2019/11/06 by Shanshan Chen, Chen, Shanshan, Junping Shi +5 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #37N25 #92D30 #92D40 #COVID-19 epidemiological studies #Dynamical Systems (math.DS) #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.1911.02219
openalex publication_date 2019/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The dynamics of an SIS epidemic patch model with asymmetric connectivity matrix is analyzed. It is shown that the basic reproduction number R0 is strictly decreasing with respect to the dispersal rate of the infected individuals, and the model has a unique endemic equilibrium if R0>1. The asymptotic profiles of the endemic equilibrium for small dispersal rates are characterized. In particular, it is shown that the endemic equilibrium converges to a limiting disease-free equilibrium as the dispersal rate of susceptible individuals tends to zero, and the limiting disease-free equilibrium has a positive number of susceptible individuals on each low-risk patch. Moreover a sufficient and necessary condition is found to guarantee that the limiting disease-free equilibrium has no positive number of susceptible individuals on each high-risk patch. Our results extend earlier results for symmetric connectivity matrix, and we also partially solve an open problem by Allen et al. (SIAM J. Appl. Math., 67: 1283-1309, 2007).