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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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Fractional-order Modeling and Optimal Control of Dengue-Malaria Co-infection with Local and Advanced Treatment Strategies
(2026-01-01)
Pongsumpun, Puntipa
;
Ud Din, Rahim
;
Ullah, Atta
;
Pongsumpun, Puntani
Abstract: This study presents a novel fractional-order co-infection model describing the joint transmission dynamics of dengue and malaria using the generalized fractional derivative. The total human population is divided into eight epidemiological compartments that account for single infections, co-infection, treatment stages, and recovery. The proposed framework incorporates memory effects and nonlocal behavior, offering a more realistic representation of disease progression compared to classical integer-order models. Local and advanced treatment strategies are introduced based on infection severity, allowing targeted intervention for both mild and co-infected cases. The fundamental mathematical properties of the model, including positivity, boundedness, existence, and uniqueness of solutions, are rigorously established. The basic reproduction number is derived, and both local and global stability of the disease-free equilibrium are analyzed using suitable Lyapunov functions. A statistical sensitivity analysis is performed to identify key parameters influencing disease transmission. Furthermore, optimal control strategies are formulated to minimize co-infection prevalence while reducing treatment and implementation costs. Numerical simulations validate the theoretical findings and demonstrate that fractional-order dynamics provide deeper insights into long-term disease behavior. The results offer valuable guidance for policymakers in designing effective and cost-efficient strategies to control dengue and malaria co-infection. Graphic Abstract: (Figure presented.) The
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Fractional ABC Dynamics and Nonlinear Transmission Analysis of Dengue–Malaria Co-infection with Reinfection
(2026-01-01)
Lamwong, Jiraporn
;
Pongsumpun, Puntani
The persistent co-circulation of dengue and malaria in tropical regions poses a significant epidemiological challenge, particularly because classical integer-order models fail to capture the memory-driven reinfection, relapse, and recrudescence mechanisms that sustain long-term disease transmission. To overcome these limitations, this study develops a high-dimensional nonlinear co-infection model formulated using the Atangana–Baleanu–Caputo (ABC) fractional derivative, which incorporates nonsingular and nonlocal kernels to realistically represent hereditary effects in host–vector dynamics. The model integrates primary and secondary dengue infections, recurrent malaria pathways, and interactions across two mosquito species within a unified fractional-order framework. Analytical results establish positivity, boundedness, and existence–uniqueness of solutions, and the basic reproduction number R<inf>0</inf> is rigorously derived via the next-generation matrix method. Numerical simulations reveal that decreasing the fractional order substantially prolongs transient dynamics, increases infection peaks, and strengthens disease persistence relative to the classical system; in particular, when, both pathogens exhibit sustained endemicity amplified under fractional dynamics. These findings demonstrate that memory effects encoded by the ABC operator play a critical role in shaping reinfection outcomes, cross-immunity decay, and recurrent malaria episodes. The proposed framework provides a mathematically rigorous and epidemiologically insightful foundation for understanding nonlinear co-infection dynamics and underscores the importance of fractional calculus in improving predictive modeling and informing long-term vector-borne disease control strategies.
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Correction: Fractional ABC Dynamics and Nonlinear Transmission Analysis of Dengue–Malaria Co-infection with Reinfection (Earth Systems and Environment, (2026), 10.1007/s41748-026-01258-5)
(2026-01-01)
Lamwong, Jiraporn
;
Pongsumpun, Puntani
The authors wish to correct an error in Figs. 2, 3, 4, 5 and 6 of the above-referenced article (https://doi.org/10.1007/s41748-026-01258-5), with regard to the omission of several subfigures in the online published version. Specifically, subfigures 2g–2q in Fig. 2, subfigures 3g–3q in Fig. 3, subfigures 4g–4h in Fig. 4, subfigures 5g–5h in Fig. 5, and subfigures 6g–6h in Fig. 6 were omitted. The corrected figures are provided below. Time–series dynamics of the dengue–malaria co-infection model under varying fractional orders (ABC derivative) Three-dimensional surface representations of the dengue–malaria co-infection dynamics under varying fractional orders (ABC derivative) Three-dimensional surface plots comparing the effects of different mosquito biting rates on the dengue–malaria co-infection dynamics at the fractional order Three-dimensional surface plots illustrating the impact of varying transmission probabilities from aedes mosquitoes to humans during primary dengue infection at the fractional order Three-dimensional surface plots comparing the effects of different transmission probabilities from dengue-infected humans to aedes mosquitoes during primary infection at the fractional order
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The role of a vaccine booster for a fractional order model of the dynamic of COVID-19: a case study in Thailand
(2025-12-01)
Pongsumpun, Puntipa
;
Pongsumpun, Puntani
;
Tang, I. Ming
;
Lamwong, Jiraporn
This article addresses the critical need for understanding the dynamics of COVID-19 transmission and the role of booster vaccinations in managing the pandemic. Despite widespread vaccination efforts, the emergence of new variants and the waning of immunity over time necessitate more effective strategies. A fractional-order mathematical model using Caputo-Fabrizio derivatives was developed to analyze the impact of booster doses, symptomatic and asymptomatic infections, and quarantine measures. The model incorporates real epidemic data from Thailand and includes a sensitivity analysis of parameters influencing disease spread. Numerical results indicate that booster vaccinations significantly reduce transmission rates, and the model’s predictions align well with the observed data. The basic reproduction number was determined to evaluate disease control, showing that a sustained vaccination campaign, including booster doses, is essential to maintaining immunity and controlling future outbreaks. The findings underscore the importance of ongoing vaccination efforts and provide a robust framework for policymakers to design effective strategies for pandemic control.
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Dynamical Model of Hand Foot Mouth Disease With the Effect of Vaccination
(2025-10-06)
Pongsumpun, Puntani
Hand, foot and mouth disease is caused by enter viruses, including Coxsackie and Enter virus 71 or EV71. It is often found in young children. In this study, the author formulates the differential equations which describe the transmission of Hand, foot and mouth disease incorporating the vaccination. A dynamic model is proposed for the purpose. The differential equations are analyzed by standard dynamical modeling method. The basic reproduction number is found to reduce the transmission of this disease. The numerical solutions are presented to confirm analytical results.
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Dengue Disease Transmission Model in the Central and the Other Regions in Thailand
(2025-10-06)
Pongsumpun, Puntani
The disease has occurred between Aedes mosquitoes and people, called as dengue disease. The transmission of this disease between the central region and the other regions are different. We formulated the mathematical model for this disease by considering human and vector populations. Human is separated as Susceptible, infectious, and recovered population. The vector population is divided into susceptible and infectious population. We considered the spread of dengue disease in two regions. The mathematical model is analyzed. The steady states are found in the study. The condition for the stability of our steady states is determined from experiments. The numerical solutions are present in the study. The way for controlling dengue transmission is identified and possible solutions are discussed.

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