Epidemic and unemployment interplay through bi-level multi delayed mathematical model

Abstract

An epidemic causes significant financial and economic losses in addition to having negative health effects that result in fatalities.Unemployment is one of the key macroeconomic challenges that governments around the world experience when an epidemic occurs.We have presented a bi-level multi-delay model of epidemics and unemployment to understand and help in alleviating the problem of unemployment while protecting the economy during an epidemic.The epidemic model is the top level of this bi-level mathematical model, and the unemployment model is the lower level.Additionally, the delay in the effect of infection on the unemployed population and the delay in the effect of epidemic-related fatalities on both the employed and unemployed have been taken into consideration.Two equilibrium points, infection-free and interior equilibrium points, have been found.We have obtained the basic reproduction number using the Next Generation Matrix (NGM) methodology.We have also established linear stability analysis around the infection-free and interior equilibrium points, as well as properties of Hopf bifurcation and Lyapunov stability analysis around the interior equilibrium point.Finally, we have conducted numerical simulations to validate the results of our analysis.A time frame for the delays to maintain the system’s stability has been obtained, or else it will adopt instability and it will become very challenging to control unemployment.We propose that the governments implement lockdowns to restrict public social interactions in order to lower the infection rate.We have demonstrated that in order for lockdown measures to effectively reduce infections without driving up unemployment, lowering the incidence of infection-related mortality is essential.It is suggested that adequate and timely treatment be provided in order to control infection-induced mortality.In order to prevent unemployment and infection, it is also suggested that companies offer their employees the chance to work from home. To demonstrate the applicability of our work, we have employed model calibration to fit our model to the real data of COVID-19 impacted people in India, as well as an investigation of calibrated model’s dynamics due to delays has been done.This research will help tackle the serious problem of unemployment during an epidemic, which will spur general economic expansion.