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Pendekatan Geometris untuk Model Predator-Prey dengan Carrying Capacity pada Populasi Prey Marshellino; Tasman, Hengki; Rusin, Rahmi
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.2024.7.2.1

In this paper, we explore a classical predator-prey model where the birth rate of the prey is significantly lower than the mortality rate of the predators, while also considering a limited prey population. We incorporate an environmental carrying capacity factor for the prey to account for this. Given the different timescales of the predator and prey populations, some system solutions may exhibit a fast-slow structure. We analyze this fastslow behavior using geometric singular perturbation theory (GSPT), which allows us to separate the system into fast and slow subsystems. Our research investigates the existence and stability of equilibrium solutions and the behavior of solutions near the critical manifold. Additionally, we use an entry-exit function to analytically establish the connection between the solutions of the slow subsystem and those of the fast subsystem.

Numerical Bifurcations and Sensitivity Analysis of an SIVPC Cervical Cancer Model Asih, Tri Sri Noor; Adi-Kusumo, Fajar; Wiraya, Ario; Forde, Jonathan
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.2024.7.2.8

We consider a mathematical model of cervical cancer based on the Natural History of Cervical Cancer. The model is a five dimensional system of the first order of ordinary differential equations that represents the interaction between the free Human Papilloma Virus (HPV) population and four cells sub-populations, i.e., the normal cells, infected cells by HPV, precancerous cells, and cancer cells. We focus our analysis to determine the existence conditions of the nontrivial equilibrium point, the bifurcations, and the sensitivity of the parameters that play important roles in metastasis. Based on the basic reproduction ratio of the system, we found that the infection rate, the new viruses production rate, the free viruses death rate, the infected cells growth rate, and the precancerous cells progression rate play important roles for the cancer spreads in the cellular level. By applying sensitivity and numerical bifurcation analysis, we found that there are some important bifurcations that trigger some irregular behaviours of the system, i.e., fold, Hopf, cusp and Bogdanov-Takens.

Modeling the Co-Infection Dynamics of COVID-19 and Dengue: Well-posedness, Analysis of Equilibrium Properties, and Policy Implications through Numerical Simulations Blase, Wyeth Ian C.; Balsomo, Alexander J.; Sabinay, Stephen G.
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.2024.7.2.2

COVID-19 is an infectious disease primarily transmitted to individuals through direct contact with respiratory droplets. The infection, caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), continues to spread globally infecting around 776 million confirmed cases, including over 7 million deaths. Meanwhile, dengue is a vector-borne disease caused by the Flaviviridae virus and is transmitted through bites from female mosquitoes, primarily Aedes aegypti and Aedes albopictus. It is estimated that 390 million dengue virus infections occur per year caused by four distinct virus serotypes–DENV-1, DENV-2, DENV-3, and DENV-4. The COVID-19 pandemic has further strained public health systems, particularly in tropical and subtropical regions where dengue is endemic. The overlapping presence of these infectious diseases heightens the risk of co-infection, posing additional diagnostic and treatment challenges. Co-infection of COVID-19 and dengue cases were already reported and confirmed in several countries. In this study, an 11-compartmentalized deterministic mathematical model was developed to understand the transmission dynamics of COVID-19 and dengue co-infection. This modeling approach was described by a system of ordinary differential equations (ODEs), examining disease progression over time, offering insights into potential co-infection scenarios andcontrol strategies to help guide public health interventions. The well-posedness of the model was verified, ensuring the existence and uniqueness of its solutions based on continuity, local Lipschitz conditions, and invariance over a compact feasible region. The basic reproduction number (R0), a significant indicator of disease transmission, was calculated using the Next Generation Method (NGM). Four equilibrium points were identified: the disease-free, COVID-19-only, dengue-only, and COVID-19-dengue co-infection equilibrium points. Threshold values of the basic reproduction number were calculated to establish the conditions for the existence and stability of the equilibrium points. These equilibrium points and threshold values provide critical insight into the conditions necessary for eradicating or controlling each disease, serving as a guide for developing interventions during different stages of an epidemic or pandemic. Furthermore, a phase diagram of two parameters sensitive to R0 (COVID-19 transmission βc and dengue vector-to-human transmission Cvh) was established which presented six distinct regions of existence and stability states of the equilibrium points. These regions described different stable epidemiological scenarios whenever the parameter values were varied. Numerical simulations were conducted to verify the stability results and to analyze the effects of varied parameter values on the model solution. The simulations illustrated the positive impacts of reducing the recovery period on the spread of infections even with increasing transmission rates. This demonstrates the effectiveness of timely interventions, such as accelerated recovery through early diagnosis and treatment, in mitigating the severity of outbreaks. All the algebraic calculations, analysis, and numerical simulations were conducted with the aid of MATLAB R2023b and Maple software.

