Impact of general incidence function on three-strain SEIAR model

Manoj Kumar Singh; Anjali.; Brajesh K. Singh; Carlo Cattani; Manoj Kumar Singh; Anjali.; Brajesh K. Singh; Carlo Cattani

doi:10.3934/mbe.2023873

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 11: 19710-19731. doi: 10.3934/mbe.2023873

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Impact of general incidence function on three-strain SEIAR model

1.
Faculty of Mathematics & Computing, Department of Mathematics & Statistics, Banasthali Vidyapith, Rajasthan 304022, India
2.
Department of Mathematics, Babasaheb Bhimrao Ambedkar University, Lucknow 226025, India
3.
Department of Mathematics and Informatics, Azerbaijan University, J. Hajibeyli str., AZ1007, Baku
4.
Azerbaijan Engineering School, DEIM, University of Tuscia, P.le dellUniversità, Viterbo 01100, Italy

Academic Editor: Yang Kuang

Received: 11 June 2023 Revised: 26 September 2023 Accepted: 27 September 2023 Published: 26 October 2023

We investigate the behavior of a complex three-strain model with a generalized incidence rate. The incidence rate is an essential aspect of the model as it determines the number of new infections emerging. The mathematical model comprises thirteen nonlinear ordinary differential equations with susceptible, exposed, symptomatic, asymptomatic and recovered compartments. The model is well-posed and verified through existence, positivity and boundedness. Eight equilibria comprise a disease-free equilibria and seven endemic equilibrium points following the existence of three strains. The basic reproduction numbers $ \mathfrak{R}_{01} $, $ \mathfrak{R}_{02} $ and $ \mathfrak{R}_{03} $ represent the dominance of strain 1, strain 2 and strain 3 in the environment for new strain emergence. The model establishes local stability at a disease-free equilibrium point. Numerical simulations endorse the impact of general incidence rates, including bi-linear, saturated, Beddington DeAngelis, non-monotone and Crowley Martin incidence rates.
- general incidence rate,
- reproduction number,
- multi-strain,
- asymptomatic,
- Liénard Chipart criterion
Citation: Manoj Kumar Singh, Anjali., Brajesh K. Singh, Carlo Cattani. Impact of general incidence function on three-strain SEIAR model[J]. Mathematical Biosciences and Engineering, 2023, 20(11): 19710-19731. doi: 10.3934/mbe.2023873

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Abstract

We investigate the behavior of a complex three-strain model with a generalized incidence rate. The incidence rate is an essential aspect of the model as it determines the number of new infections emerging. The mathematical model comprises thirteen nonlinear ordinary differential equations with susceptible, exposed, symptomatic, asymptomatic and recovered compartments. The model is well-posed and verified through existence, positivity and boundedness. Eight equilibria comprise a disease-free equilibria and seven endemic equilibrium points following the existence of three strains. The basic reproduction numbers $ \mathfrak{R}_{01} $, $ \mathfrak{R}_{02} $ and $ \mathfrak{R}_{03} $ represent the dominance of strain 1, strain 2 and strain 3 in the environment for new strain emergence. The model establishes local stability at a disease-free equilibrium point. Numerical simulations endorse the impact of general incidence rates, including bi-linear, saturated, Beddington DeAngelis, non-monotone and Crowley Martin incidence rates.

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