Engineering : MBE·Fred Brauer
Apr 14, 2018·Bulletin of Mathematical Biology·P van den Driessche, Abdul-Aziz Yakubu
Jan 1, 2013·Advances in Difference Equations·Xia MaHui Cao

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