A NOVEL MATHEMATICAL MODEL FOR VACCINE ALLOCATION CONSIDERING GOVERNMENTAL HEALTH POLICIES AND SEIR EPIDEMIC MODEL

Spread of infectious disease forces the nations to cope with the eects of disease using dierent protocols. Vaccination is an eective tool to immunize the individuals against the epidemic. In the case of limited resources of vaccine doses, there should be an appropriate plan to allocate the vaccine properly. During the Covid-19 epidemic, the vaccination was based on age groups while the other protocols like the lockdown policy was implemented which resulted in shop closures. It should be considered that implementing lockdown policies and consequently shop closing result in dierent economic and psychological impacts. Therefore, a new strategy should be designed to cope with such impacts in the similar cases. In this paper, we propose a new strategy, i.e. parallel vaccination, to minimize the social cost of infected individuals as well as economic impact of lockdown policy using SEIR epidemic model. To do so, we consider retailers and shopkeepers as a priority group in addition to the age group. We develop a bi-objective mathematical model to minimize the social cost of infected individuals and economic impact of implementing the lockdown policy. Also, dierential equations of SEIR epidemic model are considered as the constraints of the model to re ect on the dynamicity of the infectious disease. Finally, we determine the required doses of vaccine that should be allocated to each priority group in order to control the epidemic using optimal control theory. An illustrative example inspired by a real case is presented to evaluate the model's performance, and its numerical result is discussed. The results show that applying the new strategy for vaccine allocation leads to reduction in the social cost of infected people and economic impact of lockdown policy simultaneously. Therefore, the policymakers should consider such strategies to control the outbreak of epidemic diseases as well as their side eects like economic and psychological eects.