Gravity Model Approach to Model Epidemic with Human Dispersal Behaviors Dinasiri, A.S.K.; Jayathunga, Y.
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.2024.7.2.5

The gravity model which is based on Newton’s gravitational law, has been widely used as a spatial interaction model in the past few decades. Spatial interactions are important in epidemic modeling as different populations in the world are interconnected by them. Human dispersal behaviors are spatial interactions and they are crucial aspects of infectious disease spread. However, many existing compartmental models model epidemics in a single area. Hence, a gravity model approach to model epidemics incorporated with a multipatch compartmental model is studied here. Both human dispersal behaviors within a patch and between patches are considered. When the human dispersal behaviors within a patch are modeled, the denominator of the general gravity model becomes zero. An alternative power-based distance decay function is introduced to the gravity model to address that research gap. The parameters of the modified gravity model are estimated using a hybrid method combining ordinary least squares (OLS) and nonlinear least squares (NLS) methods (Hybrid OLS-NLS method).

Penyebaran Rumor dalam Masyarakat: Sebuah Pendekatan Pemodelan Matematika dalam Studi Kasus Pemilihan Umum Septyawan, Stefanus Raynaldo; Bunga, Esther Yolandyne; Nuraini, Nuning; Arcede, Jayrold P.
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.2022.7.2.3

Rumors can be defined as unverified information or statements shared by people that may be positive or negative and circulate without confirmation. Since humans naturally seek factual information for social and self-enhancement purposes, rumors become an inevitable aspect of human life, including in politics, such as elections. The complexity of the electoral process, with various factors such as individual candidates, social circumstances, and particularly the media, leads to the dynamic spread of rumors in society. Thus, it is both interesting and important to understand the dynamics of rumor spreading, particularly in the context of elections. In this article, we formulate a mathematical model of rumor spread dynamics based on different attitudes of people toward rumors. The model considers the spread of rumors about two candidates in the electoral context. From the model, we derived and investigated the basic reproductive number (R0) as a threshold for rumor spread and conducted a sensitivity analysis with respect to all the model parameters. Based on numerical experiments and simulations, it was revealed that the number of people resistant to or disbelieving in rumors increases significantly in the first ten days and remains higher than other subpopulations for at least after first seven days. Furthermore, we found that a high number of people directly affected by rumors, combined with the rumor transmission rate for both candidates being greater than each other, are necessary and sufficient conditions for rumors to circulate rapidly and remain stable in society. The results of this study can be interpreted and considered as a campaign strategy in an electoral context.

Modeling of Abstinence Behavior on the Electoral Lists with Awareness Campaigns and Argumentative Schemes Beay, Lazarus Kalvein; Panigoro, Hasan S.; Rahmi, Emli; Savitri, Dian
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.2024.7.2.4

The most reasonable way to promote individual abstinence and increase voter turnout is through campaign interventions and schemes. Our paper introduces a deterministic model that captures the dynamics of citizens exercising their right to vote and the detrimental effect of abstainers on potential voters. The existence, basic reproductive number (R0) and local stability of abstinence behavior equilibrium points are determined by certain necessary conditions. The global stability of the abstaining-free point and abstaining point is achieved through the use of suitable Lyapunov functions. In addition, a sensitivity analysis of R0 was also performed. Moreover, we offer an ideal plan for an awareness program that supports politicians and officials in enhancing the registration rate of citizens on electoral lists with a level of effort. Our investigation reveals that utilizing the combination of an awareness campaign and argumentation schemes as time-dependent interventions drastically reduces abstention rates and greatly increases voter participation. By raising the values of awareness and registration rates, we can observe a decline in the basic reproductive number (R0). Our analytical results are supported by numerical simulations.

Age-Structured SILV Epidemic Model on HPV and Cellular Dynamics with Implicit Impact of Vaccination Akimenko, Vitalii
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.2024.7.2.7

The implicit impact of vaccination on susceptible cells (epithelial layer) is studied on the basis of stability analysis of age-structured epidemic model of susceptible cells, infected cells and cells of lesion tissue (dysplasia and cancer), human papillomavirus (HPV). The efficacy of the vaccine indirectly influences the coefficients of the system, thereby determining the types of dynamical regime of the HPV and cellular population. The model possesses unique disease-free (DFE) and unique endemic equilibria (EE) (Theorem 1). The asymptotically stable DFE is associated with the resilience of epithelial layer of vaccinated organism to HPV infection while the asymptotically stable EE is associated with the resilience of the lesion tissue of epithelial layer to treatment. The analysis of the model reveals independent factors affecting the stability/instability of DFE and EE (Theorems 2, 3): (i) cell death rate and proliferation rate, (ii) HPV infection rate, budding number of HPV virions, apoptosis rate of infected cells and HPV death rate (parameters of the implicit influence of vaccine efficacy), and (iii) DFE value of epithelial tissue size (environmental capacity of HPV depending on the initial size of the epithelial layer). Thus, HPV vaccine efficacy should be sufficiently high to guarantee the asymptotic stability of DFE with the epithelial tissue of large possible size, which can be taken into account when studying the efficacy of new vaccines in control groups in clinical trials.

