Abstract
In this paper, we study the qualitative behavior of a discrete-time host-pathogen model for spread of an infectious disease with permanent immunity. The time-step is equal to the duration of the infectious phase. Moreover, the local asymptotic stability, the global behavior of unique positive equilibrium point, and the rate of convergence of positive solutions is discussed. Some numerical examples are given to verify our theoretical results.MSC:39A10, 40A05.
Highlights
It is a well-known fact that in the population growth, the disease is an important agent controlling the population dynamics
Conclusion and future work This work is related to the qualitative behavior of an exponential discrete-time hostpathogen model for spread of an infectious disease with permanent immunity
We proved that system ( ) has a unique positive equilibrium point, which is locally asymptotically stable
Summary
It is a well-known fact that in the population growth, the disease is an important agent controlling the population dynamics. The transfer continues until all individuals become infected This type of model is very simple, but may represent some complicated dynamical properties. Most of the SI type models consist of the mass action principle, i.e., the assumption that the new cases arise in a simple proportion to the product of the number of individuals which are susceptible and the number of which are infectious. This principle has a limited validity and in the discrete models, this principle leads to biologically irrelevant results, unless some restrictions are suggested for the parameters.
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