Abstract
This paper addresses a time-delayed SIQRS model with a linear incidence rate. Immunity gained by experiencing the disease is temporary; whenever infected, the disease individuals will return to the susceptible class after a fixed period of time. First, the local and global stabilities of the infection-free equilibrium are analyzed, respectively. Second, the endemic equilibrium is formulated in terms of the incidence rate, and locally asymptotic stability. Finally we use the adomian decomposition method is applied to the system epidemiologic. This method yields an analytical solution in terms of convergent infinite power series.
Highlights
In the past, the epidemiology is restricted to the study of morbid phenomena resulting in an increase in sudden sharp and localized in space, the number of cases and time
This paper addresses a time-delayed SIQRS model with a linear incidence rate
The endemic equilibrium is formulated in terms of the incidence rate, and locally asymptotic stability
Summary
The epidemiology is restricted to the study of morbid phenomena resulting in an increase in sudden sharp and localized in space, the number of cases and time. A model contains a disease-free equilibrium and one or multiple equilibria are endemic. When endemic equilibrium is global attractor, epidemiologically, it means that the disease will prevail and persist in a population and overall stability of these models is relatively low, especially models with delays. We discuss the equilibrium and stability of the model SIQR epidemic with constant infectious period which is made of a delay time. In order to describe the effects of disease immunity temporal delays are often incorporated in such models [15-19]
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