On the Optimization Dynamical Behavior of a Lassa Haemorrhagic Fever with Exposed Rodents and Saturated Incidence Rate

This paper extends a system of first order nonlinear ordinary differential equations ( ODEs ) for Lassa Hemorrhagic Fever ( LHF ) to an innovative fractional-order optimal control model. The fractional-order derivatives are incorporated to better reflect memory and anomalous diffusion effects in disease dynamics, whereas the optimal control strategies incorporates four control strategies, representing early intervention through treatment and rodent evacuation measures. Thus the combination of fractional and optimal control strategies is aimed at improving the our approach of capturing the disease's transmission dynamics, long-term effects, as well as the memory-dependent processes. Qualitative analyses, employing well-established mathematical methods, confirm that the extended dynamics are well-posed. This implies that the established effective reproduction number is effective when is less than unity and ineffective otherwise. The sensitivity analysis, conducted using the Partial rank correlation coefficient ( PRCC ), also identifies the effective contact rates and the rodents' recruitment rate as the most influential parameters, under the extended dynamics. This implies that the extended dynamic is formulated and analyzed, focusing on minimizing the disease burden and intervention costs through the controls strategies. Numerical simulations validate the theoretical findings and demonstrate the influence of fractional dynamics on disease progression and control effectiveness. The results indicate that fractional dynamics provide a more nuanced understanding of the system, enabling the design of optimal control policies that reduce disease prevalence more effectively compared to classical models. The presence of saturation effects and fractional memory processes drives the system toward a fractional-order disease free equilibrium ( DFE ) under optimal control implementation.