AN SVIQR EPIDEMIC MODEL FOR COVID-19

Vijai Shanker Verma; Laxman Bahadur Kunwar; Archana Singh Bhadauria; Vikash Rana

doi:10.56827/SEAJMMS.2022.1803.9

Vijai Shanker Verma Department of Mathematics & Statistics Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, (U.P.), INDIA
Laxman Bahadur Kunwar Department of Mathematics & Statistics Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, (U.P.), INDIA
Archana Singh Bhadauria Department of Mathematics & Statistics Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, (U.P.), INDIA
Vikash Rana Department of Mathematics & Statistics Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, (U.P.), INDIA

DOI: https://doi.org/10.56827/SEAJMMS.2022.1803.9

Abstract

We have proposed an SVIQR epidemic model for COVID-19 with vac- cination in this research. Some fundamental characteristics such as positivity of the solution, boundedness and invariance of the model are analyzed. Expressions for disease-free equilibrium (DFE) and endemic equilibrium (EE) points with certain criteria for existence are derived. Rigorous analysis of the model reveals that as- sociated DFE is locally asymptotically stable whenever the effective reproduction number is less than one. Also, the EE point is stable whenever certain restric- tions are satisfied. Sensitivity analysis is performed to identify key parameters that significantly affect the effective reproduction number. Analytical results are illustrated using parameter values and the results are analyzed using numerical simulation which suggests that the disease will eventually die out, particularly if the control measures are implemented above a specified level for a sustained period of time.

Author Biographies

Vijai Shanker Verma, Department of Mathematics & Statistics Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, (U.P.), INDIA

Laxman Bahadur Kunwar, Department of Mathematics & Statistics Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, (U.P.), INDIA

Archana Singh Bhadauria, Department of Mathematics & Statistics Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, (U.P.), INDIA

Vikash Rana, Department of Mathematics & Statistics Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur, (U.P.), INDIA