1 Research Work
Preventing the rapid spread of an infectious disease without available immunity poses a significant challenge. Non-pharmaceutical interventions, such as lockdowns and travel bans, are often the initial defence when medical treatments or vaccinations are lacking. However, these measures can cause severe economic and social disruptions. As a result, intervention policies must be carefully designed to achieve optimal control of the pandemic while minimizing risks and considering social and economic aspects. Timing is crucial when it comes to implementing control policies for infectious diseases. Simply initiating controls at the earliest stage may not yield the best results. Instead, by strategically considering the timing, we can achieve a balance between control effectiveness and cost efficiency. The momentum effect indicates that implementing control policies closer to the herd immunity threshold can effectively curb the spread of infections. As a result, the total number of infected individuals is more likely to approach the herd immunity threshold. We utilize mathematical models like SIR and SIRV to simulate the spread of a pandemic. By formulating an objective cost that considers factors such as lockdown implementation, hospitalization expenses, and vaccination costs, we employ Pontryagin’s principle to determine an optimal control strategy. The numerical analysis highlights the effectiveness of implementing restrictions closer to the peak of infection spread to minimize active cases and prevent healthcare overload. Moreover, incorporating the SIRV model with vaccinations and mobility controls demonstrates the crucial role of vaccinations in controlling the virus.