Age Structured Mathematical Modeling Studies on COVID-19 with respect to Combined Vaccination and Medical Treatment Strategies

Abstract

In this study, we develop a mathematical model incorporating age-specific transmission dynamics of COVID-19 to evaluate the role of vaccination and treatment strategies in reducing the size of COVID-19 burden. Initially, we establish the positivity and boundedness of the solutions of the non controlled model and calculate the basic reproduction number and do the stability analysis. We then formulate an optimal control problem with vaccination and treatment as control variables and study the same. Pontryagin’s Minimum Principle is used to obtain the optimal vaccination and treatment rates. Optimal vaccination and treatment policies are analysed for different values of the weight constant associated with the cost of vaccination and different efficacy levels of vaccine. Findings from these suggested that the combined strategies (vaccination and treatment) worked best in minimizing the infection and disease induced mortality. In order to reduce COVID-19 infection and COVID-19 induced deaths to maximum, it was observed that optimal control strategy should be prioritized to the population with age greater than 40 years. Varying the cost of vaccination it was found that sufficient implementation of vaccines (more than 77 %) reduces the size of COVID-19 infections and number of deaths. The infection curves varying the efficacies of the vaccines against infection were also analysed and it was found that higher efficacy of the vaccine resulted in lesser number of infections and COVID induced deaths. The findings would help policymakers to plan effective strategies to contain the size of the COVID-19 pandemic.

Learning from the COVID-19 pandemic: a systematic review of mathematical vaccine prioritization models

“…(2023); Shen et al (2021); Zaitri et al (2022). In particular, some works have combined optimal control with age-structured models to find the optimal vaccination allocation Avcı and Yurtoglu (2023); Chhetri et al (2022); Kumar et al (2021). Optimal control employed on infectious disease models represents a powerful tool to identify optimal vaccine allocation strategies.…”

“…There exist numerous other works that use classical optimal control to identify optimal COVID-19 vaccination strategies, most of them minimizing an objective functional which accounts for infected cases, deaths or the number of vaccines Agossou et al (2021); Al-arydah (2023); Salcedo-Varela et al (2023); Shen et al (2021); Zaitri et al (2022). In particular, some works have combined optimal control with age-structured models to find the optimal vaccination allocation Avcı and Yurtŏglu (2023); Chhetri et al (2022); Kumar et al (2021). Optimal control employed on infectious disease models represents a powerful tool to identify optimal vaccine allocation strategies.…”

Optimal age-specific vaccination control for COVID-19: An Irish case study

“…In [ 52 ] two objectives are explored, namely the minimisation of infections and the minimisation of deaths, and the problem is solved through the interior point method, for China, Brazil, and Indonesia. In [ 53 ], the authors consider two age groups and use both vaccination and medical treatment as control variables and find that combining both works best in reducing infection and deaths. In [ 54 ], China is used as a case study and 3 control measures are considered vaccination, isolation and nucleic acid testing.…”