Abstract

This study investigates long-time behavior of solutions of a susceptible-infectious-susceptible (SIS) epidemiological model, proposed to explain an epidemiological phenomenon that pathogen spread does not necessarily keep pace with its host invasion.

When the rate of transmission of disease is small, the infected population will vanish. When the rate is of moderate size, it is shown that a local infection of disease will spread with a speed that is smaller than that of the host population; i.e., the anomalous propagation phenomena appears. For large disease transmission rates, it is shown that the infection can keep the pace with the host invasion, provided that the host does not propagate too fast.

This study also introduces a method simplified from Hamel et al. (2012) to prove the logarithmic lag of propagating front of the infected population from that of the minimum  speed traveling wave (obtained by setting host population into its capacitance).