Open Access. © 2022 Bishal Chhetri et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License. Comput. Math. Biophys. 2022; 10:281ś303 Research Article Open Access Bishal Chhetri, D. K. K. Vamsi*, D. Bhanu Prakash, S. Balasubramanian, and Carani B. Sanjeevi Age Structured Mathematical Modeling Studies on COVID-19 with respect to Combined Vaccination and Medical Treatment Strategies https://doi.org/10.1515/cmb-2022-0143 Received February 23, 2022; accepted October 14, 2022 Abstract: In this study, we develop a mathematical model incorporating age-specifc transmission dynamics of COVID-19 to evaluate the role of vaccination and treatment strategies in reducing the size of COVID-19 bur- den. 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 con- trol 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 diferent values of the weight constant associated with the cost of vaccination and diferent efcacy 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 sufcient implementation of vaccines (more than 77 %) reduces the size of COVID-19 infections and number of deaths. The infection curves varying the efcacies of the vaccines against infection were also analysed and it was found that higher efcacy of the vaccine resulted in lesser number of infections and COVID induced deaths. The fndings would help policymakers to plan efective strategies to contain the size of the COVID-19 pandemic. Keywords: COVID-19; Age Structure; Vaccine Efcacy; Vaccination Coverage; Optimal Control Problem MSC: 92Bxx; 92D30; 49-XX; 34-XX 1 Introduction Mathematical modeling of infectious diseases such as COVID-19, infuenza, dengue, HIV/AIDS etc. is one of the most important research areas today. Mathematical epidemiology has contributed to a better under- standing of the dynamical behavior of these infectious diseases, its impacts, and possible future predictions Bishal Chhetri: Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, India, E-mail: bishalchhetri@sssihl.edu.in *Corresponding Author: D. K. K. Vamsi: Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, India, E-mail: dkkvamsi@sssihl.edu.in D. Bhanu Prakash, S. Balasubramanian: Department of Mathematics and Computer Science, Sri Sathya Sai Institute of Higher Learning, India Carani B. Sanjeevi: Vice-Chancellor, Sri Sathya Sai Institute of Higher Learning, India Department of Medicine, Karolinska Institute, Stockholm, Sweden