Work

Propagation dynamics in an SIRS model with general incidence functions

Year: 2023

Type: article

Abstract: This paper studies the initial value problems and traveling wave solutions in an SIRS model with general incidence functions. Linearizing the infected equation at the disease free steady state, we can define a threshold if the corresponding basic reproduction ratio in kinetic system is larger than the unit. When the initial condition for the infected is compactly supported, we prove that the threshold is the spreading speed for three unknown functions. At the same time, this threshold is the minimal wave speed for traveling wave solutions modeling the disease spreading process. If the corresponding basic reproduction ratio in kinetic system is smaller than the unit, then we confirm the extinction of the infected and the nonexistence of nonconstant traveling waves.

Source: Mathematical Biosciences & Engineering

DOI: 10.3934/mbe.2023291

Authors: Wenhao Chen, Guo Lin, Shuxia Pan

Institutions: Lanzhou University, Lanzhou University of Technology

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

SDG: Good health and well-being

Open Access status: gold

Estimated APC paid: $1,000