Nonzero Solutions of Nonlinear Integral Equations Modeling Infectious Disease

Abstract

Sufficient conditions to insure the existence of periodic solutions to the nonlinear integral equation, $x(t) = \int_{t - \tau }^t {f(s,x(s))ds} $, are given in terms of simple product and product integral inequalities. The equation can be interpreted as a model for the spread of infectious diseases (e.g., gonorrhea or any of the rhinovirus viruses) if $x(t)$ is the proportion of infectives at time t and $f(t,x(t))$ is the proportion of new infectives per unit time.