# Mathematical Analysis of Two Strains Covid-19 Disease Using SEIR Model

## DOI:

https://doi.org/10.5614/j.math.fund.sci.2022.54.2.1## Keywords:

Covid-19 Dynamics, Mathematical Analysis, Reproduction Number, Stability Theory, Two Strains## Abstract

The biggest public health problem facing the whole world today is the COVID-19 pandemic. From the time COVID-19 came into the limelight, people have been losing their loved ones and relatives as a direct result of this disease. Here, we present a six-compartment epidemiological model that is deterministic in nature for the emergence and spread of two strains of the COVID-19 disease in a given community, with quarantine and recovery due to treatment. Employing the stability theory of differential equations, the model was qualitatively analyzed. We derived the basic reproduction number for both strains and investigated the sensitivity index of the parameters. In addition to this, we probed the global stability of the disease-free equilibrium. The disease-free equilibrium was revealed to be globally stable, provided and the model exhibited forward bifurcation. A numerical simulation was performed, and pertinent results are displayed graphically and discussed.

## References

WHO, Coronavirus Disease 2019 (Covid-19) Situation Report-62, March 2020.

Wickramaarachchi, W.P.T.M., Perera, S.S.N. & Jayasinghe, S., COVID-19 Epidemic in Sri Lanka: A Mathematical and Computational Modelling Approach to Control. Computational and Mathematical Methods in Medicine, Article ID 4045064, 9(2020), 2020.

Mohsen, A. A., Al-Husseiny, H. F., Zhou, X. & Hattaf, K., Global Stability of COVID-19 Model Involving the Quarantine Strategy and Media Coverage Effect, AIMS Public Health, 7(3), pp. 587-605, 2020.

Seidu, B., Optimal Strategies for Control of COVID-19: A Mathematical Perspective, Scientifica, 2020(12), Article ID 4676274, 2020.

Alshammari, F.S., A Mathematical Model to Investigate the Transmission of COVID-19 in the Kingdom of Saudi Arabia. Computational and Mathematical Methods in Medicine, Article ID 9136157, 2020(13), 2020.

Shaobo, H., Yuexi, P. & Kehui, S., SEIR Modelling of The COVID-19 and Its Dynamics, Nonlinear Dynamics, 101, pp. 1667-1680, 2020.

Dmitry, A., Tomchin, D.A. & Fradkov, A.L., Prediction of The COVID-19 Spread in Russia Based on SIR and SEIR Models of Epidemic, IFAC Papers online, 53(5), pp. 833-838, 2020.

Cooper, I., Argha Mondal, A. & Antonopoulos, C.G., A SIR Model Assumption for The Spread of COVID-19 in Different Communities, Chaos, Solitons and Fractals, 139, pp. 110057, 2020.

Muz-Ferndez, G.A., Seoane, J.M. & Seoane-Sepveda, J.B., A SIR-Type Model Describing the Successive Waves of COVID-19, Chaos, Solitons and Fractals, 144, pp. 110682, 2021.

Alenezi, M.N., Al-Anzi, F.S. & Alabdulrazzaq, H., Building a Sensible SIR Estimation Model for COVID-19 Outspread in Kuwait. Alexandria Engineering Journal, 60, pp. 3161-3175, 2021.

Liu, X., A Simple, SIR-Like but Individual-Based Epidemic Model: Application in Comparison of COVID-19 In New York City and Wuhan, Results in Physics, 20, pp. 103712, 2021.

Zhu, W.J. & Shen, S.F., An Improved SIR Model Describing the Epidemic Dynamics of The COVID-19 In China. Results in Physics, 25, pp. 104289, 2021.

Subrata, P.A., Animesh, M.B., Uttam, G.C. & Banamali, R. D., Study of SEIR Epidemic Model and Scenario Analysis of Covid-19 Pandemic, Ecological Genetics and Genomics, 19, pp. 100087, 2021.

Phitchayapak W. & Kiattisak P., Stability Analysis of SEIR Model Related to The Efficiency of Vaccines for COVID-19 Situation, Heliyon, 7, pp. e06812, 2021.

Castillo-Chavez, C. & Song, B., Dynamical Models of Tuberculosis and Their Applications, Math Biosci. Eng., 1, pp. 361-404, 2004.

Tang, B., Xia, F., Tang, S., Bragazzi, N.L., Li, Q., Sun, X., Liang, J., Xia, Y. & Wu, J., The Effectiveness of Quarantine and Isolation Determine the Trend of The COVID-19 Epidemics in The Final Phase of the Current Outbreak in China, International Journal of Infectious Diseases, 95, pp. 288-293, 2020.

Chitnis, N., Hyman, J.M. & Cushing, J.M., Determining Important Parameters in the Spread of Malaria Through the Sensitivity Analysis of a Mathematical Model, Bulletin of Mathematical Biology, 70, pp. 1272-1296, 2008. DOI 10.1007/s11538-008-9299-0.

Berhe, H.W., Makinde, O.D. & Theuri, D.M., Parameter Estimation and Sensitivity Analysis of Dysentery Diarrhoea Epidemic Mode, J. Appl. Math., 1(13), 2019.

Driessche, P.V. & Watmough, J., Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission, Mathematical Biosciences, 180, pp. 29-48, 2002.

Diekmann, O., Heesterbeek, J. A. P. & Roberts, M. G., The Construction of Next Generation Matrices for Compartmental Epidemic Models, Journal of the royal society interface, 7(47), pp. 873-885, 2010.

Beretta, E. & Takeuchi, Y., Global Stability of Lotka-Volterra Diffusion Models with Continuous Time Delay, SIAM J. Appl. Math., 48(3), pp. 627-651, 1988.

Goh, B. S., Global Stability in Two Species Interactions, J. Math. Biol., 3, pp. 313-318, 1976.

Korobeinikov, A., Global Properties of SIR and SEIR Epidemic Models with Multiple Parallel Infectious Stages, Bull. Math. Biol., 71(1), pp. 1-13, 2021.

Albani, V., Loria, J., Massad, E. & Zubelli, J., COVID-19 Underreporting and Its Impact on Vaccination Strategies. BMC Infectious Diseases, 21(1), pp. 75-83, 2009.

Albani, V., Loria, J., Massad, E. & Zubelli, J., The Impact of Covid-19 Vaccination Delay: Adata-Driven Modelling Analysis for Chicago and New York City, Vaccine, 39(41), pp. 76088-6094, 2009.

Tilahun, G.T., Makinde, O.D. & Malonza, D., Co-Dynamics of Pneumonia and Typhoid Fever Diseases with Cost-Effective Optimal Control Analysis, Applied Mathematics and computation, 316, pp. 438-459, 2018.

Berhe, H.W., Makinde, O.D. & Theuri, D.M., Co-Dynamics of Measles and Dysentery Diarrhea Diseases with Optimal Control and Cost-Effectiveness Analysis, Applied Mathematics and Computation, 347, pp. 903-921, 2019.

Keno, T.D., Makinde, O.D. & Obsu, L.L., Optimal Control and Cost Effectiveness Analysis of SIRS Malaria Disease Model with Temperature Variability Factor, Journal of Mathematical & Fundamental Sciences, 53(1), pp. 134-163, 2021.