ANALYSIS OF AN SEIRS EPIDEMIC MODEL WITH 2 DELAYS

A disease transmission model of SEIRS type with exponential demographi c structure is formulated. All newborns are assumed susceptible, there is a natural death rate constant, and an excess death rate constant f or infective individuals. Latent and immune periods are assumed to be constants, and the force of infection is assumed to be of the standard form, namely proportional to I(t)/N(t) where N(t) is the total (varia ble) population size and I(t) is the size of the infective population. The model consists of a set of integro-differential equations. Stabil ity of the disease free proportion equilibrium, and existence, uniquen ess, and stability of an endemic proportion equilibrium, are investiga ted. The stability results are stated in terms of a key threshold para meter. More detailed analyses are given for two cases, the SEIS model (with no immune period), and the SIRS model (with no latent period). S everal threshold parameters quantify the two ways that the disease can be controlled, by forcing the number or the proportion of infectives to zero.