Stochastic modeling and optimal intervention of COVID-19 considering human mobility and vaccination

While COVID-19 is currently at the post-pandemic phase, it provides the backdrop to prepare for the next novel virus in the future by understanding its epidemiological characteristics and developing its containment strategies. Validity of deterministic COVID-19 models remains a critical issue because of uncertainties in key epidemiological parameters. Considering the randomness of human mobility and behavior, this paper presents a stochastic SVEIRDS model for COVID-19 and develops intervention strategies for its suppression. For control or intervention methods, we consider a) social contact mitigation and suppression, b) mass vaccination, and c) the use of novel treatment modalities for hospitalized patients. We present two sets of results: first, assuming that control efforts are constant, we determine conditions for disease-free equilibrium. Then, assuming that control parameters are time-varying functions, we consider the intervention problem as a dynamic optimization problem for minimization of infections and fatalities at minimum cost. Numerical results show that with optimal levels of social contact mitigation and mass vaccination, the number of infections and fatalities can be significantly reduced. While the emergence of a deadly novel virus cannot be predicted, scientists and government regulators can use the proposed methodology for developing the first level of defense against the virus.