Multiple-stage non-homogeneous Markov models for the acquired immune deficiency syndrome epidemic. (English) Zbl 0801.92020
Summary: Numerous particular models have been introduced in recent years to explain various specific aspects of the underlying mechanism associated with the spread of the acquired immune deficiency syndrome (AIDS) epidemic. Many of these modes can be classified as compartmental models.
We establish the mathematical framework and provide solutions for the class of compartmental stochastic models for which the transition probabilities between stages of the model are both time and state dependent. We obtain expressions for the state probabilities, and for the mean and variance of the number of AIDS cases as a function of time. To illustrate the theoretical results we compare a four- and five-stage model with the actual number of reported AIDS cases for several populations.
We establish the mathematical framework and provide solutions for the class of compartmental stochastic models for which the transition probabilities between stages of the model are both time and state dependent. We obtain expressions for the state probabilities, and for the mean and variance of the number of AIDS cases as a function of time. To illustrate the theoretical results we compare a four- and five-stage model with the actual number of reported AIDS cases for several populations.
MSC:
| 92D30 | Epidemiology |
| 60J20 | Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 60J99 | Markov processes |
