Abstract
This paper is concerned with the stability of an age-structured susceptible–exposed– infective–recovered–susceptible (SEIRS) model with time delay. Firstly, the traveling wave solution of system can be obtained by using the method of characteristic. The existence and uniqueness of the continuous traveling wave solution is investigated under some hypotheses. Moreover, the age-structured SEIRS system is reduced to the nonlinear autonomous system of delay ODE using some insignificant simplifications. It is studied that the dimensionless indexes for the existence of one disease-free equilibrium point and one endemic equilibrium point of the model. Furthermore, the local stability for the disease-free equilibrium point and the endemic equilibrium point of the infection-induced disease model is established. Finally, some numerical simulations were carried out to illustrate our theoretical results.
Highlights
In recent years, the study of epidemiology has been a vital problem in ecology
The main aim of this paper is to study the stability of an age-structured susceptible–exposed– infective–recovered–susceptible (SEIRS) model with time delay
We can obtain the existence and uniqueness of the continuous traveling wave solution of system according to hypotheses
Summary
The study of epidemiology has been a vital problem in ecology. The research of population dynamics has developed rapidly, and many mathematical models have been used to analyze various infectious diseases. Models [3,4,5,6,7] It is well known, in the spread of infectious diseases, some infective individuals of population are immune after being recovered (e.g., measles, smallpox, mumps, and others). De la Sena [13] discussed the stability of the SEIR epidemic models with distributed delay respectively. As far as we can tell, there have been no results on an age-structured SEIRS model with time delay. The main aim of this paper is to study the stability of an age-structured SEIRS model with time delay. The existence and uniqueness of the continuous traveling wave solution of the age-structured SEIRS model is investigated.
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