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

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.


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
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