ABC Fractional Order Vaccination Model for Covid-19 with Self-Protective Measures

G M Vijayalakshmi; P Roselyn Besi

doi:10.1007/s40819-022-01316-2

ABC Fractional Order Vaccination Model for Covid-19 with Self-Protective Measures

Int J Appl Comput Math. 2022;8(3):130. doi: 10.1007/s40819-022-01316-2. Epub 2022 May 12.

Authors

G M Vijayalakshmi¹, P Roselyn Besi²

Affiliations

¹ Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R & D Institute of Science and Technology, Avadi, Tamilnadu 600062 India.
² PG and Research Department of Mathematics, Auxilium College, Vellore, Tamilnadu 632006 India.

Abstract

A mathematical model delineating the control strategies in transference of Covid-19 pandemic is examined through Atangana-Baleanu Caputo type fractional derivatives. The total count of people under observation is classified into Susceptible, Vaccinated, Infected and Protected groups (SVIP). The designed model studies the efficiency of vaccination and personal precautions incorporated qualitatively by every individual via fixed point theorem. Stability of the system has been investigated with spectral characterisation of Ulam Hyer's kind. Numerical interpolation has been derived by Adam's semi-analytical technique and we have approximated the solution. We have proved the theoretical analysis through graphical simulations that vaccination and self protective interventions are the significant role to decrease the contagious expansion of the virus among the people in process.

Keywords: ABC derivatives; Adam’s Bashforth interpolation; Covid-19 pandemic; Fixed point theorems; Multi control measures; Stability of Hyer Ulam’s kind.