Mathematical Modelling of the Impact of Screening, Treatment and Media Campaigns of Breast Cancer Cell Population Dynamics in Kenya
Robert Njue Muriithi *
Department of Mathematics and Actuarial Science, Kenyatta University, P.O Box 43844, Nairobi, Kenya.
Kennedy Otieno Awuor
Department of Mathematics and Actuarial Science, Kenyatta University, P.O Box 43844, Nairobi, Kenya.
Jeremiah Savali Kilonzi
Department of Mathematics, Meru University of Science and Technology, P.O. Box 972-60200, Meru, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Aims/Objectives: To formulate a mathematical model and quantify the impacts of screening, treatment, and media campaigns on breast cancer cells. The basic reproduction number is derived, sensitivity analysis is performed, and the model is simulated using the Ministry of Health data. We suggested a classical mathematical model comprising six compartments: healthy cells, cancerous cells, awareness, screened individuals, treated population, and recovered population.
Methodology: The study employed the Next Generation Matrix Method (NGM) to determine the basic reproduction number . The results obtained indicated that the Tumor-Free Equilibrium is locally asymptotically stable whenever and globally asymptotically stable if . On the other hand, the Endemic Equilibrium was globally asymptotically stable if The numerical solutions are obtained using ODE45 in MATLAB R2025b for the analysis.
Results: The simulation results showed that increasing the rate of media awareness by 6.32% led to a 2.179% increase in the screened population, while a 52.31% increase in the rate of screening for the treated population resulted in a 1.866% increase in the treated population, and a 65% decrease in the treatment rate caused a 15.26% increase in the number of cancerous cells in the body.
Conclusions: To effectively control breast cancer progression, screening and media campaigns should be enhanced to minimize the cancerous cell population and consequently reduce the mortality rate.
Keywords: Mathematical model, breast cancer, treatment, screening, media campaigns