. Breast cancer is the second most common cause of death among women worldwide. Trastuzumab is the first humanised monoclonal antibody against HER2-positive metastatic breast cancer. However, the most serious side effect of trastuzumab is cardiotoxicity, which has become a limiting factor in the drug’s safe use. In this study, we investigated the effect of trastuzumab treatment on breast cancer stages and cardiac function. Therefore, we constructed a mathematical model based on breast cancer patients. The model was created using a differential equation system, and equilibrium point and stability analysis were employed to study the associated temporal dynamics. The stability of the equilibrium point was analysed using the Routh-Hurwitz criteria, which identified an asymptotically stable equilibrium point. To valudate these findings, numerical simulations were performed, which demonstrated that the equilibrium point is always stable regardless of the initial conditions. Finally, our results suggest that the five sub-populations of patients will reach a stable state upon reaching the equilibrium point.
{"title":"Analysing the effect of trastuzumab treatment on breast cancer stages and cardiac function: A mathematical modeling and numerical simulation","authors":"Maryem EL Karchani, N. I. Fatmi, Karima Mouden","doi":"10.28919/cmbn/7970","DOIUrl":"https://doi.org/10.28919/cmbn/7970","url":null,"abstract":". Breast cancer is the second most common cause of death among women worldwide. Trastuzumab is the first humanised monoclonal antibody against HER2-positive metastatic breast cancer. However, the most serious side effect of trastuzumab is cardiotoxicity, which has become a limiting factor in the drug’s safe use. In this study, we investigated the effect of trastuzumab treatment on breast cancer stages and cardiac function. Therefore, we constructed a mathematical model based on breast cancer patients. The model was created using a differential equation system, and equilibrium point and stability analysis were employed to study the associated temporal dynamics. The stability of the equilibrium point was analysed using the Routh-Hurwitz criteria, which identified an asymptotically stable equilibrium point. To valudate these findings, numerical simulations were performed, which demonstrated that the equilibrium point is always stable regardless of the initial conditions. Finally, our results suggest that the five sub-populations of patients will reach a stable state upon reaching the equilibrium point.","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69242310","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}
{"title":"The dynamics of a stage-structure prey-predator model with hunting cooperation and anti-predator behavior","authors":"Dahlia Khaled Bahlool, 𝑦, −𝑦, 𝑤, 𝑑𝐿, 𝑤 −, Clearly, −𝛿, 𝛿, 𝐽, 𝐽𝑒","doi":"10.28919/cmbn/8003","DOIUrl":"https://doi.org/10.28919/cmbn/8003","url":null,"abstract":",","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69245321","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}
Arinze Luke Ozioko, Remigius Okeke, Sunday Emmanuel Fadugba, Kekana Malesela, Godwin Christopher, E. Mbah
. In this work, we look at the vaccine and condom Nipah virus model using an optimum control analysis. We implemented measures to limit infection dissemination and control. We examine four distinct controls: personal protection, rapid testing, burying infected pigs, and therapy control. We construct an ideal control model and demonstrate the mathematical results using the suggested controls. The results of optimum control suggest that measures can be useful in decreasing infected individuals and increasing the health of society
{"title":"Optimal Nipah virus (NiV) spread control dynamics","authors":"Arinze Luke Ozioko, Remigius Okeke, Sunday Emmanuel Fadugba, Kekana Malesela, Godwin Christopher, E. Mbah","doi":"10.28919/cmbn/8045","DOIUrl":"https://doi.org/10.28919/cmbn/8045","url":null,"abstract":". In this work, we look at the vaccine and condom Nipah virus model using an optimum control analysis. We implemented measures to limit infection dissemination and control. We examine four distinct controls: personal protection, rapid testing, burying infected pigs, and therapy control. We construct an ideal control model and demonstrate the mathematical results using the suggested controls. The results of optimum control suggest that measures can be useful in decreasing infected individuals and increasing the health of society","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69245719","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}
{"title":"New techniques to estimate the solution of autonomous system","authors":"Mahdi A. Sabea, Maha A. Mohammed","doi":"10.28919/cmbn/8079","DOIUrl":"https://doi.org/10.28919/cmbn/8079","url":null,"abstract":",","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69246084","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}
In this paper, we present a fractional bi-modal SIT R mathematical model to study the Covid-19 spread in a human population under vaccination influence. The study depends on the stability of the disease-free and endemic equilibrium. To demonstrate the validity of the results, we give a numerical example. The results show that the infected and treatment subpopulations decrease if the susceptible subpopulations are vaccinated. Moreover, the recovered subpopulation increased.
