Mathematical modeling of COVID-19 dynamics with health consciousness strategies in Italy

Abstract

Different strategies are considered in order to control the spread of an epidemic disease when it occurs. The dynamic behavior of the spread of the disease changes by the implementation of these strategies. In this study, we have analyzed the dynamical behavior of the spread of COVID-19 with different strategies such as health consciousness, vaccination, and isolation with the help of a mathematical model. We have tested the positivity and boundedness of the model. The basic reproduction number of the model was obtained. Conditions for local stability for the disease-free equilibrium and endemic equilibrium have been obtained in this study. Dulac's criterion has been applied to check if the model had a periodic orbit. Nelder-Mead algorithm has been used to find optimized values of the unknown biological parameters of the model by using COVID-19 data of Italy. Sensitivity analysis of the parameters in basic reproduction number has also been conducted. Finally, Range-Kutta 4th order has been utilized to solve the model numerically and obtain graphical representation of the dynamic behavior of the model. The presented study suggests emphasizing on the health consciousness such as wearing face-masks, maintaining social distancing, etc. as well as vaccinating the population in order to control the spread of the disease. From the results of numerical simulations, it is confirmed that, if 25% of the entire population maintains health consciousness and gets vaccinated also, and at least 5% of the population gets vaccinated, the spread of the disease can be brought under control within 200 days.