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Optimal Control for Resource Allocation in a Multi-Patch Epidemic Model with Human Dispersal Behavior Adikari, A.U.S.; Jayathunga, Y.
Communication in Biomathematical Sciences Vol. 8 No. 1 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.1.1

A multi-patch epidemic compartmental model with human dispersal behavior studies the spread of the disease and it sets the model to real-world situations. The mobility matrix (M) applies human dispersal behavior to the model. The optimal control theory assists in controlling the disease burden while minimizing the cost of infected individuals and implementing control measures. We formulate a multi-patch SIR model with human dispersal behavior to control and reduce communicable disease outbreaks such as COVID-19 by optimizing resource allocation in Sri Lanka. Results are represented by using the reproduction number (R0), effective reproduction number (Rt), and final epidemic size (ci). Compared to the basic reproduction number (R0), the effective reproduction number (Rt) represents the significant result in the epidemiological model incorporated with control measures. The average number of secondary cases concerning the current susceptible population is represented by Rt and the final epidemic size represents the patched-specified cost value for infected individuals. According to the results, the disease burden can be controlled by vaccination relative to social distancing.

Mathematical Model for the Growth of Mycobacterium Tuberculosis Infection in the Lungs: Dewanti, Retno Wahyu; Widianto, Wisnu Prasojo; Apri, Mochamad; Nuraini, Nuning; Fakhruddin, Muhammad
Communication in Biomathematical Sciences Vol. 8 No. 1 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.1.8

In this work, we develop a population dynamics model of Mycobacterium tuberculosis (Mtb), the bacteria responsible for tuberculosis (TB), to evaluate the impact of bacterial competition on infection prevalence. We consider two types of Mtb population growth: The first is caused by bacteria that grow inside each infected macrophage and is believed to be correlated with the number of infected macrophages; The second is that extracellular bacteria grow through self-replication. In this study, we modeled the immune response to Mtb bacterial infection in the lungs using a five-dimensional differential equation system. This model represents changes in the number of healthy macrophages, infected macrophages, activated macrophages cells, extracellular bacterial particles, and naive T cells. Qualitative analysis and numerical results reveal the existence of two equilibrium points: disease-free equilibrium and endemic equilibrium, which represent latent or active tuberculosis based on the number of bacteria. In addition, a sensitive analysis of the model parameters shows that macrophages are not sufficient to control the initial invasion of Mtb. The immune system must therefore employ more complex defense mechanisms to contain Mtb infection, such as recruiting various elements of immune system and forming granulomas.

Linear Mixed Model for Oil Palm Parents Selection Sonhaji, Abdullah; Pasaribu, Udjianna Sekteria; Indratno, Sapto Wahyu; Pancoro, Adi
Communication in Biomathematical Sciences Vol. 8 No. 1 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.1.3

The objective of plant breeding is to obtain superior seeds. These seeds originated from parents that can pass their superior traits to their progeny. The observed characteristics of the progeny (phenotype) determined the traits of these seeds. Therefore, we performed a progeny analysis. In this analysis, the data samples were collected from Riau in Sumatera and Kumai in Kalimantan (two locations). The main objective is to find superior parents from these two locations. The superiority of the selected parents lies not only in passing high production traits but also in adaptability (fit) to the diversity or variability of the environment or locations. This analysis calculates the General Combining Ability (GCA) values for both male and female parents using the Linear Mixed Model (LMM). The experimental design, as the source of data, was an alpha lattice design, so the LMM contains locations, replicas, blocks, male and female parents, and the progeny factors. The analyzed phenotype is Fresh Fruit Bunches of third-year production. Since the data sets of the two locations were nonintersect, the model uses the coefficient of parentage (additive relationship matrix) to link both. The results of the GCA analysis showed that selected female parents were 137, 155, 126, 147, and 159 (Dura), and 101, 113, 109, and 117 for male parents. They are among the parents with highly productive progenies. There are also new potential crossings not currently available on the plantation - for example, the crossing 137 x 101 with the additive genetic value of 35.37.

