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Communication in Biomathematical Sciences
Published by Indonesian Biomathematical Society
ISSN : -     EISSN : 25492896     DOI : 10.5614/cbms
Core Subject : Social,
Social Sciences
Full research articles in the area of Applications of Mathematics in biological processes and phenomena
Arjuna Subject : Matematika - Matematika Terapan
Articles 117 Documents
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The 2021 Cholera Outbreak in Nigeria, Data and Models Used to Explore Controls and Challenges Collins, Obiora Cornelius; Duffy, Kevin Jan
Communication in Biomathematical Sciences Vol. 6 No. 2 (2023)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2023.6.2.8

Abstract

Cholera is an acute diarrhoeal illness that affects humanity globally, especially in areas where there is limited access to clean water and adequate sanitation. A Nigerian cholera outbreak from January 2021 to January 2022 resulted in many cases and deaths. A mathematical model that takes into consideration the challenges that affected effective implementation of control measures for this 2021 cholera outbreak is developed. Important epidemiological features of the model such as the basic reproduction number (R0), the disease-free equilibrium, and the endemic equilibrium are determined and analysed. The disease-free equilibrium is shown to be asymptotically stable provided R0 < 1. The model is shown to undergo forward bifurcation at R0 = 1 using the Centre Manifold Theorem. Sensitivity analysis is used to determine the parameters that have the highest influence on transmission. Fitting the model to data from the 2021 Nigerian cholera outbreak, important parameters of the model are estimated. The impact of control measures as well as challenges that affected the effective implementation of these control measures are considered.
Optimal Control Strategies on Mobility for Preventing COVID-19 Transmission: A study with A Three-Patch Compartmental Model Hansana, A.V.R.; Ganegoda, N.C.; Jayathunga, H.C.Y.
Communication in Biomathematical Sciences Vol. 7 No. 1 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.1.2

Abstract

Human mobility can be identified as one of the main factors that directly affect the spread of COVID-19. Accordingly, human mobility must be controlled in a proper way to deficit the spread of COVID-19 as the economy of a country depends on human mobility. Nevertheless, due to the lack of proper management of the lockdown restrictions, the economy of many countries has already suffered a severe decline. In this research, a compartmental model (SIR) has been presented using optimal control theory to deficit the spread of COVID-19. Thus, the districts of Sri Lanka were divided into three regions (three-patch), and two control variables, were used to control the normal human mobility within the region and between the region. Also, when designing the cost function, two competing factors which deficit the spread of COVID-19 and save the country's economy were considered. Furthermore, optimal solutions were obtained using the Pontryagin's maximum principle and the data related to the spread of COVID-19 in Sri Lanka from April 15 to May 15, 2021, have been used here. In this research, a lockdown policy has been mainly focused on formally imposing and removing lockdown restrictions to compromise both the competing factors of economic security and control the spread of disease. Based on the results, a clear idea could be obtained about the time limits that should be imposed lockdown restrictions within the region and between the regions. Consequently, it was apparent that starting the systematic removal of the lockdown limits within the regions and between the regions are approximately equal. Furthermore, effective reproductive number are used to check the spread of COVID-19. Hence, it can be assumed that the spread of disease is less when mobility controls are activated. The results which were obtained here can be used not only for COVID-19 but for any pandemic and endemic.
Impact of Nanomaterial in the Marine Environment: Through Mathematical Modelling by Eco-Path Framework Das, Kalyan; Srinivas, M.N.; Saikh, Aktar; Biswas, Md. Haider Ali
Communication in Biomathematical Sciences Vol. 7 No. 1 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.1.8

Abstract

We propose and analyze a simple modification to the Rosenzweig-MacArthur predator (zooplankton)-prey (phytoplankton) model to account for the interference of the predators with the impacts of nanoparticles. We have taken into account the influence of predators by quantifying the impact of nanoparticles in actual environments. It is shown that the influence of the nanoparticles may reduce the prey's maximum physiological per-capita growth rate. An elementary Lotka-Volterra uptake term is taken into consideration in order to investigate the nanoparticle dynamics or interactions. Most importantly, our research shows that phytoplankton growth suppression caused by nanoparticles can destabilize the system and cause periodic oscillation. Additionally, it was demonstrated that a decrease in the equilibrium densities of both phytoplankton and zooplankton might occur from an increase in the rate of interaction between the nanoparticles and phytoplankton. Additionally, the study shows that the stable coexistence of the system dynamics depends critically on the aquatic system's nanoparticles being depleted. We also looked into the system using different kinds of functional reactions. Compared to other commonly used ecology, The complex relationship that exists between phytoplankton and nanoparticles in the natural environment is better described by the Monod-Haldane functional response.
Combatting Malaysia's Dengue Outbreaks with Auto-Dissemination Mosquito Traps: A Hybrid Stochastic-Deterministic SIR Model Wells, Jonathan; Greenhalgh, David; Liang, Yanfeng; Megiddo, Itamar; Nazni, Wasi Ahmad; Guat-Ney, Teoh; Lee, Han Lim
Communication in Biomathematical Sciences Vol. 6 No. 2 (2023)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2023.6.2.7

