Modelling The Impact of Screening, Treatment and Underlying Health Conditions on Dynamics of Covid-19

Jeremiah Savali Kilonzi; Cyrus Gitonga Ngari; Stephen Karanja

Jeremiah Savali Kilonzi Department of Mathematics, Meru University of Science and Technology, Kenya
Cyrus Gitonga Ngari Department of Pure and Applied Science, Kirinyaga University, Kenya
Stephen Karanja Department of Mathematics, Meru University of Science and Technology, Kenya

Keywords: COVID-19 transmission, underlying health conditions, Screening, Treatment, Sustained Development Goals, Severe Acute Respiratory Syndrome Coronavirus 2

Abstract

This study formulated a SIRS classical mathematical model which is modified to incorporate the exposed and the treated individuals where COVID-19 is modelled. The model stratifies the population into two categories depending whether they have underlying health conditions or not, and describes disease transmission within or between the groups. Five compartments are considered in the model for each group that is; Susceptible individuals, exposed population, Infected individuals, treated population and the Recovered population. The objectives were to; Formulate a mathematical deterministic model based on classical SIRS model incorporating screening, treatment and underlying health conditions on covid-19 dynamics. Determine the Reproduction number and use it to analyze the model. Determining sensitivity analysis and Bifurcation. Simulating the model using data from the ministry of health. The Next generation matrix method was used to determine the basic reproduction number denoted of the proposed model. The results of the simulation indicated that the Disease Free Equilibrium is locally asymptotically stable whenever and globally asymptotically stable if . On the other hand, Endemic Equilibrium was globally asymptotically stable if .The results obtained showed that increasing the rate of screening and treatment on the exposed population and weakening the disease transmission route between the susceptible, exposed and infected population are crucial to curb the spread of COVID-19 virus. The Government of Kenya should advocate treatment and screening of the exposed and infected individuals.

Downloads

Download data is not yet available.