An Isolation Model for Tuberculosis Dynamics with Optimal Control Application Sangotola, Adekunle Oluseye; Adigun, Aanuoluwapo Joshua; Nuga, Oluwole Adegoke; Adeyemo, Simeon; Kataboh, Pascal Kingsley; Akinde, Oluwashola Temitayo; Obabiyi, Olawale Sunday
Communication in Biomathematical Sciences Vol. 8 No. 1 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.1.4

Tuberculosis (TB) remains a persistent global health challenge, worsened by asymptomatic carriers who contribute to undetected transmission. An SIQR mathematical model that classifies infected individuals into symptomatic and asymptomatic classes, with isolation as the primary intervention, is formulated in this study. We establish the positivity and invariant region to ensure epidemiological relevance and derive the basic reproduction number, R0, as a threshold for disease persistence. The model analysis reveals that the diseasefree equilibrium is both locally and globally asymptotically stable if R0 < 1, while an endemic equilibrium also exists if R0 > 1. The key parameters influencing transmission dynamics are identified through sensitivity analysis. Furthermore, an optimal control framework is formulated using the Pontryagin’s maximum principle to assess the efficacy of isolation in reducing disease burden while minimizing associated costs. Numerical simulations demonstrate that well-implemented isolation significantly curtails TB spread, highlighting its potential as a targeted intervention.

A Vaccination and Isolation Strategy Based on an Adaptive Sliding Mode Control Design for the COVID-19 Virus (Omicron Variant) in Jakarta, Indonesia Suhika, Dewi; Saragih, Roberd; Handayani, Dewi; Apri, Mochamad
Communication in Biomathematical Sciences Vol. 8 No. 1 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.1.2

The Omicron variant, identified as B.1.1.529, has been recognized as a variant of concern (VOC) by the World Health Organization (WHO), necessitating continuous monitoring and a proactive response. This study develops a mathematical model to analyze the spread of COVID-19 mutations, considering a population that, despite vaccination, remains susceptible to infection. The model also accounts for key epidemiological factors, including the incubation period, quarantine measures, and various intervention strategies. This study focuses on the epidemiological conditions in Jakarta Province, where the highest number of Omicron cases in Indonesia has been recorded. Real-world epidemiological data related to Omicron in Jakarta were collected between February 6, 2022, and May 6, 2022. Model parameters were estimated using genetic algorithm optimization. A significant challenge in epidemic modeling is the uncertainty of parameters, which can substantially affect the effectiveness of control measures. To address this challenge, an adaptive sliding mode control approach is introduced, allowing dynamic adjustments to parameter variations without requiring precise parameter estimation. This approach maintains system stability by enforcing a predefined sliding surface, making it inherently robust against uncertainties. The main goal of this approach is to gradually minimize infections attributed to the initial COVID-19 strain and the Omicron variant, while simultaneously decreasing the count of susceptible individuals by ensuring the system follows a specified reference trajectory. Additionally, an adaptive mechanism is implemented to account for unknown variations in the system using the Lyapunov stability theorem. Numerical simulations illustrate that adaptive sliding mode control significantly improves epidemic management, reducing infections by 92.8% for the original strain and by 96.87% for the Omicron variant when compared to an uncontrolled scenario. Furthermore, the basic reproduction number (R0) is lowered by 85.92%, confirming the efficiency of adaptive sliding mode control in mitigating the outbreak. Moreover, this study incorporates a cost-effectiveness analysis to assess the viability of various vaccination and isolation strategies. The findings contribute to epidemiological research by offering valuable insights for policymakers in designing effective and resilient intervention strategies for epidemic management.

Regresi Multiskala Tertimbang Geografis dan Temporal dengan LASSO dan Adaptif LASSO untuk Pemetaan Kejadian Tuberkulosis di Jawa Barat Habsy, Muhammad Yusuf Al; Rachmawati, Ro'fah Nur; Khotimah, Purnomo Husnul; Natari, Rifani Bhakti; Riswantini, Dianadewi; Munandar, Devi; Izzaturrahim, Muh. Hafizh
Communication in Biomathematical Sciences Vol. 8 No. 1 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.1.6

Tuberculosis (TB) is a global health issue caused by Mycobacterium tuberculosis and can affect any organ of the body, especially the lungs. The trend of TB cases varies between regions, and analytic assessment is required to identify the predictor variables. The purpose of this research is to compare the Multiscale Geographically and Temporally Weighted Regression (MGTWR) and the Geographically and Temporally Weighted Regression (GTWR) method, which both use Gaussian, Exponential, Uniform, and Bi-Square kernel functions, to identify significant variables in each region annually. The MGTWR method has the advantage of using a flexible bandwidth for each observation, that results in more accurate coefficient estimates. The sample used was 27 districts and cities in West Java Province, involving 36 variables divided into 5 dimensions, namely global climate, health, demography, population, and government policy, with a time span of 2019–2022. To overcome the problem of multicollinearity, the approach was carried out using the Least Absolute Shrinkage Selection Operator (LASSO) and Adaptive LASSO methods. In determining the best model, the prioritized criteria are to achieve the highest R2, which indicates the optimal level of model fit, as well as the smallest AIC, which indicates the most efficient model goodness of fit. The best model is MGTWR with LASSO variable selection on the Bi-Square kernel. This model has an R2 of 91.25% and the smallest AIC of 139.868. From the best model, each region emerged with a cluster structure affected by various variables from 2019 to 2022, providing an in-depth understanding of TB mapping that can assist in formulating more effective intervention measures.

