Dynamics of Covid-19 disease with its economic implications and optimal control: An exploitation of variational iteration method

Abstract

Recent outbreak of Covid-19 disease has impacted the global economy negatively due to diminished productivity, loss of life, business closures, trade disruption, and obliteration of the tourism industry. Since this disease is not likely to disappear soon, proactive measures are required to save lives and protect economic prosperity. In this paper, the transmission dynamics of Covid-19 disease and its economic impact with constant and variable control strategies are theoretically examined via a system of nonlinear differential equations. A qualitative analysis of the model with constant control strategies was performed. Positivity and invariant region of solutions together with disease-free and endemic equilibria were determined. The basic reproduction number R0 of the model was obtained via the next generation matrix method and the sensitivity analysis of parameters in R0 were investigated. Using the Routh–Hurwitz criterion and the appropriate Lyapunov function, the equilibria's local and global stability were revealed. The model exhibits a forward bifurcation; this validates the stability of the Covid-19 disease-free equilibrium whenever R0 < 1. The optimal control analysis based on Pontraygin's maximum principle with two variable control strategies (i.e. protective strategy and environmental fumigation) together with their cost-effectiveness analysis were implemented. Numerical simulation was conducted using variational iteration method (VIM) and the results obtained favourably compared with that of 4th order Runge-Kutta integration scheme. Our qualitative and numerical results suggest that the use of protective control (Strategy B) is the most cost-effective strategy to combat the Covid-19 pandemic and boost the economy.