Hepatitis B virus (HBV) continues to pose a significant global health burden, necessitating the development of accurate and effective mathematical models to understand its transmission dynamics and devise optimal control strategies. In this research paper, we present a fractional order model for Hepatitis B virus transmission, incorporating the complexities of memory effects and non-local interactions in disease spread. The proposed fractional order model is formulated as a system of differential equations, with distinct compartments. We employ fractional order derivatives to capture the long-term memory and non-local interactions inherent in HBV transmission, offering a more realistic representation of the epidemic dynamics. To assess the stability and control potential of the model, we conduct rigorous mathematical analysis. The basic reproduction number is computed using the next generation matrix approach to determine the disease’s potential for spreading in the population. Critical points of the model are identified, and disease-free equilibrium points are obtained to assess their stability conditions. Furthermore, we derive endemic equilibrium points for the model, and their stability is analyzed using Jacobian transformation.To optimize control measures, sensitivity analysis of the model parameters is performed to identify influential factors affecting disease transmission. Numerical simulations of the fractional order model are implemented using the Adams-type Predictor-Corrector method, and the results demonstrate the effectiveness of the proposed control strategies in curbing the spread of HBV.
{"title":"Modeling and control of hepatitis B virus transmission dynamics using fractional order differential equations","authors":"","doi":"10.28919/cmbn/8174","DOIUrl":"https://doi.org/10.28919/cmbn/8174","url":null,"abstract":"Hepatitis B virus (HBV) continues to pose a significant global health burden, necessitating the development of accurate and effective mathematical models to understand its transmission dynamics and devise optimal control strategies. In this research paper, we present a fractional order model for Hepatitis B virus transmission, incorporating the complexities of memory effects and non-local interactions in disease spread. The proposed fractional order model is formulated as a system of differential equations, with distinct compartments. We employ fractional order derivatives to capture the long-term memory and non-local interactions inherent in HBV transmission, offering a more realistic representation of the epidemic dynamics. To assess the stability and control potential of the model, we conduct rigorous mathematical analysis. The basic reproduction number is computed using the next generation matrix approach to determine the disease’s potential for spreading in the population. Critical points of the model are identified, and disease-free equilibrium points are obtained to assess their stability conditions. Furthermore, we derive endemic equilibrium points for the model, and their stability is analyzed using Jacobian transformation.To optimize control measures, sensitivity analysis of the model parameters is performed to identify influential factors affecting disease transmission. Numerical simulations of the fractional order model are implemented using the Adams-type Predictor-Corrector method, and the results demonstrate the effectiveness of the proposed control strategies in curbing the spread of HBV.","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":"2010 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136202370","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. Idmbarek, Nossaiba Baba, Y. E. Foutayeni, N. Achtaich
. We consider the interaction between mullets and osprey populations. The main objective of this work is that the osprey must choose the predation intensity over time in a way that maximizes the present value of the utility stream derived by consuming mullets. The model has features of both convex and concave optimal control problems and therefore, phase plane analysis has to be combined with the problem of synthesis of bang-bang, singular and chattering solution pieces
{"title":"Optimal mullets consumption by osprey population using utility function","authors":"A. Idmbarek, Nossaiba Baba, Y. E. Foutayeni, N. Achtaich","doi":"10.28919/cmbn/7987","DOIUrl":"https://doi.org/10.28919/cmbn/7987","url":null,"abstract":". We consider the interaction between mullets and osprey populations. The main objective of this work is that the osprey must choose the predation intensity over time in a way that maximizes the present value of the utility stream derived by consuming mullets. The model has features of both convex and concave optimal control problems and therefore, phase plane analysis has to be combined with the problem of synthesis of bang-bang, singular and chattering solution pieces","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69243598","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":"Effect of partially and fully vaccinated individuals in some regions of India: A mathematical study on COVID-19 outbreak","authors":"M. Aakash, C. Gunasundari","doi":"10.28919/cmbn/7825","DOIUrl":"https://doi.org/10.28919/cmbn/7825","url":null,"abstract":",","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69239134","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}
: This study discussed modeling poverty levels in South Sulawesi through Spline Nonparametric Regression Approach. Since no specific pattern was formed from the relation between the poverty level in South Sulawesi and the factors that influence it, the researchers used nonparametric regression modelling with Spline approach. The Spline model is very good in modelling data that has changeable patterns at certain subintervals. The aimed of this study were to investigate the factors that have the most influence on the poverty level and modelling the poverty level in South Sulawesi through nonparametric regression. The scope of this study was the use of Generalized Cross-Validation (GCV) in selecting optimal knot points; in this case, it used 1, 2
