Immunity boosted by low level of exposure to infection in an SIRS model

The development of immunity in the susceptible class by a continuous low level of infection is a commonly observed phenomenon in many infectious diseases. This important feature has been incorporated in an SIRS epidemiological model with both the rates of incidence and increase of immunity being nonlinear in nature, instead of being bilinear, of the form β1IpS and β2Ip′S (0 < p′ < p, p ≠ 1 and p′ ≠ 1) respectively. The local and global behaviour of the dynamics of the model have been investigated.