Epidemic model of COVID-19 outbreak by inducing behavioural response in population

Sangeeta Saha; G P Samanta; Juan J Nieto

doi:10.1007/s11071-020-05896-w

Epidemic model of COVID-19 outbreak by inducing behavioural response in population

Nonlinear Dyn. 2020;102(1):455-487. doi: 10.1007/s11071-020-05896-w. Epub 2020 Aug 26.

Authors

Sangeeta Saha¹, G P Samanta¹, Juan J Nieto²

Affiliations

¹ Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, 711103 India.
² Instituto de Matematicas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain.

Abstract

COVID-19 has spread around the world since December 2019, creating one of the greatest pandemics ever witnessed. According to the current reports, this is a situation when people need to be more careful and take the precaution measures more seriously, unless the condition may become even worse. Maintaining social distances and proper hygiene, staying at isolation or adopting the self-quarantine method are some of the common practices that people should use to avoid the infection. And the growing information regarding COVID-19 and its symptoms help the people to take proper precautions. In this present study, we consider an SEIRS epidemiological model on COVID-19 transmission which accounts for the effect of an individual's behavioural response due to the information regarding proper precautions. Our results indicate that if people respond to the growing information regarding awareness at a higher rate and start to take the protective measures, then the infected population decreases significantly. The disease fatality can be controlled only if a large proportion of individuals become immune, either by natural immunity or by a proper vaccine. In order to apply the latter option, we need to wait until a safe and proper vaccine is developed and it is a time-taking process. Hence, in the latter part of the work, an optimal control problem is considered by implementing control strategies to reduce the disease burden. Numerical figures show that the control denoting behavioural response works with higher intensity immediately after implementation and then gradually decreases with time. Further, the control policy denoting hospitalisation of infected individuals works with its maximum intensity for quite a long time period following a sudden decrease. As, the implementation of the control strategies reduce the infected population and increase the recovered population, so, it may help to reduce the disease transmission at this current epidemic situation.

Keywords: Behavioural response; COVID-19; Epidemic model; Optimal control.