A problem in the theory of epidemics, II

Abstract In an earlier article the authors considered a deterministic epidemic model that accounts for certain threshold phenomena occuring in the spread of infection. The present article includes a major modification of the earlier model that allows individuals recovered from the infection to eventually become susceptible again to the infection. A set of five integral equations is derived from the basic assumptions concerning the spread of the infection. The basic theorem asserts existence, uniqueness, and continuous dependence of a solution of these equations. The proof of these results is accomplished by a contraction mapping argument that also gives a simple proof of the earlier result. A minor modification of the earlier model also is included, which brings into the scope of this study some of the older epidemic models. Some numerical computation carried out for this problem is also described.