报告题目：Construction of positivity preserving numerical method for stochastic SIVS epidemic model

报告时间：2019年01月06日  8:00-10:00

报告地点：数学与统计学院金融实验室

报告人：宁夏大学  张启敏教授

报告摘要：We propose the balanced implicit numerical techniques for maintaining the nonnegative path of the solution in stochastic susceptible-infected-vaccinated-susceptible (SIVS) epidemic model. We can hardly acquire the explicit solution for the SIVS model, so we often use the numerical scheme to produce approximate solutions. The Euler-Maruyama (EM) method is a useful and effective means in product numerical solutions of SIVS model. The EM method to simulate the stochastic SIVS model often result in the problem that the numerical solution is not positive. In order to eliminate the negative path of the solution in stochastic SIVS epidemic model, we construct a numerical method preserving positivity for the SIVS model. It is proved that the balanced implicit method (BIM) can preserve positivity and show the convergence of the BIM numerical approximate solution to the exact solution. Finally, a numerical example is carried out to support the theoretical result and verify the availability of the approach.