Communications in Information and Systems

Volume 23 (2023)

Number 3

Special issue dedicated Professor Avner Friedman in celebration of his 90th birthday

Guest Editors: Jong-Shenq Guo, Bei Hu, Robert Jensen, and Stephen S.-T. Yau

Exploring the evolutionary dynamics of infectious diseases through SIS epidemic models

Pages: 289 – 324



King-Yeung Lam (Department of Mathematics, Ohio State University, Columbus, Oh., U.S.A.)

Yuan Lou (School of Mathematical Sciences, CMA-Shanghai, Shanghai Jiao Tong University, Shanghai, China)

Shizhao Ma (Institute for Mathematical Sciences, Renmin University of China, Beijing, China)


To study the evolution and interaction among multiple strains of a given infectious disease, we incorporate phenotypic structure into Susceptible-Infected-Susceptible (SIS) epidemic models of the reaction-diffusion type. It is shown that the unique disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less than one, and the infected population persists when the basic reproduction number is greater than one. In the latter case, the asymptotic profile of the endemic equilibrium is determined when the mutation rate of the infected population converges to zero. We integrate analytical results with numerical simulations of the proposed model to investigate how multiple phenotypic traits evolve. Our findings confirm that the susceptible population evolves to be primarily made up of individuals with low immunity, while the infected population is eventually comprised of highly infectious individuals with low mutation rate. These results indicate that as the disease infectivity continues to increase, the group immunity will decrease. In addition, if the virus mutation rate is initially small, it will first increase rapidly before eventually decreasing. Finally, those strains with low mutation rates are more advantageous in the long run, i.e. the virus might first employ the high mutation rate to increase infectivity rapidly, and then use the low mutation rate to maintain its advantageous position of high infectivity.

This work is partially supported by NSF grant DMS-1853561 and DMS-2325195 (KYL), NSFC grants No. 12250710674, 12261160366 (YL), NSFC grant No. 12071476, 12171478 (SZM).

Received 26 January 2023

Published 12 October 2023