Impact of media awareness in mitigating the spread of an infectious disease with application to optimal control
Department of Mathematics, Diamond Harbour Women’s University, 743368, Sarisha, West Bengal, India
2 Department of Mathematics, Presidency University, 86/1 College Street, 700073, Kolkata, India
Accepted: 5 August 2022
Published online: 29 August 2022
This paper describes the nonlinear mathematical model for an infectious disease with vaccination which is one of the effective control measures for the disease. We studied the basic properties of the model including the existence and stability of both the disease-free and endemic steady state. We compute the basic reproduction number by using next generation matrix method. An optimal control problem is constructed to minimize the cost and disease-induced death by taking into account the impact of media awareness (non-pharmaceutical intervention) and vaccination as control variables. We have considered three possible functions (linear, exponential and hyperbolic) to delineate the impact of media awareness for the disease transmission and vaccination. In the objective functional, both the linear and nonlinear effect of controls are considered. We characterized the optimal control problem with the help of Pontryagin’s Maximum Principle. A comparative study is done by considering the following control strategies: (A) implementation of single control strategy for media awareness, (B) execution of only one control strategy for vaccination and (C) implementation of combined control strategies. Our numerical simulation shows that the hyperbolic function is more effective in mitigating the epidemic burden while compared with the exponential and linear one. Numerical illustrations demonstrate that if single control via media coverage is implemented, it is successful for early stage of epidemic outbreak whereas vaccination plays a vital role for long-run control apart from an initial stage. Furthermore, extensive utilization of both the control strategies is very influential than implementation of only one control strategy and it mitigates the number of infected population and minimizes the cost created from disease burden. We analyzed the impact of media awareness under three different phenomena that may aid in creating guidelines for public health officials in mitigating the infectious diseases.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.