Mathematical modeling of infectious disease spread using fractional-order differential equations an‎d its numerical method

9/22/2026 12:00:00 AM

This thesis provides a comprehensive analysis of intraspecific infectious rivalry within the framework of a dynamic contagious disease model, incorporating multiple population classes to more accurately represent realistic patterns of disease transmission. In the framework of this thesis, parameter sensitivities are analyzed through system sensitivity analysis to eva‎luate their combined influence on the progression an‎d control of infectious diseases. The Caputo–Fabrizio (C–F) fractional derivative is applied to explore the model’s dynamic behavior an‎d inherent complexity, enabling fractional-order solutions that retain more historical an‎d structural information than their classical counterparts. Sensitivity analysis in this thesis examines how variations in key parameters affect the qualitative an‎d quantitative behavior of the system. The theoretical foundation is supported by fixed-point theory, which ensures the existence an‎d uniqueness of solutions, while the Ulam–Hyers (U–H) stability criterion is employed to determine the robustness of the system under perturbations. A core contribution of this thesis is the development an‎d application of a numerical method based on the C–F fractional operator, designed to enhance both the understan‎ding an‎d potential control strategies of the infectious disease model. MATLAB-based numerical simulations are implemented in the thesis to demonstrate the accuracy an‎d efficiency of the proposed method. The results are presented through time series plots an‎d phase diagrams for various fractional orders an‎d parameter configurations, highlighting the system’s dynamic transitions. This work also demonstrates that the proposed modeling an‎d computational framework may be effectively applied in designing intervention strategies to promote faster recovery of patients an‎d to limit the spread of infection within communities. Overall, the findings of this thesis provide valuable contributions to the fields of fractional calculus, mathematical epidemiology, an‎d numerical modeling, offering both theoretical insights an‎d practical tools for future research.

اپيدميولوژي رياضي , حساب كسري كاپوتو–فابريتزيو , تحليل حساسيت , وجود و يكتايي , روش عددي

Mathematical epidemiology , Caputo–Fabrizio fractional calculus , Sensitivity analysis , Existence an‎d uniqueness , Numerical method

Dheyaa AL-Chaabawi

Maboubeh Molavi-Arabshahi