Fractional –order analysis of malaria and tuberculosis co-dynamics: A Laplace Adomian decomposition approach

Malaria and tuberculosis (TB) remain two of the world’s most persistent infectious diseases, often coexisting in regions with limited healthcare resources. Co-infection with both diseases poses significant challenges for diagnosis, treatment, and control, as the interaction between them can complicate disease progression and outcomes. In this study, we develop a fractional-order mathematical model to better understand the transmission dynamics of malaria-TB co-infection within a human population. The model captures the complex interplay between the two diseases through a detailed compartmental framework and introduces fractional calculus to more accurately reflect memory and hereditary properties in disease spread. To solve the model, we apply the Laplace-Adomian Decomposition Method, which provides approximate analytical solutions in the form of a rapidly converging series. Key epidemiological parameters are estimated by fitting the model to real-world malaria and TB data using MATLAB’s fmincon optimization algorithm. The strength of this approach lies in its ability to combine mathematical rigor with real data to uncover meaningful trends and relationships. Our findings indicate that enhancing treatment coverage and effectiveness has a significant impact on reducing the burden of both infections. The study emphasizes the importance of integrated disease management strategies, particularly in regions where co-infection is prevalent. By providing a more nuanced view of malaria and TB co-infection dynamics, this work offers valuable insights for policymakers and public health practitioners aiming to design more effective intervention programs.