Abstract

Classical mosquito control methods (e.g. chemical fogging) struggle to sustain long-term reductions in mosquito populations to combat vector-borne diseases like dengue. The Mosquito Home System (MHS) is an auto-dissemination mosquito trap, that kills mosquito larvae before they hatch into adult mosquitoes. A novel hybrid stochastic-deterministic model is presented, that successfully predicts the effect of deploying MHSs within high-rise flats in Selangor, Malaysia. Stochastic SIR (Susceptible-Infected-Recovered) equations (flats) are paired with an existing deterministic SIR model (wider Kuala Lumpur population). Model predictions provide excellent agreement with data from a 44 week MHS trial within the flats. The stochastic model is validated as a powerful tool for predicting short- and long-term impacts of deploying this style of trap within similar environments. Significant, sustainable reductions in mosquito populations are predicted when the MHS is active: with a mean of 9 (95% Uncertainty Range (UR): 1; 30) during the 44 week trial period, compared to 35 (95% UR: 1; 234) dengue cases with no MHSs. Long-term predictions for endemic equilibrium show MHSs significantly narrow the mosquito population distribution and reduce dengue prevalence: from a mean of 5 (95% UR: 0; 52) (no MHS), to 1 (95% UR: 0; 8) dengue cases annually (with MHS).
Deterministic Double Dose Vaccination Model of COVID-19 Transmission Dynamics - Optimal Control Strategies with Cost-Effectiveness Analysis Abidemi, Afeez; Fatmawati; Peter, Olumuyiwa James
Communication in Biomathematical Sciences Vol. 7 No. 1 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.1.1

Abstract

In this study, we propose a deterministic double dose vaccination model of COVID-19 transmission dynamics optimal control with cost-effectiveness analysis. It is imperative for decision-makers and the government to prioritize the application of preventive and control measures for COVID-19 based on efficiency and costbenefit analysis. This is pivotal in resource-constrained regions where the disease is endemic. Thus, this work is mainly devoted with the development and analysis of an optimal control for COVID-19 dynamics with five timevarying functions; first dose vaccination, second dose vaccination, personal protection, testing or screening, and treatment. The model is qualitatively analysed with the overall goal to minimize the spread of COVID-19 and the costs related to control implementation with the aid of optimal control theory. The effect of adopting each control intervention in each of the three distinct groups which are created by classifying all conceivable combinations of at least three control interventions is demonstrated through the numerical simulations of the optimality system. Using the average cost-effectiveness ratio and incremental cost-effectiveness ratio techniques, the most economical control intervention is determined for each group. The study reveals that when the resources are readily available, application of the strategy that combines optimal first dose vaccination, personal protection, screening or testing and treatment is as efficient as implementing all the five optimal control interventions simultaneously as they both avert the same number of infections. However, in resource-limited communities when joint implementation of only three interventions is possible, the strategy combining personal protection, testing or screening and treatment is strongly recommended. Out of all the intervention options being considered, this strategy is also affirmed to be the most cost-effective overall. Economic evaluation of the control intervention strategies further suggests that combination of first dose vaccination, second dose vaccination, testing or screening and treatment is the most cost-effective strategy when implementation of only four interventions is strictly allowed.
Optimal Control Analysis in the Treatment of Solid Tumors using Combined Therapy Omer, Salaheldin; Mambili-Mamboundou, Hermane
Communication in Biomathematical Sciences Vol. 7 No. 1 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.1.7

Abstract

In this paper, we develop and analyze a mathematical model that describes the dynamic interactions and competitions among tumor cells, normal cells, immune cells, and transforming growth factor-beta within the tumor microenvironment. We conducted qualitative analyses to examine the persistence or extinction of each cell population and analyzed the regions of stability and instability across various equilibria. Additionally, we formulated and solved an optimal control problem using the Pontryagin’s maximum principle, aiming to minimize tumor size and the concentration of transforming growth factor-beta while also reducing chemotherapy and siRNA drug-induced toxicity in patients. Numerical simulations are performed for the model with and without treatment. We demonstrate scenarios where neither individual treatment is capable of reducing both tumor and TGF-β, but their combination achieves a substantial reduction.
A Mathematical Model of Social Interaction between the Sufferers of Cardiovascular and Type 2 Diabetes Mellitus Jannah, Nur Wahidiyatil; Aryati, Lina; Adi-Kusumo, Fajar
Communication in Biomathematical Sciences Vol. 7 No. 1 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.1.5

