Cost-Effectiveness and Optimal Control Strategies for Managing Marburg Virus Infections

Zasmin Haque; Md. Mashih Ibn Yasin Adan; Md. Kamrujjaman

doi:10.22342/jims.v32i1.1858

Zasmin Haque ⁽¹⁾ , Md. Mashih Ibn Yasin Adan ⁽²⁾ , Md. Kamrujjaman ⁽³⁾

(1) Department of Mathematics, American International University-Bangladesh, Bangladesh,

(2) Department of Mathematics, Kishoreganj University, Bangladesh,

(3) Department of Mathematics, University of Dhaka, Bangladesh

https://doi.org/10.22342/jims.v32i1.1858

Issue
Vol. 32 No. 1 (2026): MARCH

Submitted
November 24, 2024

Accepted
November 29, 2025

Published
April 14, 2026

Keywords:

Optimal control, cost-effectiveness,, natural immunity, numerical simulation, protective measure

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Abstract

This study develops a mathematical model to investigate the transmission dynamics of Marburg Virus Disease (MVD), integrating two time-dependent control strategies, primarily focusing on isolating infected individuals. Optimal control strategies are designed using Pontryagin's Maximum Principle to minimize the spread of the infection. The basic reproduction number is calculated to identify the disease-free and endemic equilibrium points. The analysis highlights the effectiveness of interventions such as personal protective measures (e.g., wearing masks, maintaining hand hygiene, and avoiding risky dietary practices) combined with supportive hospital therapy in curbing disease transmission. Model simulations validate the impact of these optimal control strategies, while a cost-effectiveness analysis identifies the most efficient approach for disease management. Additionally, the study examines how individuals with robust immune systems can influence the overall dynamics of Marburg virus transmission.

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Authors

Zasmin Haque

Department of Mathematics, American International University-Bangladesh

Md. Mashih Ibn Yasin Adan

Department of Mathematics, Kishoreganj University

Md. Kamrujjaman

Department of Mathematics, University of Dhaka

kamrujjaman@du.ac.bd (Primary Contact)

Haque, Z., Adan, M. M. I. Y., & Kamrujjaman, M. (2026). Cost-Effectiveness and Optimal Control Strategies for Managing Marburg Virus Infections. Journal of the Indonesian Mathematical Society, 32(1), 1858. https://doi.org/10.22342/jims.v32i1.1858

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1. Introduction

Marburg disease is a rare but severe hemorrhagic fever caused by the Marburg virus, a member of the Filoviridae family. This disease can lead to serious illness and has a high fatality rate, with case fatality rates varying from 24% to 88% depending on the virus strain and case management [1,2]. The virus was first identified in 1967 in West Germany and is transmitted through direct contact with infected individuals or animals, not through the air. Symptoms include sustained high fevers, confusion, irritability, and, in advanced stages, orchitis[3]. Since its emergence, Marburg virus outbreaks have been reported in several countries, including Angola, Kenya, and Uganda, with a recent outbreak in Ghana in June 2022[2]. These incidents highlight the ongoing risk of transmission, particularly through unprotected contact in healthcare settings and communities. The disease’s impact varies significantly across regions. For instance, Uganda reported a total of 19 cases from 2012 to 2017, resulting in a mortality rate of 42%. Angola recorded the highest number of cases in 2005, with 374 cases and a mortality rate of 88%. The Democratic Republic of the Congo documented 154 cases between 1998 and 2000, exhibiting an 83% mortality rate. In contrast, both the United States and Yugoslavia showed significantly lower case counts and fatalities, with mortality rates of 0%[2]. This variability underscores the importance of context in understanding the disease’s epidemiology. This study employs a mathematical model to investigate the transmission dynamics of Marburg virus disease (MVD), focusing on two time-dependent control strategies that prioritize the isolation of infected individuals. Utilizing optimal control strategies based on Pontryagin’s Maximum Principle [4,5], we calculate the basic reproduction number \(\left( R _ { B } \right)\) to identify disease-free and endemic equilibrium points. Our findings indicate that efective control measures, including isolation of infected individuals and personal protective practices, can significantly reduce disease transmission. Additionally, we explore the role of robust immune systems in influencing infection dynamics, providing valuable insights for efective MVD management and highlighting the importance of both individual behaviors and broader healthcare strategies in combating infectious diseases.

In this study, we constructed a deterministic mathematical model to analyze the transmission dynamics of Marburg Virus Disease (MVD). The model incorporates two time-dependent control strategies, primarily focusing on the isolation of infected individuals. By employing Pontryagin’s Maximum Principle [6,7,8], we determined optimal control strategies that minimize infection levels[9]. The main goal of our research is to explore how isolating infected individuals afects the spread of MVD [10,11]. We assessed the influence of individuals with natural immunity and the importance of supportive hospital care in controlling the overall infection rate. To achieve this, we calculated the basic reproduction number \(\left( R _ { B } \right)\) a crucial epidemiological metric representing the average number of secondary infections generated by a single infected individual in a fully susceptible population. This calculation helps identify both disease-free and endemic equilibrium points [12,13], providing insights into the conditions required for disease eradication or persistence. Our model also accounts for personal protective measures, such as wearing masks and practicing good hygiene, which are vital for managing infection spread. Furthermore, we explored complementary and alternative medicine (CAM) practices, including herbal remedies and nutritional support, as adjuncts to conventional care [14,15]. While these treatments can improve health and well-being, they should be used under the guidance of qualified practitioners to ensure safety and efectiveness. Simulations of the optimal control model consistently demonstrate a significant reduction in infection levels when these strategies are applied [16,17]. This highlights the importance of a multifaceted approach to combating

MVD, where isolation, natural immunity[18], personal protective measures, and supportive medical care work together to mitigate disease impact. Maintaining a healthy diet is crucial for a strong immune system, which is essential for eradicating viral infections [19,20]. Key recommendations include:

Incorporating a diverse selection of fruits and vegetables rich in essential vitamins, minerals, and antioxidants.

Including lean protein sources such as poultry, fish, beans, and legumes to support tissue repair and growth.

Consuming healthy fats from avocados, nuts, seeds, and olive oil.

Incorporating probiotics through yogurt and fermented foods to maintain gut health.

Staying hydrated and engaging in regular physical activity.

Additionally, adequate sleep, stress management techniques (such as meditation and yoga), and good hygiene practices are vital for overall health. Avoiding smoking and limiting alcohol intake further enhance immune function. Spending time outdoors for sunlight exposure helps produce vitamin D, crucial for immune health. Numerous herbal formulations have demonstrated efectiveness in treating viral infections [21,22]. Herbal supplements like echinacea, elderberry, and garlic are believed to enhance immunity. Maintaining a healthy weight, fostering social connections, and engaging in regular exercise contribute to overall health and improved immune responses. This study ofers valuable insights into the efective management of Marburg Virus Disease, emphasizing the significance of individual actions in strengthening the immune system and the role of systemic healthcare strategies in controlling infectious diseases.

2. Model Formulation

Mathematical modeling provides representations of real-world situations, enabling predictions and insights into viral diseases [23,24,25]. In this study, we develop a deterministic SEIR (Susceptible, Exposed, Infected, Recovered) model that

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Cost-Effectiveness and Optimal Control Strategies for Managing Marburg Virus Infections

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