Communication in Biomathematical Sciences最新文献

A Numerical Study of Codimension-Two Bifurcations of an SIR-Type Model for COVID-19 and Their Epidemiological Implications COVID-19 SIR 型模型的二维分岔及其流行病学意义的数值研究

Communication in Biomathematical Sciences Pub Date : 2023-12-19 DOI: 10.5614/cbms.2023.6.2.6

Livia Owen, Jonathan Hoseana, Benny Yong

{"title":"A Numerical Study of Codimension-Two Bifurcations of an SIR-Type Model for COVID-19 and Their Epidemiological Implications","authors":"Livia Owen, Jonathan Hoseana, Benny Yong","doi":"10.5614/cbms.2023.6.2.6","DOIUrl":"https://doi.org/10.5614/cbms.2023.6.2.6","url":null,"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.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":" 48","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138963416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dynamical Behaviour of Pro- and Anti-Inflammatory Cytokines during Pathogenesis of Atherosclerosis 动脉粥样硬化发病过程中促炎和抗炎细胞因子的动态行为

Communication in Biomathematical Sciences Pub Date : 2023-12-19 DOI: 10.5614/cbms.2023.6.2.3

Asish Adak, Arpita Devi, Praveen Kumar Gupta

{"title":"Dynamical Behaviour of Pro- and Anti-Inflammatory Cytokines during Pathogenesis of Atherosclerosis","authors":"Asish Adak, Arpita Devi, Praveen Kumar Gupta","doi":"10.5614/cbms.2023.6.2.3","DOIUrl":"https://doi.org/10.5614/cbms.2023.6.2.3","url":null,"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.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":" 493","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138960439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Interplay of Common Noise and Finite Pulses on Biological Neurons 普通噪声和有限脉冲对生物神经元的相互作用

Communication in Biomathematical Sciences Pub Date : 2023-12-19 DOI: 10.5614/cbms.2023.6.2.5

Afifurrahman Afifurrahman, Mohd Hafiz Mohd, Farah Aini Abdullah

{"title":"The Interplay of Common Noise and Finite Pulses on Biological Neurons","authors":"Afifurrahman Afifurrahman, Mohd Hafiz Mohd, Farah Aini Abdullah","doi":"10.5614/cbms.2023.6.2.5","DOIUrl":"https://doi.org/10.5614/cbms.2023.6.2.5","url":null,"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.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":" 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138961491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Data-Driven Generating Operator in SEIRV Model for COVID-19 Transmission COVID-19传播SEIRV模型中的数据驱动生成算子

Communication in Biomathematical Sciences Pub Date : 2023-07-04 DOI: 10.5614/cbms.2023.6.1.6

Nadia Nadia, Afdol Zikri, Sila Rizqina, K. Sukandar, M. Fakhruddin, C. J. Tay, N. Nuraini

{"title":"Data-Driven Generating Operator in SEIRV Model for COVID-19 Transmission","authors":"Nadia Nadia, Afdol Zikri, Sila Rizqina, K. Sukandar, M. Fakhruddin, C. J. Tay, N. Nuraini","doi":"10.5614/cbms.2023.6.1.6","DOIUrl":"https://doi.org/10.5614/cbms.2023.6.1.6","url":null,"abstract":"The COVID-19 (SARS-CoV-2) vaccine has been extensively implemented through large-scale programs in numerous countries as a preventive measure against the resurgence of COVID-19 cases. In line with this vaccination effort, the Indonesian government has successfully inoculated over 74% of its population. Nevertheless, a significant decline in the duration of vaccine-induced immunity has raised concerns regarding the necessity of additional inoculations, such as booster shots. Prior to proceeding with further inoculation measures, it is imperative for the government to assess the existing level of herd immunity, specifically determining whether it has reached the desired threshold of 70%. To shed light on this matter, our objective is to ascertain the herd immunity level following the initial and subsequent vaccination programs, while also proposing an optimal timeframe for conducting additional inoculations. This study utilizes COVID-19 data from Jakarta and employs the SEIRV model, which integrates time-dependent parameters and incorporates an additional compartment to represent the vaccinated population. By formulating a dynamic generator based on the cumulative cases function, we are able to comprehensively evaluate the analytical and numerical aspects of all state dynamics. Simulation results reveal that the number of individuals protected by the vaccine increases following the vaccination program; however, this number subsequently declines due to the waning effect of the vaccine. Our estimates indicate that the vaccination program in Jakarta has achieved herd immunity levels exceeding 70% from October 2021 to February 2022, thus underscoring the necessity of rolling out further inoculations no later than February 2022.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45275565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Assessing The Impact of Medical Treatment and Fumigation on The Superinfection of Malaria: A Study of Sensitivity Analysis 医疗和熏蒸对疟疾重叠感染影响的敏感性分析研究

