Construction of positivity-preserving numerical method for stochastic SIVS epidemic model

Abstract

In this paper 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 producing numerical solutions of SIVS model. The EM method to simulate the stochastic SIVS model often results in the problem that the numerical solution is not positive. In order to eliminate the negative path of the solution in a 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 we show the convergence of the BIM numerical approximate solution to the exact solution. Finally, a numerical example is offered to support the theoretical results and verify the availability of the approach.

Measures to assess a warning vaccination level in a stochastic SIV model with imperfect vaccine

“…Some of them introduce vaccination as a control or strategy on a selected model [14][15][16] but most of the studies rely on models including additional compartments for vaccinated individuals. [17][18][19][20] Models are flexible enough to match vaccine characteristics, such as efficacy, 21,22 life-long or waning protection, 23,24 eligibility, 25 number of doses, 26 vaccine uptake, 27 and so forth.…”