A SIQ mathematical model on COVID-19 investigating the lockdown effect

Abstract

This research paper aims at studying the impact of lockdown on the dynamics of novel Corona Virus Disease (COVID-19) emerged in Wuhan city of China in December 2019. Perceiving the pandemic situation throughout the world, Government of India restricted international passenger traffic through land check post (Liang, 2020) and imposed complete lockdown in the country on 24 March 2020. To study the impact of lockdown on disease dynamics we consider a three-dimensional mathematical model using nonlinear ordinary differential equations. The proposed model has been studied using stability theory of nonlinear ordinary differential equations. Basic reproduction ratio is computed and significant parameters responsible to keep basic reproduction ratio less than one are identified. The study reveals that disease vanishes from the system only if complete lockdown is imposed otherwise disease will always persist in the population. However, disease can be kept under control by implementing contact tracing and quarantine measures as well along with lockdown if lockdown is imposed partially.

Keywords: 34D; 34H; 90A; 92B; Persistence; Sensitivity analysis; Stability; System.

Fig. 1

Schematic flow diagram of the SIQ COVID-19 model.

Fig. 2

Variation in infective population with no. of migrants ‘m’.

Fig. 3

Effect of transition rate ′σ′ on infective population.

Fig. 4

Effect of contact tracing ‘k′ on infective population.

Fig. 5

Effect of transmission rate β on susceptible, infective and quarantined population.

Fig. 6

Effect of different parameters on Reproduction number ‘R₀′.