Communication in Biomathematical Sciences Pub Date : 2023-07-04 DOI: 10.5614/cbms.2023.6.1.5

B. Handari, D. Aldila, Evllyn Tamalia, S. Khoshnaw, M. Shahzad

{"title":"Assessing The Impact of Medical Treatment and Fumigation on The Superinfection of Malaria: A Study of Sensitivity Analysis","authors":"B. Handari, D. Aldila, Evllyn Tamalia, S. Khoshnaw, M. Shahzad","doi":"10.5614/cbms.2023.6.1.5","DOIUrl":"https://doi.org/10.5614/cbms.2023.6.1.5","url":null,"abstract":"Malaria is a disease caused by the parasite Plasmodium, transmitted by the bite of an infected female Anopheles. In general, five species of Plasmodium that can cause malaria. Of the five species, Plasmodium falciparum and Plasmodium vivax are two species of Plasmodium that can allow malaria superinfection in the human body. Typically, the popular intervention for malaria eradication is the use of fumigation to control the vector population and provide good medical services for malaria patients. Here in this article, we formulate a mathematical model based on a host-vector interaction. Our model considering two types of plasmodium in the infection process and the use of medical treatment and fumigation for the eradication program. Our analytical result succeeds in proving the existence of all equilibrium points and how their existence and local stability criteria depend not only on the control reproduction number but also in the invasive reproduction number. This invasive reproduction number represent how one plasmodium can dominate other plasmodium. Our sensitivity analysis shows that fumigation is the most influential parameter in determining all control reproduction numbers. Furthermore, we find that the order in which numerous intervention measures are taken will be very crucial to determine the level of success of our malaria eradication program.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48700282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Mathematical Model and Study of Viral Hepatitis among Population in Afghanistan 阿富汗人群病毒性肝炎的数学模型与研究

Communication in Biomathematical Sciences Pub Date : 2023-07-04 DOI: 10.5614/cbms.2023.6.1.4

A. Hasmani, Burhanuddin Safi, A. Das

{"title":"Mathematical Model and Study of Viral Hepatitis among Population in Afghanistan","authors":"A. Hasmani, Burhanuddin Safi, A. Das","doi":"10.5614/cbms.2023.6.1.4","DOIUrl":"https://doi.org/10.5614/cbms.2023.6.1.4","url":null,"abstract":"Despite availability of strategies against viral hepatitis, it is still a serious disease, which millions of people are already infected with, hence it yet needs to be focused on. As an attempt, we formulated a single mathematical model describing behaviour of all strains of viral hepatitis, presented in the literature. The basic reproduction number(R_0) at disease free equilibrium point is computed, feasible region has been determined. For local stability of the model, R_0 has been taken into account and for global stability of the model Lyapunov method is followed. The model is then applied to the data available for Afghanistan for the year 2020. Based on the data, values of the parameters are estimated, using Minimum Mean Absolute Error (MAE) method. Numerical simulation is performed to support the model and then the results are plotted and represented graphically. One-at-a-time sensitivity analysis (OAT) method is used for sensitivity analysis and involved parameters have been examined for the propose of sensitivity analysis, it indicated that infection rates of acute and chronic states of viral hepatitis are the most sensitive and critical parameters. It has been observed that large number of populations can become infected followed by small increment of infection rates. It has also been noticed that, entire population of Afghanistan could become infected, if no prevention measures were taken. The model presented in this paper is useful for forecasting outbreak by viral hepatitis and it can further be modified by including prevention measures.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41714963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Nonstandard Numerical Scheme for a Predator-Prey Model Involving Predator Cannibalism and Refuge 涉及捕食者自相残杀和避难的捕食者-猎物模型的非标准数值格式

