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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 8 Documents
 1 
Search results for , issue "Vol. 6 No. 2 (2023)" : 8 Documents clear
Blood Glucose Control on Diabetic Patient Type I using Sliding Mode Adaptive Control Aminatus Sa'adah; Prihantini
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.2023.6.2.1

Abstract

Diabetes is a metabolic disorder due to insufficient insulin synthesis or inadequate insulin sensitivity. The Bergman’s minimal model describes the dynamics of blood glucose levels in type 1 diabetics. The model has control inputs in the form of insulin injections and covers external disturbance factors in the form of meal disturbances. This research developed a control design using an sliding mode adaptive control to reduce blood glucose levels in hyperglycemic patients and keep it within normal glucose levels. Sliding mode adaptive control is an adaptive controller updates the model based on measured performance while in operation. A numerical simulation of the proposed controller is carried out by giving eating disorders three times, namely at breakfast, lunch, and dinner. Based on the numerical simulation, to lower the high blood glucose in the hyperglicemic patient, the insulin injection should be given starting at 30 minutes before breakfast for the next four hour, with a maximal dose of injection is 13 mU/min. It can decrease the high blood pressure until 54.83%.
Dynamical Behaviour of Pro- and Anti-Inflammatory Cytokines during Pathogenesis of Atherosclerosis Adak, Asish; Devi, Arpita; Gupta, Praveen Kumar
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.2023.6.2.3

Abstract

The role of anti-cytokines in atherosclerosis is to reduce inflammation in the intima. In some situations, certain anti-inflammatory cytokines like TGF-beta and IL-6 have shown the characteristics like a pro-inflammatory cytokines, which are showing different natures. In this study, a dynamical atherosclerosis model is proposed in the form of reaction-diffusion equation with consideration of immune cells, pro-inflammatory cytokines, and anti-inflammatory cytokines. The existence and uniqueness of the solutions are discussed for the proposed reaction dynamical system. The three equilibrium points, non-inflammatory, chronic, and coexistence, and their local stability are also determined for the model. Bellman and Cooke’s theorem is applied to illustrate the global stability at the coexistence equilibrium point. The effects of pro- and anti-inflammatory cytokines have also been discussed. The analytical and numerical studies evidently indicate that inflammation behaves differently when a certain number of anti-inflammatory cytokines behave like pro-inflammatory cytokines. The numerical simulations are demonstrated for different impacts of the reduction rate of macrophages due to the presence of anti-inflammatory cytokines, inhibition time, and the portion of anti-inflammatory cytokines behaving like pro-inflammatory cytokines through graphically. The results of this study suggest that chronic inflammation of the disease is likely to persist when a high concentration of ox-LDL and moderate concentration of cytokines are present in the intima. Coexistence inflammation is characterized by a high concentration of ox-LDL, moderate concentration of pro-inflammatory and high concentration of anti-cytokines; whereas a non-inflammatory condition would persevere if a low concentration of ox-LDL has been present in the intima.
Modeling Infectious Disease Trend using Sobolev Polynomials Castillo, Rolly Czar Joseph; Mendoza, Victoria May; Lope, Jose Ernie; Mendoza, Renier
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.2023.6.2.2

Abstract

Trend analysis plays an important role in infectious disease control. An analysis of the underlying trend in the number of cases or the mortality of a particular disease allows one to characterize its growth. Trend analysis may also be used to evaluate the effectiveness of an intervention to control the spread of an infectious disease. However, trends are often not readily observable because of noise in data that is commonly caused by random factors, short-term repeated patterns, or measurement error. In this paper, a smoothing technique that generalizes the Whittaker-Henderson method to infinite dimension and whose solution is represented by a polynomial is applied to extract the underlying trend in infectious disease data. The solution is obtained by projecting the problem to a finite-dimensional space using an orthonormal Sobolev polynomial basis obtained from Gram-Schmidt orthogonalization procedure and a smoothing parameter computed using the Philippine Eagle Optimization Algorithm, which is more efficient and consistent than a hybrid model used in earlier work. Because the trend is represented by the polynomial solution, extreme points, concavity, and periods when infectious disease cases are increasing or decreasing can be easily determined. Moreover, one can easily generate forecast of cases using the polynomial solution. This approach is applied in the analysis of trends, and in forecasting cases of different infectious diseases.
Analysis of Stability, Sensitivity Index and Hopf Bifurcation of Eco-Epidemiological SIR Model under Pesticide Application Balajied Me Syrti; Anuradha Devi; Ankur Jyoti Kashyap
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.2023.6.2.4

