# Mathematical Model of the Transmission Dynamics of Corona Virus Disease (COVID-19) and Its Control

## Abstract

This work is aimed at formulating a mathematical model for the transmission dynamics and control of corona virus disease in a population. The Disease Free Equilibrium state of the model was determined and shown to be locally asymptotically stable. The Endemic Equilibrium state of the model was also established and proved to be locally asymptotically stable using the trace and determinant method, after which we determined the basic reproduction number ( ) of the model using the next generation method. When ( ), the disease is wiped out of a population, but if ( ), the disease invades such population. Local sensitivity analysis result shows that the rate at which the exposed are quarantined ( ), the rate at which the infected are isolated ( ), the rate at which the quarantined are isolated ( ), and the treatment rate ( ) should be targeted by the control intervention strategies as an increase in the values of these parameters (  and ) will reduce the basic reproduction number  ( ) of the COVID-19 and as such will eliminate the disease from the population with time. Numerical simulation of the model shows that the disease will be eradicated with time when enlightenment control measure for the susceptible individuals to observe social distance, frequent use of hand sanitizers, covering of mouth when coughing or sneezing are properly observed. Moreso, increasing the rates at which the suspected and confirmed cases of COVID-19 are quarantined and isolated respectively reduce the spread of the global pandemic.

Keywords:
Corona, virus, model, quarantine, isolation, treatment.

## Article Details

How to Cite
William, A., David, O., Tenuche, B. S., Samuel, O. K., Alih, D. M., & Johnson, A. (2021). Mathematical Model of the Transmission Dynamics of Corona Virus Disease (COVID-19) and Its Control. Asian Research Journal of Mathematics, 16(11), 69-88. https://doi.org/10.9734/arjom/2020/v16i1130244
Section
Original Research Article

## References

“Corner virus disease 2019” World Health Organization; 2020. Retrieved 15th March, 2020.

“Novel Corona virus in China’’ World Health Organization; 2020. Retrieved 19 th April, 2020.

“Statement on the second meeting of the International Health Population (2005) emergency committee regarding the outbreak of Novel Corona virus” World Health Organization; 2020.

“Director-general opening remarks at the media briefing on Covid-19”. World Health Organization; 2020. Retrieved 11th March, 2020.

“Corona virus (Covid-19) global cases by the centre for systems science and engineering at Johns Hopkins University” Johns Hopkins CSSE; 2020. Retrieved 14th April 2020.

“Corona Virus update (live)” World meter ncov2019 live; 2020.

“Global Covid19 case fatality rates” Centre for evidence-base medicine; 2020. Retrieved 10th April 2020.

“Symptoms of Novel Corona virus (2019- ncov)” US centres for Disease Control and Prevention; 2020. Retrieved 11th February, 2020.

“Interim clinical guidance for management of patients with confirmed Corona virus”. Centre for Disease Control and Prevention; 2020. Retrieved,11th April, 2020.

“New Corona virus Stables for hours on Surfaces” National Instituted of Health (NIH); 2020. Retrieved 24th March, 2020.

“Caring for yourself at home” Centres for disease control and prevention; 2020. Retrieved 23rd March 2020.

“Questions and answers on Corona virus” World Health Organisation; 2020. Retrieved 13th April, 2020.

“Corona Virus Disease 2019-transmission”. Centres for disease control and prevention; 2020. Retrieved 23th March, 2020.

“World Health Organisation”. Laboratory testing for Corona virus Disease 2019 insuspected human cases. Interim guidance “; 2020.

Science daily, “Computed Tomography (CT) best diagnosis for COVID-19; 2020. Retrieved 14th March, 2020.

Azad AR. “FDA authorizes first corona virus antibody test” CNN; 2020. Retrieved 6th April, 2020.

New York Times “A list of what is been Cancelled because of Corona Virus”; 2020. Retrieved 11th April, 2020.

Wu JT, Leung K, Leung GM. “Forecasting the potential domestic and International Spread of the 2019-nCOV outbreak originating in Wuhan, China; a modelling study. Lancet. 2020;395:689-697

Read JM, Bridgen JRE, Cummings DAT, Ho A, Jewell CP. Novel Corona virus 2019-nCov: early estimation of epidemiological Parameters and epidemic predictions. MedRxiV; 2020.

Tang B, Wang X, Li Q, Bregazzi L, Tang S, Xiao Y. Estimation of the transmission risk of 2019-ncov and its implication for public health interventions. J. Clin. med. 2020;9:462-469.

Zhu H, Gao Q, Li M, Wang C, Feng Z, Wang P. Host and infectivity prediction of Wuhan 2019 novel Corona virus Using deep Learning Algorithm. bioRxiv; 2020.

Diekmann O, Heesterbeck JAP. Mathematical epidemiology of infections disease. Wiley series in mathematical and computational biology. John Wiley & Sons. West Sussex, England; 2000.

Nthiiri TK. Mathematical modelling of typhoid fever disease incorporating perfection against infection. British Journal of Mathematics & Computer Sciences. 2016;14(1):1-10.