Quantitative Pharmacology and Pharmacometrics, Merck & Co., Inc., Rahway, NJ 07065, USA.
Department of Applied Mathematics and Statistics, Montclair State University, 1 Normal Avenue, Montclair, NJ 07043, USA.
J R Soc Interface. 2022 Jul;19(192):20220253. doi: 10.1098/rsif.2022.0253. Epub 2022 Jul 6.
In this article, we take a mathematical approach to the study of population-level disease spread, performing a quantitative and qualitative investigation of an model which is a susceptible-infectious-susceptible () model with exposure to an external disease reservoir. The external reservoir is non-dynamic, and exposure from the external reservoir is assumed to be proportional to the size of the susceptible population. The full stochastic system is modelled using a master equation formalism. A constant population size assumption allows us to solve for the stationary probability distribution, which is then used to investigate the predicted disease prevalence under a variety of conditions. By using this approach, we quantify outbreak vulnerability by performing the sensitivity analysis of disease prevalence to changing population characteristics. In addition, the shape of the probability density function is used to understand where, in parameter space, there is a transition from disease free, to disease present, and to a disease endemic system state. Finally, we use Kullback-Leibler divergence to compare our semi-analytical results for the model with more complex susceptible-infectious-recovered () and susceptible-exposed-infectious-recovered () models.
在本文中，我们采用数学方法研究人群疾病传播，对一个模型进行定量和定性研究，该模型是一个具有接触外部疾病储库的易感染-感染-易感染（SIS）模型。外部储库是非动态的，并且假设来自外部储库的暴露与易感人群的大小成正比。使用主方程形式对完整的随机系统进行建模。假设人口规模不变，我们可以求解固定概率分布，然后使用该分布在各种条件下预测疾病流行率。通过这种方法，我们通过对疾病流行率对人口特征变化的敏感性分析来量化爆发脆弱性。此外，概率密度函数的形状用于理解在参数空间中，疾病从无到有，再到疾病流行系统状态的过渡点在哪里。最后，我们使用 Kullback-Leibler 散度将我们对 SIS 模型的半解析结果与更复杂的易感-感染-恢复（SIR）和易感-暴露-感染-恢复（SEIR）模型进行比较。
