Tilahun Getachew Teshome, Demie Seleshi, Eyob Alemayehu
Haramaya University, Department of Mathematics, Haramaya, Ethiopia.
Infect Dis Model. 2020 Jul 3;5:478-494. doi: 10.1016/j.idm.2020.06.003. eCollection 2020.
In this paper we developed a stochastic model of measles transmission dynamics with double dose vaccination. The total population in this model was sub-divided in to five compartments, namely Susceptible , Infected Vaccinated first dose Vaccinated second dose and Recovered First the model was developed by deterministic approach and then transformed into stochastic one, which is known to play a significant role by providing additional degree of realism compared to the deterministic approach. The analysis of the model was done in both approaches. The qualitative behavior of the model, like conditions for positivity of solutions, invariant region of the solution, the existence of equilibrium points of the model and their stability, and also sensitivity analysis of the model were analyzed. We showed that in both deterministic and stochastic cases if the basic reproduction number is less than 1 or greater than 1 the disease free equilibrium point is stable or unstable respectively, so that the disease dies out or persists within the population. Numerical simulations were carried out using MATLAB to support our analytical solutions. These simulations show that how double dose vaccination affect the dynamics of human population.
在本文中，我们建立了一个带有双剂量疫苗接种的麻疹传播动力学随机模型。该模型中的总人口被细分为五个部分，即易感人群（Susceptible）、感染人群（Infected）、接种第一剂疫苗人群（Vaccinated first dose）、接种第二剂疫苗人群（Vaccinated second dose）和康复人群（Recovered）。首先通过确定性方法建立模型，然后将其转化为随机模型，众所周知，与确定性方法相比，随机模型通过提供额外的现实程度发挥着重要作用。对该模型在两种方法下都进行了分析。分析了模型的定性行为，如解的正性条件、解的不变区域、模型平衡点的存在性及其稳定性，以及模型的敏感性分析。我们表明，在确定性和随机两种情况下，如果基本再生数小于1或大于1，无病平衡点分别是稳定的或不稳定的，从而疾病在人群中消失或持续存在。使用MATLAB进行了数值模拟以支持我们的解析解。这些模拟表明了双剂量疫苗接种如何影响人群动态。
