Threshold dynamics of a time-periodic two-strain SIRS epidemic model with distributed delay

• Published in: AIMS mathematics Vol. 7; no. 4; pp. 6331 - 6355
• Main Authors: Guo, Jinsheng, Wang, Shuang-Ming
• Format: Journal Article
• Language: English
• Published: AIMS Press 2022
• Subjects: distributed delay; sirs epidemic model; spatiotemporal heterogeneity; threshold dynamics
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2022352

In this paper, a two-strain SIRS epidemic model with distributed delay and spatiotemporal heterogeneity is proposed and investigated. We first introduce the basic reproduction number $ R_0^i $ and the invasion number $ \hat{R}_0^i\; (i = 1, 2) $ for each strain $ i $. Then the threshold dynamics of the model is established in terms of $ R_0^i $ and $ \hat{R}_0^i $ by using the theory of chain transitive sets and persistence. It is shown that if $ \hat{R}_0^i > 1\; (i = 1, 2) $, then the disease in two strains is persist uniformly; if $ R_0^i > 1\geq R_0^j\; (i\neq j, i, j = 1, 2) $, then the disease in $ i $-th strain is uniformly persist, but the disease in $ j $-th strain will disappear; if $ R_0^i < 1 $ or $ R_0^i = 1\; (i = 1, 2) $ and $ \beta_i(x, t) > 0 $, then the disease in two strains will disappear.