10th U6+ Consortium of African Universities International Conference

Mathematical frameworks that effectively represent both historical memory e
effects and regional system changes are necessary for modeling the non-linear dynamics of infectious illnesses. The parameters required to account for the hereditary features and localized transmission fluctuations observed in public health data streams throughout Sub-Saharan Africa are frequently absent from traditional integer-order compartmental models. In order to overcome this restriction, this work will provide a fractional-order Susceptible-Infectious-Recovered (SIR) model in which the algebraic features of star-like transformation semigroup classes constrain the fractional differential operators. In order to create a mathematically rigorous operator framework, we will describe the structural invariants of these transformation algebras. This approach will be included in a fractional-order Caputo differential system to model localized non-linear transmission dynamics, with parameter limits that reflect regional epidemic trends in Nigeria. We will test the model's ability to monitor localized transmission waves by perturbing the fractional order and transformation semigroup parameters. The numerical simulations will show that integrating star-like algebraic structures into fractional-order transmission matrices improves numerical convergence stability and minimizes parameter estimation errors as compared to traditional classical SIR models. Our findings will provide a clearly delimited, deterministic computational method to regional epidemic forecasting, providing a dependable analytical tool to enhance healthcare resource allocation and long-term public well-being policies in Nigeria.