We consider models for the spread of infectious diseases which include nonlinear population dynamics, contact rates which depend on total population size, and variable infective periods. We show that there is a single asymptotically stable equilibrium for diseases with recovery either with no immunity or with full immunity. This equilibrium is the disease-free equilibrium if the contact number is less than one and an endemic equilibrium if the contact number exceeds one.
|Number of pages
|Differential and Integral Equations
|Published - Jan 1990
ASJC Scopus subject areas
- Applied Mathematics