Abstract

Type 2 diabetes mellitus is a non-communicable medical condition that is most commonly suffered in compare to type 1 diabetes, gestational diabetes, or diabetes that is caused by pathogen or disorders. The other important non-communicable medical condition is cardiovascular disease that occurs due to impaired blood circulation in the heart and blood vessels. The unhealthy lifestyle behaviors that mainly influenced by social interactions play an important role to increase the number of prevalence for those diseases. In this paper, we consider a mathematical model of the social interactions effects to the sufferers of the cardiovascular and type 2 diabetes mellitus diseases. We separate the population to five sub populations, i.e., individuals with normal weight, individuals who have obesity, individuals with cardiovascular disease only, individuals with type 2 diabetes mellitus disease only, and individuals with both cardiovascular and type 2 diabetes mellitus diseases. By using linear analysis and bifurcation theory, we determine the steady state conditions analytically and show some scenarios for the population based on variation of the parameters value numerically.
On the Role of Early Case Detection and Treatment Failure in Controlling Tuberculosis Transmission: A Mathematical Modeling Study Aldila, Dipo; Ramadhan, Derio A.; Chukwu, Chidozie W.; Handari, Bevina D.; Shahzad, Muhammad; Putri Zahra Kamalia
Communication in Biomathematical Sciences Vol. 7 No. 1 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.1.4

Abstract

Tuberculosis (TB) remains a pressing global health concern, demanding urgent attention to mitigate its spread and impact. In this study, we present a rigorous mathematical model of TB transmission that incorporates early case detection and addresses the critical issue of treatment failure. Through the development of a system of nonlinear ordinary differential equations, we conduct comprehensive analyses to assess the dynamics of TB transmission and the efficacy of intervention strategies. Our findings underscore the urgent need for effective TB control measures. Mathematical analyses reveal that the model exhibits a TB-free equilibrium, which is globally asymptotically stable only if the control reproduction number falls below one. However, we identify a concerning phenomenon: the model demonstrates a forward bifurcation when the control reproduction number equals one, suggesting that the disease-free equilibrium loses its stability, while simultaneously, the stable unique endemic equilibrium begins to emerge. Moreover, sensitivity analysis highlights the complex interplay between case detection rates, treatment failure probabilities, and TB transmission dynamics. Contrary to expectations, increasing case detection rates and minimizing treatment failure probabilities may not consistently reduce the basic reproduction number or the size of the infected population. Instead, there exists a critical threshold for intervention effectiveness, beyond which TB transmission can be significantly curtailed. Biologically, this phenomenon may occur if there is no balance between case detection and treatment efforts. If treatment quality does not improve, then case detection will not have a significant impact, and in the worst case scenario, it can exacerbate the intervention’s negative effects. These findings underscore the urgency of implementing targeted intervention strategies to combat TB transmission effectively. Failure to meet the critical intervention threshold risks undermining TB elimination efforts and exacerbating the global TB burden. Through numerical simulations, we elucidate potential intervention scenarios necessary for achieving TB elimination goals in human populations. In conclusion, our study highlights the urgent imperative for coordinated action to control TB transmission effectively. By elucidating the dynamics of TB spread and intervention efficacy, we provide valuable insights to inform evidence-based policy decisions and accelerate progress towards TB elimination on a global scale.
On Data Driven SIRD Model of Delta and Omicron Variants of COVID-19 Ihsan, Aditya Firman
Communication in Biomathematical Sciences Vol. 7 No. 1 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.1.3

Abstract

The compartmental model stands as a cornerstone in quantitatively describing the transmission dynamics of diseases. Through a series of assumptions, this model can be formulated and subsequently validated against real-world conditions. Leveraging the abundance of COVID-19 data presently available, this study endeavors to reverse engineer the model construction process. Specifically, we analyse the compartmental model governing two notable variants of COVID-19: Delta and Omicron, utilizing empirical data. Employing the SINDy method, we extract parameters that define the model by effectively fitting the available data. To ensure robustness, the obtained model undergoes validation via comparison with real-world data through numerical integration. Additionally, we conduct fine-tuning in regularization techniques and input features to refine model selection. The constructed model then undergoes thorough analysis to gain qualitative insights and interpretations regarding the transmission dynamics of COVID-19.
A Simple Modelling of Microscopic Epidemic Process with Two Vaccine Doses on a Synthesized Human Interaction Network Seprianus; Nuraini, Nuning; Saputro, Suhadi Wido
Communication in Biomathematical Sciences Vol. 7 No. 1 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.1.6

Abstract

In this study, we illustrate the incorporation of two vaccine doses into a discrete SIR model to aid in the decision-making process for optimal vaccination strategies. We present a basic model of a human interaction network synthesized to depict social contacts within a population, taking into account the number of connections and the level of interaction among individuals. Under a limited number of available vaccine doses, we explore various vaccination scenarios considering factors such as the distribution of vaccines, the proportion of vaccinated individuals, and the timing of vaccination commencement. Our research demonstrates that the most effective vaccination strategy, which focuses on re-characterized hubs or redefining the individual who has high connectivity, will cover fewer individuals and result in the smallest total number of infected individuals.

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