Periodic solutions in a seasonally forced epidemic model

2013/09/14 by Bai, Zhenguo, Zhou, Yicang
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1309.3666

Abstract

We study an SIR epidemic model with a seasonal contact rate and saturated treatment function. It is shown that the basic reproduction number (\mathcal R₀) cannot be acted as a threshold that predicts the spread of an infection. Based on this finding, we establish a set of sufficient conditions for the existence of multiple positive periodic solutions by using Gaines-Mawhin's continuation theorem. This is very similar to backward bifurcation for an autonomous model. Further, we investigate the stability of positive periodic solution under small seasonal perturbation by means of Floquet theory. Numerical simulations support our theoretical analysis.

Related

• Dynamics of epidemic models with asymptomatic infection and seasonal succession
• Periodic orbits for periodic eco-epidemiological systems with infected prey
• Multistability and chaos in SEIRS epidemic model with a periodic time-dependent transmission rate
• Pulse vaccination in a SIR model: global dynamics, bifurcations and seasonality
• Global dynamics of a periodic SEIRS model with general incidence rate