Compartmental mathematical modelling of dynamic transmission of COVID-19 in Rwanda

Lydie Mpinganzima; Jean Marie Ntaganda; Wellars Banzi; Jean Pierre Muhirwa; Betty Kivumbi Nannyonga; Japhet Niyobuhungiro; Eric Rutaganda; Innocent Ngaruye; Denis Ndanguza; Joseph Nzabanita; Emmanuel Masabo; Marcel Gahamanyi; Justine Dushimirimana; Bosco Nyandwi; Célestin Kurujyibwami; Léon Fidèle Uwimbabazi Ruganzu; Venuste Nyagahakwa; Solange Mukeshimana; Jean Pierre Ngendahayo; Jean Paul Nsabimana; Jean De Dieu Niyigena; Jeanne Uwonkunda; Isambi Sailon Mbalawata

doi:10.1016/j.ijregi.2023.01.003

Compartmental mathematical modelling of dynamic transmission of COVID-19 in Rwanda

IJID Reg. 2023 Mar:6:99-107. doi: 10.1016/j.ijregi.2023.01.003. Epub 2023 Jan 9.

Authors

Lydie Mpinganzima¹, Jean Marie Ntaganda¹, Wellars Banzi¹, Jean Pierre Muhirwa¹, Betty Kivumbi Nannyonga², Japhet Niyobuhungiro³, Eric Rutaganda⁴, Innocent Ngaruye¹, Denis Ndanguza¹, Joseph Nzabanita¹, Emmanuel Masabo^{1

5}, Marcel Gahamanyi¹, Justine Dushimirimana¹, Bosco Nyandwi¹, Célestin Kurujyibwami¹, Léon Fidèle Uwimbabazi Ruganzu¹, Venuste Nyagahakwa¹, Solange Mukeshimana¹, Jean Pierre Ngendahayo¹, Jean Paul Nsabimana¹, Jean De Dieu Niyigena¹, Jeanne Uwonkunda⁶, Isambi Sailon Mbalawata⁷

Affiliations

¹ Department of Mathematics, School of Science, College of Science and Technology, University of Rwanda, Kigali, Rwanda.
² Department of Mathematics, School of Physical Sciences, College of Natural Sciences, Makerere University, Kampala, Uganda.
³ National Council for Science and Technology, Kigali, Rwanda.
⁴ Department of Internal Medicine, Kigali University Teaching Hospital, Kigali, Rwanda.
⁵ African Centre of Excellence in Data Science, Kigali, Rwanda.
⁶ Great Mind for Career Development Group Ltd, Kigali, Rwanda.
⁷ African Institute of Mathematical Sciences, NEI Global Secretariat, Kigali, Rwanda.

Abstract

Objectives: Mathematical modelling is of interest to study the dynamics of coronavirus disease 2019 (COVID-19), and models such as SEIR (Susceptible-Exposed-Infected-Recovered) have been considered. This article describes the development of a compartmental transmission network model - Susceptible-Exposed-Quarantine-Infectious-Infectious, undetected-Infectious, home-based care-Hospitalized-Vaccinated-Recovered-Dead - to simulate the dynamics of COVID-19 in order to account for specific measures put into place by the Government of Rwanda to prevent further spread of the disease.

Methods: The compartments of this model are connected by parameters, some of which are known from the literature, and others are estimated from available data using the least squares method. For the stability of the model, equilibrium points were determined and the basic reproduction number $R_{0}$ was studied; R ₀ is an indicator for contagiousness.

Results: The model showed that secondary infections are generated from the exposed group, the asymptomatic group, the infected (symptomatic) group, the infected (undetected) group, the infected (home-based care) group and the hospitalized group. The formulated model was reliable and fit the data. Furthermore, the estimated $R_{0}$ of 2.16 shows that COVID-19 will persist without the application of control measures.

Conclusions: This article presents results regarding predicted spread of COVID-19 in Rwanda.

Keywords: COVID-19; Home-based care; Metzler matrix; Undetected infections; Vaccinated.