Communication in Biomathematical Sciences Pub Date : 2023-07-01 DOI: 10.5614/cbms.2023.6.1.2

Maya Rayungsari, A. Suryanto, W. M. Kusumawinahyu, I. Darti

引用次数: 0

Qualitative Behavioral Analysis in Mosquito Dynamics Model with Wolbachia Wolbachia蚊子动力学模型的定性行为分析

Communication in Biomathematical Sciences Pub Date : 2023-01-25 DOI: 10.5614/cbms.2023.6.1.1

D. Suandi, F. Ilahi, Randi Ramdhani, E. S. Nugraha

{"title":"Qualitative Behavioral Analysis in Mosquito Dynamics Model with Wolbachia","authors":"D. Suandi, F. Ilahi, Randi Ramdhani, E. S. Nugraha","doi":"10.5614/cbms.2023.6.1.1","DOIUrl":"https://doi.org/10.5614/cbms.2023.6.1.1","url":null,"abstract":"The Aedes Aegypti mosquito is the primary vector that can transmit diseases to humans such as zika, dengue fever, chikungunya, and yellow fever. This mosquito species is controlled to reduce the frequency of its bites on humans. Several methods have been developed to control mosquito populations, ranging from natural insecticides to artificial ones. However, the impact of these insecticides leads to resistance. Wolbachiabacteria as a promising alternative in reducing the spread of viruses on humans due to free resistance. This work constructs a genetic population model in the form of differential equation system that describes mosquitopopulation dynamics by involving random mating between mosquito populations with and without Wolbachia bacteria. The stability of the equilibrium was analyzed locally here. Numerical simulations and sensitivity analyzes are presented to confirm the analytical results and investigate the effect of the parameters involved on the model. The results show that the success of the expansion of Wolbachia-infected mosquitoes depends on the fitness level of the mosquito species. The more Wolbachia mosquitoes are released into nature, the more possibility this mosquito expansion will be successful.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49345028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Fractional-Order Food Chain Model with Omnivore and Anti-Predator 具有杂食和反捕食者的分数阶食物链模型

Communication in Biomathematical Sciences Pub Date : 2023-01-03 DOI: 10.5614/cbms.2022.5.2.2

Adin Lazuardy Firdiansyah

引用次数: 0

Control Design for Dengue Fever Model with Disturbance 具有扰动的登革热模型控制设计

Communication in Biomathematical Sciences Pub Date : 2023-01-03 DOI: 10.5614/cbms.2022.5.2.3

Hanna Hilyati Aulia, R. Saragih, D. Handayani

{"title":"Control Design for Dengue Fever Model with Disturbance","authors":"Hanna Hilyati Aulia, R. Saragih, D. Handayani","doi":"10.5614/cbms.2022.5.2.3","DOIUrl":"https://doi.org/10.5614/cbms.2022.5.2.3","url":null,"abstract":"A mathematical model has become a useful tool to predict and control dengue fever dynamics. In reality, the dynamic of dengue fever transmission can be disturbed by uncertainty measurements, so it is needed to consider the disturbance in the model. Then, dengue fever model with disturbance is constructed by using a gain matrix consisting a covariance matrix and random vector. As dengue vaccine has been challenging to reduce the pandemic, a dengue model with vaccination as control is constructed. The aim is to propose a feedback controller that can reduces the infected human (H2 control problem) and the uncertainty measurements (H∞ control problem). The control u denotes the proportion of susceptible humans that one decides to vaccinate at time t. A random mass vaccination with wanning immunity is chosen because vaccine still on development process. A Design of mixed H2 - H∞ control with State-dependent Riccati Equation (SDRE) approach is applied. The SDRE has been an effective method to solve for synthesizing nonlinear feedback controller by transforming the system to an State-dependent coefficient (SDC) form. By comparing the mixed scheme with basic H∞, numerical simulation shows that the control application effectively decreases the number of infected humans and reduces the disturbance.","PeriodicalId":33129,"journal":{"name":"Communication in Biomathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46718253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0