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| Numerical Solution of Fractional Order Typhoid Fever Model via the Generalized Fractal-Fractional Approach |
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| KeyWord:Typhoid fever, fractal-fractional operators, stability, existence and uniqueness, numerical scheme |
| Author Name | Affiliation | | Enejoh Jalija | Department of Mathematical Sciences, Prince Abubakar Audu University, Anyigba, 272102, Nigeria
Laboratory of Mathematical Epidemiology and Applied Sciences, Prince Abubakar Audu University, Anyigba, Nigeria | | Jeremiah Amos | Department of Mathematical Sciences, Prince Abubakar Audu University, Anyigba, 272102, Nigeria
Laboratory of Mathematical Epidemiology and Applied Sciences, Prince Abubakar Audu University, Anyigba, Nigeria | | William Atokolo | Department of Mathematical Sciences, Prince Abubakar Audu University, Anyigba, 272102, Nigeria
Laboratory of Mathematical Epidemiology and Applied Sciences, Prince Abubakar Audu University, Anyigba, Nigeria | | Emmanuel Abah | Department of Mathematical Sciences, Prince Abubakar Audu University, Anyigba, 272102, Nigeria
Laboratory of Mathematical Epidemiology and Applied Sciences, Prince Abubakar Audu University, Anyigba, Nigeria | | Bolarinwa Bolaji | Department of Mathematical Sciences, Prince Abubakar Audu University, Anyigba, 272102, Nigeria |
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| Abstract: |
| Typhoid fever remains a significant public health concern in developing countries, necessitating comprehensive mathematical modeling to understand its transmission dynamics and inform control strategies. In this study, we establish a non-linear mathematical model of Typhoid fever through Atangana Baleanu fractional dynamics for human population. The theoretical solution existence and uniqueness was analyzed through a combination of Banach's theorem and Krasnoselskii's fixed-point type theorem functions. Our research presents equilibrium stability characteristics of equilibrium points and establishes basic reproduction number calculations and global asymptomatically stable findings together with sensitivity analysis outcomes. The model incorporates realistic epidemiological parameters including transmission rates, recovery rates, and treatment efficacy to capture the complex dynamics of typhoid transmission. We implemented the Adams-Bashforth scheme to create numeric algorithms for our model system. The calculated results received verification through numerical testing which revealed the effects of adjusting both fractional orders and fractal dimensions. Comprehensive parameter estimation and model validation were conducted using available epidemiological data to ensure biological relevance of our findings. Disease propagation in the population depends on parameter sets along with fractional-order values computed from fractal fractional numerical approaches. Higher contact rates create increased prevalence of Typhoid fever yet decreased treatment rates decrease the spread of typhoid fever based on simulation outcomes. The research shows that lowering contact intensities together with boosted treatment interventions serve effectively to slow down Typhoid fever population spread. Our results provide quantitative insights for public health officials in designing optimal intervention strategies, particularly highlighting the critical importance of early treatment programs and community-based prevention measures in typhoid-endemic regions. The fractional-order modeling approach offers enhanced flexibility in capturing memory effects and non-local dynamics inherent in disease transmission processes. |
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