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On a partially observed illness-death model. (English) Zbl 1006.62090

Summary: A biological population with \(N\) individuals assumed to be healthy is monitored over time. A portion of these individuals die from natural causes while other may get infected with a disease and become sick. A number of the sick individuals will then die from natural causes and other may die from the disease. A stochastic model for the various transitions ‘healthy, sick, death’, is studied where it is assumed that the only observed states are deaths. Based on this information, optimal filters for the number of individuals in each state are derived.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
92C60 Medical epidemiology
62M20 Inference from stochastic processes and prediction
93E11 Filtering in stochastic control theory
60G35 Signal detection and filtering (aspects of stochastic processes)
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