Optimal Control Strategies for the Population Management of the Bali Starling: A Mathematical Modeling Approach Gandhiadi, G.K.; Tastrawati, N.K.; Gautama, P.W.; Dharmawan, K.
Communication in Biomathematical Sciences Vol. 8 No. 2 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.2.3

The Bali Starling (Leucopsar rothschildi), an endemic species of Bali, faces severe threats from habitat loss, poaching, and environmental changes, necessitating effective conservation strategies. This study presents a mathematical model to describe the population dynamics of the Bali Starling within the breeding center at USS Tegal Bunder, TNBB, integrating optimal control theory to improve conservation efforts. The model incorporates key biological factors such as growth, transfer, and habituation processes, and utilizes Pontryagin’s Maximum Principle to determine an optimal control strategy that balances population sustainability with resource efficiency. Numerical simulations compare controlled and uncontrolled scenarios, highlighting the impact of different control cost weights (q) on population management. The results suggest that moderate control interventions (q = 0.06 − 0.10) are most effective, ensuring sustainable population growth while min- imizing intervention costs. These findings provide valuable insights for optimizing captive breeding programs and offer a scientific basis for adaptive conservation strategies to protect endangered species like the Bali Starling.

Analyzing Mask-Wearing Decisions Using Game Theory and the SIR Model with a Replicator Equation in Post-Pandemic Situations Nasution, Yuki Novia; Rizqo, Muhammad Abyan; Nuraini, Nuning; Apri, Mochamad; Susanto, Hadi
Communication in Biomathematical Sciences Vol. 9 No. 1 (2026)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2026.9.1.1

During the COVID-19 pandemic, many countries implemented policies on using masks to control the outbreak. This policy has been relaxed in almost all countries, after which. Respiratory disease outbreaks re-emerged in several countries, including Indonesia. This article presents a game-theoretic model of mask use by the community during the spread of the disease. Both the effectiveness of masks in preventing the spread of the disease and the proportion of the infected population are included in the payoff calculation. The model is combined a with the Susceptible-Infectious-Recovered (SIR) epidemic model with the replicator equation. The model is also evaluated under Nash equilibrium conditions. Simulations are carried out to effect of mask-wearing behavior on the incidence of acute respiratory infection in Jakarta. The results show that an individual's decision to use a mask is directly proportional to mask users. To reduce the number of infections, more than 10% of the population need to wear masks when the disease first appears. In the Nash equilibrium, we obtain a threshold value of the infected population at which the players decide not to use the mask. The results suggest that when respiratory infectious diseases emerge, governments must implement a stringent mask policy to control their spread and reduce infections.

A Nonlinear Delay Mathematical Model for Predicting Chlamydia Dynamics and Intervention Effects Zeb, Shah; Mohd Yatim, Siti Ainor; Kamran, Ayesha; Zulfiqar, Sabahat; Rafiq, Muhammad; Mohamad Noor, Nursyazwani
Communication in Biomathematical Sciences Vol. 8 No. 2 (2025)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2025.8.2.1

Chlamydia is a widespread sexually transmitted infection in Europe, often leading to complications such as rectal discomfort, throat inflammation, and reactive arthritis. This study presents a novel nonlinear delay differential equation model that enhances the classical SEIAISR framework to more accurately represent Chlamydia transmission dynamics. The model integrates biologically justified exponential time delays to reflect incubation periods and the delayed impact of interventions like condom use, routine screening, partner reduction, and microbiome health. We establish the existence and uniqueness of solutions using the Banach fixed point theorem and analyze the model’s dynamics by computing the basic reproduction number and studying equilibria and their stability via Lyapunov functions and Routh-Hurwitz criteria. A sensitivity analysis identifies key epidemiological drivers. For numerical simulation, we employ Euler’s method, the Runge-Kutta 4th order (RK4) method, and a specially developed non-standard finite difference (NSFD) scheme. The NSFD approach preserves critical properties such as positivity and stability, making it suitable for realistic long-term predictions. Results highlight the importance of timely interventions and show the superiority of structurepreserving numerical methods. The findings support the development of more targeted and effective strategies to reduce chlamydia transmission and complications among high-risk groups, reinforcing evidence-based decisionmaking within the healthcare system.

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Contact Name
-

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Journal Mail Official
cbms@lppm.itb.ac.id

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

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Unknown,

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INDONESIA