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Author: search.filters.author.Aalam, BalalSubject: search.filters.subject.Sensitivity analysis

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    Modeling and numerical simulation of control policies for co-infection Leishmaniasis–Chagas disease in Brazil via classical and fractional RK4-scheme
    (2026-08-01)
    Aalam, Balal
    ;
    ur-Rehman, Daniyal
    ;
    Ghaffar, Maryam
    ;
    Pongsumpun, Puntani
    Vector-borne diseases have long played a significant role in human mortality and public health crises in Brazil. Among these, neglected tropical diseases such as Leishmaniasis and Chagas disease require urgent attention. This paper develops a deterministic mathematical dynamical model to study the dynamics of mono and co-infection with Leishmaniasis and Chagas disease. We begin with a rigorous mathematical analysis of the model, including the computation of the basic reproduction number R<inf>0</inf><sup>LC</sup> and its sensitivity indices, which help identify key parameters driving disease dynamics. The population's equilibrium states are studied in relation to this threshold parameter. Furthermore, we incorporate four control prevention into the model to evaluate the best intervention policy. Using a reliable data set from Brazil over a specified time period, we estimate model parameters and fit the data, demonstrating strong agreement between the model predictions and the actual data. Our graphical simulations further support the findings. Additionally, we compute and analyze the controlled reproduction number, confirming that the proposed policy 5 is the most effective in reducing the disease burden in Brazil. Finally, we rewrite the fractional version of the model and perform numerical simulations for different values of α. The fractional-order model is conceptually suitable for capturing memory effects and delay response in disease transmission dynamics. This study provides valuable insights for public health stakeholders and health care centers aiming to design efficient prevention and control programs for neglected vector-borne diseases.
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    Mathematical modeling and optimal control analysis of classical and fractional order SVEITR model for TB infection disease in KPK Province of Pakistan
    (2026-08-01)
    Aalam, Balal
    ;
    Pongsumpun, Puntani
    In Pakistan, tuberculosis (TB) is still a significant public health concern. To address the socioeconomic and healthcare issues in the Khyber Pakhtunkhwa (KPK) province, this study offers a novel mathematical model of tuberculosis transmission. To the best of my knowledge, this is the first optimal control study of SVEITR-TB dynamics in KPK, Pakistan, incorporating both classical and fractional-order modeling frameworks to capture memory effects and complex disease behavior. Model validity is ensured through existence and uniqueness analysis, and the basic reproduction number is used to predict future disease dynamics. Model stability is assessed using Routh-Hurwitz criteria, Castillo–Chavez theorem, and Lyapunov functions for disease-free and endemic scenarios. In addition, backward bifurcation analysis is discussed near the bifurcation point. A sensitivity analysis is conducted to identify the key parameters that affect disease spread. The Nonstandard Finite Difference (NSFD) technique is used for numerical simulations of the deterministic model, and the fractional RK2 approach is used to simulate the fractional-order formulation, showing the disease can be controlled over time. The findings show that the fractional RK2 scheme successfully captures the memory effects present in the fractional-order dynamics and improves numerical accuracy. Furthermore, optimal control strategies, including enhanced vaccination and enhanced treatment, are assessed using Pontryagin’s maximum principle. Simulations using the RK4 forward-backward sweep method show that strategy A is the most reliable for controlling TB among the control measures, with a highest cumulative efficiency index. This demonstrates that strategy A is the most suitable control measure, providing the greatest reduction in disease burden. Thus, we conclude that stockholders and policymakers can use strategy A to control TB in the future.