{"title":"A study for fractional order epidemic model of COVID-19 spread with vaccination","authors":"","doi":"10.28919/cmbn/8214","DOIUrl":"https://doi.org/10.28919/cmbn/8214","url":null,"abstract":"In this paper, we present a fractional bi-modal SIT R mathematical model to study the Covid-19 spread in a human population under vaccination influence. The study depends on the stability of the disease-free and endemic equilibrium. To demonstrate the validity of the results, we give a numerical example. The results show that the infected and treatment subpopulations decrease if the susceptible subpopulations are vaccinated. Moreover, the recovered subpopulation increased.","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135107139","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}
: The mortality rate serves as one measure of the health sector as well as a tool for identifying populations that should receive specific health and development programs. The mortality rate can be used to determine a nation's level of welfare and standard of living. The mortality rate also affects the pricing of insurance premiums, the calculation of the benefit reserve for annuity products, actuarial risk management, and pension plans. A model is required to predict the mortality rate in the future because it is a random variable that varies over time and is in the range of (0,1). The Beta Autoregressive Moving Average (βARMA) model is a development of Beta regression and can be used to model and forecast mortality rates. Based on data on Indonesia's annual death rates from 1960 to 2020, we constructed a βARMA model for forecasting Indonesia's mortality rate. The best βARMA model was selected using Akaike's Information Criterion (AIC) value, and forecasting accuracy was assessed using Root Mean Square Error (RMSE). For Indonesia's annual mortality rate data, the best βARMA model produces an RMSE value of 0.0001.
{"title":"Forecasting Indonesia mortality rate using beta autoregressive moving average model","authors":"","doi":"10.28919/cmbn/8184","DOIUrl":"https://doi.org/10.28919/cmbn/8184","url":null,"abstract":": The mortality rate serves as one measure of the health sector as well as a tool for identifying populations that should receive specific health and development programs. The mortality rate can be used to determine a nation's level of welfare and standard of living. The mortality rate also affects the pricing of insurance premiums, the calculation of the benefit reserve for annuity products, actuarial risk management, and pension plans. A model is required to predict the mortality rate in the future because it is a random variable that varies over time and is in the range of (0,1). The Beta Autoregressive Moving Average (βARMA) model is a development of Beta regression and can be used to model and forecast mortality rates. Based on data on Indonesia's annual death rates from 1960 to 2020, we constructed a βARMA model for forecasting Indonesia's mortality rate. The best βARMA model was selected using Akaike's Information Criterion (AIC) value, and forecasting accuracy was assessed using Root Mean Square Error (RMSE). For Indonesia's annual mortality rate data, the best βARMA model produces an RMSE value of 0.0001.","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135317675","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}
A mathematical model is a beautiful and powerful way to depict the condition of epidemiological disease transmission. In this work, we used a nonlinear differential equation to construct a mathematical model of COVID-19. Nonlinear differential equation illustrates the spread of COVID-19 disease incorporating the vaccinated and quarantined subpopulations. A compartment of a model of COVID-19 disease was carried out involving several control variables and several biological assumptions. Applying the control variables to a mathematical model is the prevention of direct contact between infected and susceptible subpopulations, a vaccination control process, and an intensive handling of infected and quarantined populations. In the next section, an investigation of the positivity and boundedness of the solution COVID-19 disease, and an analysis of the existence and uniqueness of the solution was carried out. Then, the existence of the control variables involved in the mathematical model that has been designed is demonstrated. Furthermore, by applying the Pontryagin Principle to determine the optimal conditions and best values for each control variable that holds on. On the other hand, in addition to the mathematical analysis result, provides numerical simulations using MATLAB software as one of the steps in describing the behavior of the dynamical solution or the phase portrait. Finally, the last section shows that the optimal control condition carried out is able to reduce the density of infected and quarantined subpopulations, respectively. Hence, it is in line with the functional objective that has been constructed.
