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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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Erratum to “Modeling and numerical simulation of control policies for co-infection Leishmaniasis–Chagas disease in Brazil via classical and fractional RK4-scheme” [Comput. Biol. Chem. 123 (2026) 108990] (Computational Biology and Chemistry (2026) 123, (S1476927126001155), (10.1016/j.compbiolchem.2026.108990))
(2026-08-01)
Aalam, Balal
;
Daniyal-ur-Rehman
;
Ghaffar, Maryam
;
Pongsumpun, Puntani
The publisher regrets that the incorrect graphical abstract was displayed in the published online version of the article. The incorrect graphical abstract has been replaced with the correct graphical abstract provided below.[Figure presented] The publisher would like to apologise for any inconvenience caused.
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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.
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Mathematical modeling with optimal control analysis of the spread and persistence of PUBG mobile addiction
(2026-06-01)
Aalam, Balal
;
Pongsumpun, Puntani
PUBG Mobile addiction has become a growing global public health concern, particularly among adolescents and young adults, due to its highly fascinating gameplay and widespread accessibility through mobile devices. Excessive engagement with PUBG Mobile has been linked to serious psychological, behavioral, and social consequences, including anxiety, depression, sleep disorders, academic decline, and impaired interpersonal relationships. The rapid increase in problematic gaming behavior highlights the urgent need for scientifically grounded strategies to understand, predict, and effectively control the spread of PUBG Mobile addiction at the population level. In this study, we created a deterministic mathematical model of PUBG Mobile addiction (PMA) and an optimal control model for it. Qualitative analysis was analyzed, including the basic reproduction number, the addiction-free equilibrium point, and the addicted persistence equilibrium point. The PUBG Mobile addiction-free equilibrium point (PMAFE) is locally asymptotically stable if. The Castillo-Chavez theorem is used to establish the global asymptotic stability of PMAFE. If, the unique addicted persistence equilibrium points is asymptotically stable locally. The model exhibits a forward bifurcation using the Center Manifold theorem at. The sensitivity analysis is performed to determine the most sensitive parameters. In the numerical simulation of the PMA model, the NSFD scheme is implemented, and the addicted and treated populations gradually decrease, stabilize, and drop over time, demonstrating the model’s accuracy. We also created an optimal control model, added two time-dependent controls to the original model, and applied Pontryagin’s maximum principle to perform optimal control analysis. The efficiency analysis is performed to investigate the optimal control strategy. The numerical simulations of the suggested optimal control PMA model approach utilize the fourth-order Runge-Kutta forward-backward sweep method. Finally, we conclude that stakeholders and policymakers must use the integrated control strategy C to control the PUBG Mobile addiction population worldwide.
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A BEHAVIOR–CLIMATE COUPLED SIR MODEL FOR DENGUE TRANSMISSION: A DATA-DRIVEN APPROACH FOR BANGLADESH
(2026-01-01)
Parvez, Md Mashud
;
Kholil, Md Ibrahim
;
Rehman, Daniyal Ur
;
Aalam, Balal
We investigate the joint roles of climate variability and human preventive behavior in dengue transmission in Bangladesh by developing a Behavior–Climate Coupled Susceptible–Infected–Recovered (BC–SIR) model. The model integrates a climate suitability index derived from rainfall and temperature with a behavioral compliance variable that represents both adoption and fatigue of preventive actions. The transmission rate is jointly modulated by climate and behavior, enabling data-informed parameter estimation. We establish positivity and boundedness of solutions, derive the basic reproduction number ℛ<inf>0</inf>, and analyze the local stability of the disease-free equilibrium. Sensitivity analysis identifies climate suitability and behavioral efficacy as key drivers of transmission intensity. Numerical experiments indicate that sustained behavioral adherence can substantially mitigate outbreaks even under favorable climatic conditions. The BC–SIR framework provides a flexible basis for incorporating environmental and behavioral factors into dengue control strategies.

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