Discrete stochastic metapopulation model with arbitrarily distributed infectious period

作者：Hernandez Ceron Nancy^*; Chavez Casillas Jonathan A; Feng Zhilan

来源：Mathematical Biosciences, 2015, 261: 74-82.

DOI：10.1016/j.mbs.2014.12.003

• SIR epidemic model
• Probability of minor and major epidemic
• Basic reproduction number
• Arbitrarily distributed infectious period

In this study, a stochastic discrete-time model is developed to study the spread of an infectious disease in an n-patch environment. The model includes an arbitrary distribution of the (random) infectious period T, and the results are used to investigate how the distribution of T may influence the model outcomes. General results are applied to specific distributions including Geometric, Negative Binomial, Poisson and Uniform. The model outcomes are contrasted both numerically and analytically by comparing the corresponding basic reproduction numbers R-0 and probability of a minor epidemic (or probability of disease extinction) P-0. It is shown analytically that for n = 2 the reproduction numbers corresponding to different distributions of T can be ordered based on the probability generating function phi(T) of T. In addition, numerical simulations are carried out to examine the final epidemic size F and duration of the epidemic D of a two-patch model.

• 出版日期2015-3