{"title":"A Pontryagin principle and optimal control of spreading COVID-19 with vaccination and quarantine subtype","authors":"","doi":"10.28919/cmbn/8157","DOIUrl":"https://doi.org/10.28919/cmbn/8157","url":null,"abstract":"A mathematical model is a beautiful and powerful way to depict the condition of epidemiological disease transmission. In this work, we used a nonlinear differential equation to construct a mathematical model of COVID-19. Nonlinear differential equation illustrates the spread of COVID-19 disease incorporating the vaccinated and quarantined subpopulations. A compartment of a model of COVID-19 disease was carried out involving several control variables and several biological assumptions. Applying the control variables to a mathematical model is the prevention of direct contact between infected and susceptible subpopulations, a vaccination control process, and an intensive handling of infected and quarantined populations. In the next section, an investigation of the positivity and boundedness of the solution COVID-19 disease, and an analysis of the existence and uniqueness of the solution was carried out. Then, the existence of the control variables involved in the mathematical model that has been designed is demonstrated. Furthermore, by applying the Pontryagin Principle to determine the optimal conditions and best values for each control variable that holds on. On the other hand, in addition to the mathematical analysis result, provides numerical simulations using MATLAB software as one of the steps in describing the behavior of the dynamical solution or the phase portrait. Finally, the last section shows that the optimal control condition carried out is able to reduce the density of infected and quarantined subpopulations, respectively. Hence, it is in line with the functional objective that has been constructed.","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135402165","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}
{"title":"Global stability of a delayed HIV-1 dynamics model with saturation response with cure rate, absorption effect and two time delays","authors":"N. Rathnayaka, J. Wijerathna, B. Pradeep","doi":"10.28919/cmbn/7877","DOIUrl":"https://doi.org/10.28919/cmbn/7877","url":null,"abstract":",","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69239286","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}
{"title":"Parameter estimation of Weibull distribution on type III censored survival data by maximum likelihood estimator method: Case study of lung cancer patient data at Dr. Kariadi Hospital Semarang","authors":"Ardi Kurniawan, Rendi Kurnia, Eko Rahmanta, Tjahjono","doi":"10.28919/cmbn/7937","DOIUrl":"https://doi.org/10.28919/cmbn/7937","url":null,"abstract":",","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69240820","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}
. The COVID-19 virus is still spreading around the world. Several SARS-CoV-2 variants have been identified during this COVID-19 pandemic. In this study, we present a compartmental mathematical model using ordinary differential equations to investigate the impact of four different SARS-CoV-2 variants on the transmission of SARS-CoV-2 across India. The proposed mathematical model incorporates the alpha variant, beta variant, gamma variant, and delta variant subpopulations apart from the typical susceptible, exposed, recovered, and dead subpopulations. As part of the India pandemic, we used the model to determine the basic reproduction number ( R 0 ) and the daily rates of infection, death, and recovery for each strain. Sensitivity analysis is employed to comprehend the influence of estimated parameter values on the number of infections that result in four variants. Then, using vaccine and therapy as the control variables, we define and analyse an optimum control problem. These optimal controls are described by the Pontryagin’s Minimal Principle. Results showed that the combination of vaccination and treatment strategies was most efficient in minimizing infection and enhancing recovery. The cost-effectiveness analysis is used to determine the best control strategy to minimize infected individuals.
{"title":"A comprehensive study of optimal control model simulation for COVID-19 infection with respect to multiple variants","authors":"A. Venkatesh, M. A. Rao, D. Vamsi","doi":"10.28919/cmbn/8031","DOIUrl":"https://doi.org/10.28919/cmbn/8031","url":null,"abstract":". The COVID-19 virus is still spreading around the world. Several SARS-CoV-2 variants have been identified during this COVID-19 pandemic. In this study, we present a compartmental mathematical model using ordinary differential equations to investigate the impact of four different SARS-CoV-2 variants on the transmission of SARS-CoV-2 across India. The proposed mathematical model incorporates the alpha variant, beta variant, gamma variant, and delta variant subpopulations apart from the typical susceptible, exposed, recovered, and dead subpopulations. As part of the India pandemic, we used the model to determine the basic reproduction number ( R 0 ) and the daily rates of infection, death, and recovery for each strain. Sensitivity analysis is employed to comprehend the influence of estimated parameter values on the number of infections that result in four variants. Then, using vaccine and therapy as the control variables, we define and analyse an optimum control problem. These optimal controls are described by the Pontryagin’s Minimal Principle. Results showed that the combination of vaccination and treatment strategies was most efficient in minimizing infection and enhancing recovery. The cost-effectiveness analysis is used to determine the best control strategy to minimize infected individuals.","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69245537","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：