Optimal intervention and vaccination strategies for the COVID-19 pandemic under limited immunity

Abstract

The COVID-19 pandemic had a tremendous socio-economic effect throughout the world. Governments around the world aimed to mitigate its rapid spread and limit the number of diseases by implementing intervention policies, such as social distancing, closing schools, encouraging working from home and imposing lock-downs. Such strict government measures, although limiting the disease spread, cause significant socio-economic costs. The development of vaccines during the pandemic offered an additional tool to mitigate its impact by offering immunity to the population. However, it was seen that the immunity for vaccinated and recovered population was temporal and had a declining effect with time. Considering the above, this thesis aims to study the progression of the pandemic and propose suitable intervention and vaccination strategies. In addition, it aims to study the impact of the declining immunity in the population. In particular, we consider a compartment LI-SIDAREV model, with Susceptible (S), Infected Undetected (I), Infected Detected (D), Acutely symptomatic (A), Recovered (R), Extinct (E), and vaccinated (V) states. The LI-SIDAREV model is modified to enable the transition of the population from the vaccinated and recovered states towards the susceptible state, in order to model the declining effect of immunity. An optimal control problem is formulated that aims to obtain the government intervention and vaccination strategies that optimize the trade-off between the socio-economic costs from imposing such policies and the number of deceases. The optimal strategies were obtained by applying Pontryagin’s minimum principal in the considered problem. A large number of case studies has been considered to investigate the effect of the costs associated with the deceased and acutely symptomatic population on the optimal government strategies. Moreover, the effect of the declining immunity for the vaccinated and the recovered population is studied over different time periods (one and three years respectively). Our results demonstrate that the effect of the declining immunity is significant in terms of the number of diseases and required intervention strategies. In addition, when a larger time duration was considered, the optimal intervention strategies demonstrated a fluctuating behaviour similar to what observed in practice. Furthermore, the increased time duration resulted in increased deceases and cost associated with intervention measures but a decreased optimal vaccination rate. We envision that our results will find practical applications in designing effective and efficient intervention strategies and motivate further research on the topic.