On spatio-temporal dynamics of COVID-19 epidemic 𝑆𝐸_1𝐸_2𝐼_1𝐼_2𝑅𝑆 model incorporating virus mutations and vaccinations effects

Elsadany, Abdelalim A.; Aljuaidi, Sara; Elsonbaty, Amr; Aldurayhim, A

doi:10.21608/ejmaa.2023.228645.1056

On spatio-temporal dynamics of COVID-19 epidemic 𝑆𝐸_1𝐸_2𝐼_1𝐼_2𝑅𝑆 model incorporating virus mutations and vaccinations effects

Document Type : Regular research papers

Authors

¹ Basic Science Dept., Faculty of computers and Information, Suez Canal University,Ismailia 41522 - Egypt

² Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia.

³ Mathematics and Engineering Physics Department, Faculty of Engineering, Mansoura University

10.21608/ejmaa.2023.228645.1056

Abstract

This work is devoted to present temporal-only and spatio-temporal COVID-19 epidemic models when virus mutations and vaccination influences are considered. Firstly, the proposed non-diffusive COVID-19 model is introduced. The nonlinear incidence rate is employed to better model the strict measures forced by governmental authorities to control pandemic spread. The immunity acquired by vaccinations are assumed to be incomplete for realistic considerations. The existence, uniqueness and continuous dependence on initial conditions are studied for the solution. The study of stability along with bifurcation analysis are carried out to investigate the influences of variations in model’s parameters. Moreover, the basic reproduction number is obtained for the proposed model. The stability regions for equilibrium points are depicted in space of parameters to explore their effects. Secondly, the diffusive version of the model is considered where possible occurrence of Turing instability is investigated. Finally, numerical simulations are employed to verify theoretical results of the work.

Keywords