Abstract

In this paper, a deterministic SIR plant mathematical model is proposed and analysed with the application of pesticides as a control measure. The primary purpose of this model is to study the role of pesticides in controlling disease prevalence in plant populations. The total plant population is subdivided into three categories: susceptible, infected, and recovered. Pesticides are considered to be applied to both susceptible and infected populations to prevent the spread of infection to unaffected plant populations. It is considered that plant populations can be recovered only through the use of pesticides. To ensure the biological validity and well-defined nature of the model, the positivity, boundedness, uniqueness and existence of solutions are analysed. The basic reproduction number (R0) of the infection is determined and observed that the disease-free equilibrium state is locally asymptotically stable whenever (R0) is less than unity and unstable otherwise. The sensitivity analysis of the basic reproduction number is carried out, and it is observed that the value of R0 decreases as the value of the death rate and the recovery rate of plants increases. Moreover, it is revealed that above a critical parameter value of the infective induce rate, the population starts oscillating periodically, and the endemic equilibrium state becomes unstable. Finally, numerical simulations are conducted in MATLAB software to compare the analytical findings. Overall, the results obtained from this analysis are both novel and significant, making them an intriguing and potentially valuable contribution to the field of theoretical ecology.
The Interplay of Common Noise and Finite Pulses on Biological Neurons Afifurrahman; Mohd Hafiz Mohd; Farah Aini Abdullah
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.2023.6.2.5

Abstract

The response of neurons is highly sensitive to the stimulus. The stimulus can be associated with a direct injection in vitro experimentation (e.g., time dependent and independent inputs); or post-synaptic potentials resulting from the interaction of many neurons. A typical incoming stimulus resembles a noise which in principle can be described as a random variable. In computational neuroscience, the noise has been extensively studied for different setups. In this study, we investigate the effect of noisy inputs in a minimal network of two identical leaky integrate-and-fire (LIF) neurons interacting with finite pulses. In particular, we consider a Gaussian white noise as a standard function for stochastic modelling of neurons, while taking into account the pulse width as an elementary component for the signal transmission. By exploring the role of noise and finite pulses, the two neurons show a synchronous spiking behaviour characterized by fluctuations in the interspike intervals. Above some critical values the synchronous regime collapses onto asynchronous dynamics. The abrupt change in such dynamics is accompanied by a hysteresis, i.e., the coexistence of synchronous and asynchronous firing behaviour.
Bifurkasi Kodimensi dua dari model SIR untuk COVID-19 dan implikasi epidemiologisnya Owen, Livia; Jonathan Hoseana; Benny Yong
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.2023.6.2.6

Abstract

We study the codimension-two bifurcations exhibited by a recently-developed SIR-type mathematical model for the spread of COVID-19, as its two main parameters -the susceptible individuals' cautiousness level and the hospitals' bed-occupancy rate- vary over their domains. We use AUTO to generate the model's bifurcation diagrams near the relevant bifurcation points: two Bogdanov-Takens points and two generalised Hopf points, as well as a number of phase portraits describing the model's orbital behaviours for various pairs of parameter values near each bifurcation point. The analysis shows that, when a backward bifurcation occurs at the basic reproduction threshold, the transition of the model's asymptotic behaviour from endemic to disease-free takes place via an unexpectedly complex sequence of topological changes, involving the births and disappearances of not only equilibria but also limit cycles and homoclinic orbits. Epidemiologically, the analysis confirms the importance of a proper control of the values of the aforementioned parameters for a successful eradication of COVID-19. We recommend a number of strategies by which such a control may be achieved.
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.
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).

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