# Dynamical model for COVID-19 in a population

Document Type : Research Paper

Authors

Department of Pure Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran.

10.22103/jmmrc.2021.17563.1146

Abstract

In this paper a new mathematical model for COVID-19, including Improved people who are susceptible to get infected again, is given. And it is used to investigate the transmission dynamics of the corona virus disease (COVID-19). Our developed model consists of five compartments, namely the susceptible class, $S(t)$, the exposed class, $E(t)$, the infected class, $I(t)$, the quarantine class, $Q(t)$ and the recover class, $R(t)$. The basic reproduction number is computed and the stability conditions of the model at the disease free equilibrium point are obtained. Finally, We present numerical simulations based on the available real data for Kerman province in Iran.

Keywords

#### References

[1] M.A. Aba Oud , A. Ali , H. Alrabaiah, S. Ullah, M. Altaf Khan and S. Islam, A fractional order mathematical model for COVID-19 dynamics with quarantine, isolation, and environmental viral load, Advances in Di erence Equations vol. 106, no. 2021 (2021).
[2] S.A. Abdullah, S. Owyed, A.H. Abdel-Aty, E.E. Mahmoud, K. Shah, H. Alrabaiah, Mathematical analysis of COVID-19 via new mathematical model, Chaos, Solitons and Fractals vol. 143 (2021) 110585.
[3] A. Askari hemmat, Z. Kalateh Bojdi and M. KEBRYAEE, An application of daubechies wavelet in drug release model, Journal of Mahani Mathematical Research Center, vol. 8(2019).
[4] F. Bruer, Mathematical epidemiology: Past, present, and future,infectious disease modelling, vol. 2, no. 2 (2017) 113-127.
[5] F. Bruer, P. van den Driessche, J. Watmough, Mathematical Epidemiology, Springer, 1945.
[6] S. Bushnaq, T. Saeed, D. F.M.Torres and A. Zeb, Control of COVID-19 dynamics through a fractional-order model, AEJ - Alexandria Engineering Journal, vol. 60, no. 4 (2021) 3587-3592.
[7] P.B. Dhandapani, D. Baleanu, J. Thippan and V. Sivakumar, On sti , fuzzy IRD-14 day average transmission model of COVID-19 pandemic disease, AIMS Bioengineering vol. 7, no. 4 (2020) 208223.
[8] P.D. En'ko, On the Course of Epidemics of Some Infectious Diseases, International journal of epidemiology vol. 18, no. 4 (1989) 749-755.
[9] H. Fattahpour and H. R. Z. Zangeneh, Bifurcation analysis of a DDE model of the coral REEF, Journal of Mahani Mathematical Research Center, vol. 5(2016).
[10] D. Fanelli, F. Piazza, Analysis and forecast of COVID-19 spreading in China, Italy and France, Chaos Solitons Fractals vol. 134 (2020) 109761.
[11] M. Farkas, Dynamical Models in Biology, Academic press, 2001.
[12] E. Hesameddini and M. Azizi, Grunwald- Letnikov scheme forsyatem of chronic myelogenous leukemia fractional di erential equations and its optimal control of drug treatment, Journal of Mahani Mathematical Research Center, vol.5(2016).
[13] S. Hussain, A. Zeb, A. Rasheed and T. Saeed, Stochastic mathematical model for the spread and control of Corona virus, Advances in Di erence Equations, vol. 574 (2020).
[14] W.O. Kermack and A.G. Mckendrick.A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society of London Series A vol. 115, no. 722 (1927)700721.
[15] M. Kizito and J, Tumwiine, A mathematical model of treatment and vaccination interventions of pneumococcal pneumonia infection dynamics, Juornal of Applied Mathematics, Article ID 2539465 (2018).
[16] A.J. Kucharski, T.W. Russell, C. Diamond, Y. Liu, J. Edmunds, S. Funk, R.M. Eggo, F. Sun, M. Jit, and J.D. Munday, Early dynamics of transmission and control of COVID-19: a mathematical modelling study, The Lancet Infectious Diseases vol. 20, no. 5 (2020) 553558.
[17] Y. Liu, A.A Gayle, A. Wilder-Smith and J. Rocklv, The reproductive number of COVID-19 is higher compared to SARS coronavirus, Journal of Travel Medicine vol. 27, no. 2 (2020).
[18] T. Sitthiwirattham, A. Zeb, S. Chasreechai, Z. Eskandari, M. Tilioua and S. Djilalif, Analysis of a discrete mathematical COVID-19 model, Results in Physics, vol. 29 (2021).
[19] G. Nazir, A. Zeb, K. Shaha, T. Saeed, R. AliKhan, S. Irfan and U. Khan, Study of COVID-19 Mathematical Model of Fractional Order Via Modi ed Euler Method, AEJ - Alexandria Engineering Journal, vol. 60, no. 6 (2021), 5287-5296.
[20] T. Waezizadeh and F. Fatehi, Entropy for DTMC SIS epidemic model, Journal of Mahani Mathematical Research Center, vol.5(2016).
[21] A. Zeb, E. Alzahrani, V. Suat Erturk, G. Zaman, Mathematical Model for Coronavirus Disease 2019 (COVID-19) Containing Isolation Class, BioMed Research International, vol. 2020 (2020).
[22] Z. Zhang, R. Gul and A. Zeb, Global sensitivity analysis of COVID-19 mathematical model, AEJ - Alexandria Engineering Journal, vol. 60, no. 1(2021), 565-572.
[23] Z. Zhang, A. Zeb, E. Alzahrani and S. Iqbal, Crowding e ects on the dynamics of COVID-19 mathematical model, Advances in Di erence Equations, vol. 675 (2020).
[24] Z. Zhang, A. Zeb, O. F. Egbelowo and V. S. Erturk, Dynamics of a fractional order mathematical model for COVID-19 epidemic, Advances in Di erence Equations, vol. 420 (2020).
[25] Z. Zhang, A. Zeb, S. Hussain and E. Alzahrani, Dynamics of COVID-19 mathematical model with stochastic perturbation, Advances in Di erence Equations, vol. 451 (2020).

### History

• Receive Date: 10 May 2021
• Revise Date: 10 November 2021
• Accept Date: 17 November 2021