Complex dynamics in an SIS epidemic model induced by nonlinear incidence

Ruixia Yuan; Zhidong Teng; Jinhui Li

see Fig. 1 (a), which can describe the effects of psychology function caused by protection measures and intervention policies. Obviously, g 1 (I) is increasing with small I and decreasing with large I, that is, g 1 (I) is non-monotone. The function g 1 (I) can be used to interpret the psychological effect: for a very large number of infective individuals, the infection force may decrease as the number of infective individuals increases, since large number of infective may lead to the reducing of the number of contacts per unit time. For example, in 2003, epidemic outbreak of severe acute respiratory syndrome (SARS) had such psychological effects on the general public (see [11] ), and aggressive measures and policies had been taken, such as border screening, mask wearing, quarantine, isolation, etc. And also [11] showed that either the number of infective individuals tends to zero as time evolves or the disease persists. Furthermore, Li, Zhao and Zhu (see [20] ) studied the following SIS model, which describes behavior change effect of susceptible individual when infectious population increases dS dt = Λ − d 0 S − g 2 (I)S + δI, dI dt = g 2 (I)S − (d 0 + d + δ)I,