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An outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), epi-centred in Hubei Province of the People’s Republic of China, quickly spread worldwide and caused COVID-19 pandemic. It infected hundreds of millions of people and caused millions of deaths. In this paper, we develop a compartmental ODE model of COVID-19 transmission. We consider a possibility of breakthrough infections after the vaccination and account for both symptomatic and asymptomatic infections and transmissions. We also incorporate game theory to study the optimal vaccination decisions from the individuals’ perspective. We show that vaccination alone is unlikely to eliminate COVID-19. To achieve herd immunity, the individuals would have to receive a dose of a vaccine more frequently than once every 3 months. It is therefore crucial to adhere to various guidelines, such as quarantine, isolate and wear a mask if tested positive for COVID-19. 

Yellow fever is a vector-borne acute viral hemorrhagic disease. It is endemic in tropical areas of Africa and Latin America but demonstrated the potential for international spread during the 2016 outbreak in Luanda, Angola. Yellow fever can be prevented by vaccination, vector control, and avoiding mosquito bites. To account for human behavior in disease dynamics, we add a game-theoretic component to a recent compartmental model of yellow fever transmission. The self-interested individuals evaluate the risks of contracting yellow fever and choose to vaccinate or avoid the bites to minimize the overall costs. We find the Nash equilibria, the optimal levels of vaccination and bite protections if the individuals can decide on the use of only one of the prevention methods as well as when they can decide on the use of both of them. In the later case, we show that vaccination is the preferred method of protection from the individual standpoint and, in the Nash equilibrium, individuals use vaccination only. Our model predicts the vaccination coverage in Angola to be around 65%, which is in reasonable agreement with the empirical value of 68%. We also study whether voluntary prevention can lead to the elimination of the disease in endemic areas. We show that voluntary vaccination alone is not enough to mitigate the risks of outbreaks, suggesting that a mandatory vaccination policy is necessary.