Discrete Mathematical Model of Fast Food Consumption: Control Approach Difaa, Youssef; Khajji, Bouchaib; Benaissa, Hicham
Communication in Biomathematical Sciences Vol. 8 No. 1 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.1.5

We investigate a discrete-time model, PLSCQ, to describe interactions among fast food consumer categories, among five population categories: potential consumers (P), moderate consumers (L), excessive consumers (S), obese individuals (C), and individuals who have ceased fast food consumption (Q). We seek for an optimal strategy that minimizes the excessive consumer and obese populations while maximizing the number of individuals who stop or recover. We incorporate three control measures, representing media and education for potential consumers, healthy eating campaigns for excessive consumers, and treatment for obese patients. Employing the discrete-time Pontryagin maximum principle, we derive optimal controls and numerically solve the system in Matlab, verifying the strategy’s effectiveness through simulation results.

Mathematical Model of Dengue Transmission Dynamics with Adaptive Human Behavior Dayap, Jonecis A.; Rabajante, Jomar F.
Communication in Biomathematical Sciences Vol. 8 No. 1 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.1.7

Dengue fever, a viral disease spread by Aedes mosquitoes, is a significant public health issue in tropical and subtropical regions. Behavioral adaptations in response to perceived infection risks can significantly reduce disease incidence and prevalence through the adoption of control measures. However, most existing models developed to assess the mitigation of dengue only implicitly account for this adaptive behavior within the dynamics of disease transmission. In this paper, we propose a mathematical model that explicitly incorporates adaptive human behavior in response to community infection levels into the transmission dynamics of dengue and investigates how this behavior affects transmission. Analytical results of the model reveal that the diseasefree equlibrium is locally asymptotically stable when the basic reproduction number (R0) is less than 1. The model parameters are calibrated using daily dengue case data from the 2015 outbreak in Kaohsiung City, Taiwan, resulting in a calculated basic reproduction number (R0) of 1.42. Sensitivity analysis indicates that to reduce the reproduction number, efforts should focus on reducing mosquito-human contact, controllingthe mosquito population, and improving hospital treatment. Numerical simulations demonstrate that positive behavioral changes in response to increasing infection levels significantly reduce dengue cases when selfprotectiveand vector control measures are effectively implemented. Our results emphasize the importance of enhancing these behavioral changes to achieve a substantial reduction in dengue incidence. This highlights the critical role of reporting disease prevalence, educating individuals on effective dengue mitigation strategies, and ensuring access to resources necessary for high-efficacy self-protection and vector control measures. By promoting awareness and providing support for control measures such as mosquito repellents, bed nets, insecticide-treated curtains, and community clean-up drives to eliminate mosquito breeding sites, governments can significantly enhance the effectiveness of dengue control programs.

Erratum: Geometric Approach to Predator-Prey Model with Carrying Capacity on Prey Population Marshellino; Tasman, Hengki; Rusin, Rahmi
Communication in Biomathematical Sciences Vol. 8 No. 1 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.1.9

This erratum addresses inaccuracies found in the figure captions of the article titled "Geometric Approach to Predator-Prey Model with Carrying Capacity on Prey Population" [Marshellino, Tasman, H. and Rusin, R., Communication in Biomathematical Sciences, 7(2), pp. 162-176, 2024. DOI: 10.5614/cbms.2024.7.2.1].

Proactive and Post-Epidemic Behavioral Responses in a Periodic Environment with Delay: A Case Study of Influenza in Nova Scotia, Canada El Hail, Khalid; Khaladi, Mohamed; Ouhinou, Aziz
Communication in Biomathematical Sciences Vol. 7 No. 2 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.2.6

We present a delayed epidemic model in a periodic environment, taking into account behavioral changes. The model combines two types of behavioral responses: one responding to the progression of the epidemic and the other based on independent education of the epidemic. We establish the global stability of the diseasefree equilibrium and validate the model using real influenza data in Nova Scotia, Canada. Using numerical simulations, we compare the effects of behavioral changes early on with those that occur as the epidemic progresses. Our results highlight the important role of early and sustained educational efforts in controlling the spread of disease. Additionally, we examine the sensitivity of the basic reproduction number to various parameters, revealing that R0 is especially responsive to those associated with continuous education.

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Center for Mathematical Modeling & Simulation, Institut Teknologi Bandung, Jalan Ganesa No. 10 Bandung 40132, Indonesia

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INDONESIA