A modification of the general stochastic epidemic motivated by AIDS modelling. (English) Zbl 0777.92018

Ball, Frank; O’Neill, Philip

Adv. Appl. Probab. 25, No. 1, 39-62 (1993).

The authors consider both deterministic and stochastic versions of a closed and homogeneously mixing epidemic model. New infections occur at rate \(\beta xy/(x+y)\), where \(x\) and \(y\) are the numbers of susceptible and infectious individuals, respectively, and \(\beta\) is an infection parameter. The general deterministic epidemic admits a complete closed- form solution. Deriving the temporal solution of the stochastic version, the authors examine the total size distribution and threshold theorems. The effect of introducing varying susceptibles to the disease into the model is considered.

Reviewer: P.R.Parthasarathy (Madras)

MSC:

92D30	Epidemiology
60J20	Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
60J27	Continuous-time Markov processes on discrete state spaces

Keywords:

AIDS modelling; size of epidemic; stochastic models; time-dependent solution; embedded random walks; closed and homogeneously mixing epidemic model; general deterministic epidemic; complete closed-form solution; total size distribution; threshold theorems; varying susceptibles