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Start date: 2020Subject: search.filters.subject.Stability 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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    Optimal control and stability analysis of influenza transmission dynamics with quarantine interventions
    (2025-08-01)
    Lamwong, Jiraporn
    ;
    Pongsumpun, Puntani
    Seasonal flu results from infection by influenza viruses of either type A or B. Common symptoms include a rapid rise in body temperature, coughing, headaches, muscle and joint aches, throat discomfort, and nasal congestion. This research addresses the need for effective modeling and control of seasonal influenza, which remains a significant health concern globally due to its high transmissibility and potential to cause severe illness. Current approaches to understanding and managing influenza focus on various mathematical models exploring transmission dynamics and control strategies. This study contributes to the field by introducing a Susceptible-Exposed-Infectious-Quarantined-Recovered (SEIQR) model, which uniquely incorporates quarantine as a key intervention, reflecting realistic disease management practices. The methodology utilized involves formulating the SEIQR model to simulate the transmission of influenza and analyze its stability. The stability of both the disease-free and endemic equilibrium points is examined using Lyapunov functions and LaSalle’s invariance principle, ensuring the rigorous validation of the model's behavior. To enhance the model's utility, optimal control theory is applied, incorporating control variables such as vaccination, social measures, and treatment for both infected and quarantined populations. The application of Pontryagin’s Maximum Principle enables the derivation of optimal control strategies that balance epidemiological impact with cost-effectiveness. Numerical simulations provide key results that demonstrate the efficacy of control interventions. Specifically, scenarios implementing control measures reveal a significant reduction in the peak and overall spread of infections. The analysis of different control policies indicates that a combined approach—employing both vaccination and social distancing—is the most effective for curbing the spread of influenza. Sensitivity analysis further underscores the critical influence of parameters like quarantine rate and infection rate on the basic reproduction number, R<inf>0</inf>, reinforcing the importance of targeted interventions. The study’s findings emphasize the importance of timely and multifaceted control measures for achieving the global asymptotic stability of the influenza model. The implications suggest that integrated strategies, particularly those involving vaccination and social controls, are crucial for public health policy to manage and prevent influenza outbreaks effectively. Future research could expand the model to include demographic variations, virus mutations, and interactions with other respiratory diseases, enhancing its predictive power and practical relevance for disease control.
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    Rectangular tunnel heading stability in three dimensions and its predictive machine learning models
    (2024-11-01)
    Shiau, Jim
    ;
    Keawsawasvong, Suraparb
    ;
    Lai, Van Qui
    ;
    Promwichai, Thanachon
    ;
    Kamchoom, Viroon
    Tunnel heading stability in two dimensions (2D) has been extensively investigated by numerous scholars in the past decade. One significant limitation of 2D analysis is the absence of actual tunnel geometry modeling with a considerable degree of idealization. Nevertheless, it is possible to study the stability of tunnels in three dimensions (3D) with a rectangular shape using finite element limit analysis (FELA) and a nonlinear programming technique. This paper employs 3D FELA to generate rigorous solutions for stability numbers, failure mechanisms, and safety factors for rectangular-shaped tunnels. To further explore the usefulness of the produced results, multivariate adaptive regression spline (MARS) is used for machine learning of big dataset and development of design equations for practical design applications. The study should be of great benefit to tunnel design practices using the developed equations provided in the paper.