Population models for diseases with no recovery. (English) Zbl 0727.92023

Pugliese, A.

J. Math. Biol. 28, No. 1, 65-82 (1990).

In numerous papers in mathematical epidemiology it is assumed that the rate at which new individuals become infected (individuals belonging to a population of N elements) is proportional to the number of susceptibles, S, times the contact rate c(N), times the probability of encountering infectious individuals. Usually the contact rate under consideration is linear. In this paper an epidemic model is described in which c(N)/N (denoted by \(\sigma\) (N)) is assumed to be a nonincreasing function while c(N) is a nondecreasing function. The asymptotic behaviour is examined, and also the effect of vaccination is thoroughly studied.

Reviewer: U.Wilczyńska (Łódź)

MSC:

92D30

Epidemiology

Keywords:

general shape of density-dependent mortality; asymptotic behaviour; global convergence; endemic equilibrium; disease-free equilibrium; threshold; nonlinear incidence rate; population regulation; susceptibles; contact rate; epidemic model; effect of vaccination