African Cancer Statistics: A Mathematical Modeling Approach to Cancer Burden Dynamics

Cancer has emerged as a major public health challenge across Africa, with increasing incidence rates, high mortality, and significantdisparities in access to early detection and treatment services. While existing studies largely provide descriptive accounts of cancerincidence and mortality patterns, limited attention has been given to the development of mathematical frameworks that explain theunderlying dynamics of cancer burden and the role of healthcare capacity in resource-constrained settings. This study proposes amathematical modeling approach for analyzing cancer burden dynamics in Africa and determining optimal intervention strategiesunder limited healthcare resources. A deterministic dynamical system is formulated to describe the interaction between cancer burden, healthcare capacity, and intervention effort. The model incorporates key drivers of cancer progression, including population growth, detection mechanisms,and treatment capacity. Fundamental qualitative properties of the system, including positivity and boundedness of solutions, areestablished to ensure biological and epidemiological feasibility. An optimal control problem is then formulated in which intervention effort, representing screening and treatment investment, is introduced as a time-dependent control variable subject to resourcelimitations. The objective is to minimize cancer burden while accounting for the cost of intervention over a finite time horizon. The existence of an optimal intervention strategy is established using standard results from optimal control theory, and necessaryconditions for optimality are derived using Pontryagin’s Maximum Principle. The analysis provides an explicit characterization ofoptimal intervention policies and demonstrates how limited healthcare resources influence the timing and intensity of cancer controlefforts. The results offer theoretical insight into the dynamics of cancer burden in Africa and provide a quantitative framework forsupporting evidence-based health policy planning in resource-limited environments.The proposed framework contributes to the mathematical understanding of cancer epidemiology and establishes a foundation forfuture data-driven and policy-oriented studies on cancer control in Africa.