Spread of COVID-19 in Odisha (India) Due to Influx of Migrants and Stability Analysis Using Mathematical Modeling

Abstract

AbstractAim/Objectives: To ascertain the effect of migrant workers on the spread of COVID-19 in Odisha, India and to examine both local and global stability. Study Design: Out-migrants are diagnosed at compartment (A), those who were confirmed positive, they were sent to the infected compartment (I) for treatment and the remaining healthy individuals are sent to quarantine compartment (Q) for a period of twenty one days under surveillance or observation. Then basing on the principle of mathematical epidemiology, the set of ordinary (nonlinear) differential equations is formulated. Methodology/Approach: Jacobian Matrices are employed to find eigen values of the system for stability behaviour. Routh-Hurwitz Criterion and Poincare-Bendixson theorem are used for stability analysis. The set of ordinary (nonlinear) differential equations are solved using Runge-Kutta fourth order method. The simulation of numerical data is performed using MATLAB. Results: The study shows that the prevalence of COVID-19 would remain nearly 250 to 300 days in Odisha since the inception of entry of infected migrants to the state till the disease is stable. Further the study proves that it persists to endemic equilibrium for global stability when basic reproduction number greater than unity. The numerical and analytical results of the study establish that the disease free equilibrium is locally stable when basic reproduction number is less than unity and unstable when it is more than unity. Conclusions: As there is no specific treatment, vaccine or medicine available for the disease till the date, so the only intervention procedure called quarantine process is devised in this model to check the stability behaviour of the disease. Due to intervention of quarantine, lock-down, shutdown and other social distancing rules, the study shows that the system is stable after a certain period of time. This mathematical modelling embedded with important risk factor like migration could be adopted for each state that will be helpful for better prediction of the entire country and world.KeywordsGlobal and local stabilityModelingMigrationEquilibriumQuarantineVirus