Optimal Vaccination Strategy under Saturated Treatment using the Stochastic SIR Model

Abstract

This paper is concerned with the control strategy by vaccination of the infectious disease spread in the populations consisting of the susceptible, the infected and the recovered (SIR). In the realistic spread of the infectious disease, changes in the environment and the weather cause some kinds of random fluctuations in the infection and the recovery rates, etc. Moreover, medical facilities have generally the maximal capacity for treatment of diseases. Taking these facts into consideration, we propose the stochastic infectious model with vaccination and saturated treatment, and we consider the stochastic optimal vaccination problem for the SIR model with saturated treatment using the stochastic maximum principle and the four-step scheme. We construct a feasible optimal vaccination system. By numerical simulations, we validate the efficacy of the optimal vaccination strategy.

Research on British epidemic forecastBased on SIR model

“…COVID-19 is a global disaster, taking away millions of lives, destroying every country's economy, and smashing many human cultures. Vaccines are the most important solution to controling the spread of this infectious disease [1,2]. On July 5, the British government announced that due to the large-scale vaccination, all restrictions would be lifted on July 19 [3].…”

Epidemic Waves in a Stochastic SIRVI Epidemic Model Incorporating the Ornstein–Uhlenbeck Process

“…Vaccination programs may help control the transmission of many diseases [9]; hence, the term vaccination must be included in epidemic modeling. The susceptible-infected-recovered-vaccination (SIRV) model in [10][11][12][13] and the susceptibleinfected-recovered-vaccination-death (SIRVD) model [14] study the effect of vaccination on disease transmission worldwide. Omae et al studied the effect of first and second doses of vaccination on the transmission of COVID-19 [15]; they proposed the SIRVVD model and concluded that appropriate vaccination measures would sufficiently reduce the number of infected individuals and reduce the mortality rate.…”