Dynamical analysis and optimal control problem of impact of vaccine awareness programs on epidemic system

Abstract

There has been an unprecedented global public health and economic crisis due to the coronavirus disease 2019 (COVID-19). For containing the infection and returning to normal routines, vaccination is an important foreseeable mean. But there are many people who do not have exposure to information about vaccinations or are either misinformed and this may take the form of vaccine hesitancy. Thus, positive vaccination awareness to even the most vulnerable section of society or remote areas of the country may be the need of the hour for full population inoculation. The role of awareness programs by government as a control to increase vaccination and control the infection is discussed in this paper. Thus we formulate a model consisting of unaware and aware population amid vaccination campaigns/awareness. The existence, local stability and global stability(through graph theoretic approach) of the equilibria are analyzed. Following our model we extend it to an optimal problem with the objective to maximise vaccination and minimise promotional costs in our system. With the help of Pontryagin’s Maximum Principle, we then obtain the optimal awareness intensity as part of intervention for vaccination for our optimal control problem. Through numerical simulations, the paper shows that awareness among general public increases the number of vaccinated individuals. Sensitivity analysis is performed for the optimal control calculated using latin hypercube sampling method. Thus, the paper highlights the necessary and crucial role of vaccine awareness programs to fight a disease in epidemic dynamics.