References

Abioye, A. I.,Peter, O. J., Ogunseye, H. A., Oguntolu, F. A., Oshinubi, K., Ibrahim, A. A., & Khan, I. (2021). Mathematical model of Covid-19 in Nigeria with optimal control. Results in Physics , 28,104598.
Baek, Y. J., Lee , T., Cho,Y., Hyun, J. H., Kim, M. H., Sohn, Y., & Choi, J. Y. (2020). A mathematical model of Covid-19 transmission in a tertiary hospital and assessment of the effects of different intervention strategies. PloS one, 15(10), e0241169.
Bandekar, S. R., & Ghosh, M. (2021). Modeling and analysis of COVID-19 in India with treatment function through different phases of lockdown and unlock. Stochastic Analysis and Applications, 1-18. doi:10.1080/07362994.2021.1962343
Brand, S. P., Aziza, R., Kombe, I. K., Agoti, C. N., Hilton, J., Rock, K. S., & Barasa, E. W. (2020). Forecasting the scale of the scale of the Covid-19 epidemic in Kenya. MedRxiv.
Centers for Disease Control and Prevention ,coronavirus(COVID-19). (n.d.). Retrieved from https://www.cdc.gov/coronavirus/2021-ncov
Diagne,M.L.,Rwezaura,H., Tchoumi,S. Y., & J. M. Tchuenche. (2021). A Mathematical Model of COVID-19 with Vaccination and Treatment. Computational and Mathematical Methods In Medicine.
Dwomoh, D., Iddi, S., Adu, B., Ahero, J. M., Sedzro, K. M., Fobil, J., & Bosomprah, S. (2021). Mathematical modeling of COVID-19 infection dynamics in Ghana: Impact evaluation of integrated government and individual level interventions. Infectious Disease Modelling,6,, 381-397.
Health, M. o. (2020). Home Based Isolation and Care Guidelines for Patients with COVID-19. Ministry of Health, 22 pages.
Isaac Mwangi Wangari,stanley Sewe,George Kimathi,Mary Wanaina, Virginia Kitetu and Winnie Kaluki. (2021). Mathematical modelling of Covid-19 Traansmission in Kenya; A model with reinfection Transmission Mechanism. Computational and Mathematical Methods in Medicine, 18 pages.
Kenya demographic profile. (2018). https://www.indexMundi.com/Kenya demographic profile.htm.
Kouidere, A., Khajji, B., Balatif, O., Rachik, M. . (2021). A multi-age mathematical modelling of the dynamics of population diabetics with effect of lifestyle using optimal control. Journal of Applied Mathematics and Computings, 375-403.
Kouidere, A., Youssoufi, L., Ferjouchia, H., Balatif, O. (2021). Optimal Control of Mathematical modeling of the spread of the COVID-19 pandemic with highlighting the negative impact of quarantine on diabetics people with cost-effectiveness. Chaos,Solitons & Fractals, 145, 110777.
Masandawa, L., Mirau, S. S., & Mbalawata, I. S. (2021). Mathematical modelling of COVID-19 transmission dynamics between healthcare workers and community. Results in Physics, 29, 104731. Retrieved from https://doi.org/10.1016/j.rinp.2021.104731
Mbogo R,W.,Orwa, T.O. (2021). SARS-COV-2 outbreak and control in Kenya - Mathematical model analysis. Infectious Disease Modelling, 6, 370-380.
Mkhize, D. Z. (2020). First Case of (COVID-19) Coronavius Reported in South Africa. National Institution for Communicable Disease, 1.
Muhammad Farman, Aamir Shehzad,Ali Akgül,Dumitru Baleanu,and Manuel De la Sen. (2023). Modelling and Analysis of a Measles Epidemic Model with the Constant Proportional Caputo Operato. Symmetry, 15,468.
Ndairou, F., Area, I., Nieto, J. J & Torres, D. F. M. (2020). Mathematical Modelling of COVID-19 Transmission Dynamics with a Case Study of Wuhan. Chaos, Solitons and Fractals, 135.
Ngari, C., Gakii, G., Mirgichan, J. k. (2020). Parameters and States Estimates of COVID-19 Model Using Lagrange Polynomial, Least Square Approximation and Kenya Quarantine Data. Annual Research & Review in Biology, 25-42.
Nyamu, M., Mutwiri, B. D., & Lawrence, B. (2020). Modelling of COVID-19 (Coronavirus) in Kenya Using SIR Model. International Journal of Statistics and Applied Mathematics, 20-24.
Peter, O. J., Qureshi, S., Yusuf, A., Al-Shomrani, M., & Idowu, A. A. (2021). A new mathematical model of COVID-19 using real data from Pakistan. Results in Physics, 24,104098.
Rotich, T., & Lagat, R. (2020). Mathematical Modelling of Covid-19 Disease Dynamics and Analyisis of Intervation Strategies. Mathematical Modelling and Applications, vol. 5(No. 3), pg 176-182.
Samuel Okyere,Joseph Ackora,Ebenezer Bonyah and Mary Osei Fokuo. (2022). A model of COVID-19 with underlying health conditions using fraction order derivative. Quantitative Biology >Population and Evolution,Cornell University, 40.
Sharon Chebet,George Kimathi and Mary Wainaina. (2022). Mathematical modelling of Impact of stigmatization and vaccination on the spread of covid-19 in Kenya. International Journal of Mathematics and physical science research , vol.10, issue 1, pg 68-81.
WHO. (2020). Coronavirus 2019 (COVID-19): . dashboard, World Heath Organizations . Retrieved from https://www.who.int/emergencies/diseases/novel-coronavirus-2019
WHO. (-updated 2021). World Health Organization ,Coronavirus disease (COVID-19) pandemic. Retrieved from https://www.who.int/emergencies/diseases/novel-coronavirus
World Health Organization ,Coronavirus disease (COVID-19) pandemic. (n.d.). https://www.who.int/emergencies/diseases/novel-coronavirus-updated 2021.
Yang, C.,& Wang. J. (2021). COVID-19 and underlying health conditions: A modelling Investigation. Mathematical Biosciences and Engineering, 18(4),3790-3812.