Kirupaharan Nadarajah, Allen Linda J S
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA.
Bull Math Biol. 2004 Jul;66(4):841-64. doi: 10.1016/j.bulm.2003.11.007.
Stochastic differential equations that model an SIS epidemic with multiple pathogen strains are derived from a system of ordinary differential equations. The stochastic model assumes there is demographic variability. The dynamics of the deterministic model are summarized. Then the dynamics of the stochastic model are compared to the deterministic model. In the deterministic model, there can be either disease extinction, competitive exclusion, where only one strain persists, or coexistence, where more than one strain persists. In the stochastic model, all strains are eventually eliminated because the disease-free state is an absorbing state. However, if the population size and the initial number of infected individuals are sufficiently large, it may take a long time until all strains are eliminated. Numerical simulations of the stochastic model show that coexistence cases predicted by the deterministic model are an unlikely occurrence in the stochastic model even for short time periods. In the stochastic model, either disease extinction or competitive exclusion occur. The initial number of infected individuals, the basic reproduction numbers, and other epidemiological parameters are important determinants of the dominant strain in the stochastic epidemic model.
用于对具有多种病原体菌株的SIS流行病进行建模的随机微分方程是从常微分方程组推导出来的。该随机模型假定存在人口统计学变异性。总结了确定性模型的动态。然后将随机模型的动态与确定性模型进行比较。在确定性模型中，可能出现疾病灭绝、竞争排斥（即只有一种菌株持续存在）或共存（即不止一种菌株持续存在）的情况。在随机模型中，所有菌株最终都会被消除，因为无病状态是一个吸收态。然而，如果种群规模和初始感染个体数量足够大，可能需要很长时间所有菌株才会被消除。随机模型的数值模拟表明，即使在短时间内，确定性模型预测的共存情况在随机模型中也不太可能发生。在随机模型中，要么发生疾病灭绝，要么发生竞争排斥。初始感染个体数量、基本再生数和其他流行病学参数是随机流行病模型中优势菌株的重要决定因素。