{"title":"Modeling of poverty level in South Sulawesi Province through spline nonparametric regression approach","authors":"Wahidah Alwi, Ermawati, Try Azisah Nurman, Hernawati, Risnawati Ibnas","doi":"10.28919/cmbn/7946","DOIUrl":"https://doi.org/10.28919/cmbn/7946","url":null,"abstract":": This study discussed modeling poverty levels in South Sulawesi through Spline Nonparametric Regression Approach. Since no specific pattern was formed from the relation between the poverty level in South Sulawesi and the factors that influence it, the researchers used nonparametric regression modelling with Spline approach. The Spline model is very good in modelling data that has changeable patterns at certain subintervals. The aimed of this study were to investigate the factors that have the most influence on the poverty level and modelling the poverty level in South Sulawesi through nonparametric regression. The scope of this study was the use of Generalized Cross-Validation (GCV) in selecting optimal knot points; in this case, it used 1, 2","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":"10 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69240987","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}
Arjun Hasibuan, Asep K. Supriatna, E. Rusyaman, M. H. A. Biswas, E. Carnia, 𝑎𝑥, 𝑏𝑦, 𝑥 𝑓𝑥2−𝑏𝑓, 𝑥, 𝑥 𝑄, −𝑄, 𝑥 𝑥, 𝑦 −𝑏𝑓, 𝑏𝑥, 𝑎𝑦, 𝑦 𝑓, 𝑦, 𝑄 𝑥 𝑠 𝑥1
,
,
{"title":"Stability analysis of the population matrix model with two iteroparous species using the M-matrix","authors":"Arjun Hasibuan, Asep K. Supriatna, E. Rusyaman, M. H. A. Biswas, E. Carnia, 𝑎𝑥, 𝑏𝑦, 𝑥 𝑓𝑥2−𝑏𝑓, 𝑥, 𝑥 𝑄, −𝑄, 𝑥 𝑥, 𝑦 −𝑏𝑓, 𝑏𝑥, 𝑎𝑦, 𝑦 𝑓, 𝑦, 𝑄 𝑥 𝑠 𝑥1","doi":"10.28919/cmbn/7994","DOIUrl":"https://doi.org/10.28919/cmbn/7994","url":null,"abstract":",","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":"29 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69244064","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 construct a SIDTR model. We develop a system of differential equations for SIDTR (Suspected, Infected, Diagnosed, Treatment and Recovered) model and analyze the outbreak of Tuberculosis (TB) infection and its effect on Indian population. We established theorems on stability analysis conditions for disease free equilibrium and endemic equilibrium. The basic reproduction number R 0 was determined by using the next generation matrix. We attempt to fit our proposed mathematical model by using real world data which was taken from WHO. We expect that this study will be effective on controlling Tuberculosis (TB) spread and also we predicted the future TB infection in India.
{"title":"A simple SIDTR endemic model to make tuberculosis free India and stop spreading","authors":"S. Priya, K. Ganesan","doi":"10.28919/cmbn/8001","DOIUrl":"https://doi.org/10.28919/cmbn/8001","url":null,"abstract":". In this paper, we construct a SIDTR model. We develop a system of differential equations for SIDTR (Suspected, Infected, Diagnosed, Treatment and Recovered) model and analyze the outbreak of Tuberculosis (TB) infection and its effect on Indian population. We established theorems on stability analysis conditions for disease free equilibrium and endemic equilibrium. The basic reproduction number R 0 was determined by using the next generation matrix. We attempt to fit our proposed mathematical model by using real world data which was taken from WHO. We expect that this study will be effective on controlling Tuberculosis (TB) spread and also we predicted the future TB infection in India.","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69244182","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}
Abang Sunday Igwe, Scott, Ozioko Arinze Luke, Atokolo William, Oziri Kingsley Emeka, A. R. Adebisi, Topman Nicholas Nnamani, Mbah Godwin, Christopher Ezike
. Ever since the first outbreak of Nipah virus disease, which occurred both in human and non-human primates in developing countries in Far East Asian between 1998 and 1999 which led to a majority of deaths, with the effect of such occurrence still witnessed up till date. We studied the spread of Nipah virus and obtained a system of equations comprising of ten equations which effectively described the transmission of Nipah Virus in a population where control measures were incorporated and two major sources of contacting the disease which are coming in contact with contaminated foods by infected bats from crop farming and pig farming, these were also incorporated. We investigated the local stability of the disease-free equilibrium using the Jacobian Matrix approach and the disease-endemic stability using the center manifold theorem. We also investigated the global
{"title":"Mathematical modelling approach for the study of Nipah virus disease transmission dynamics","authors":"Abang Sunday Igwe, Scott, Ozioko Arinze Luke, Atokolo William, Oziri Kingsley Emeka, A. R. Adebisi, Topman Nicholas Nnamani, Mbah Godwin, Christopher Ezike","doi":"10.28919/cmbn/8056","DOIUrl":"https://doi.org/10.28919/cmbn/8056","url":null,"abstract":". Ever since the first outbreak of Nipah virus disease, which occurred both in human and non-human primates in developing countries in Far East Asian between 1998 and 1999 which led to a majority of deaths, with the effect of such occurrence still witnessed up till date. We studied the spread of Nipah virus and obtained a system of equations comprising of ten equations which effectively described the transmission of Nipah Virus in a population where control measures were incorporated and two major sources of contacting the disease which are coming in contact with contaminated foods by infected bats from crop farming and pig farming, these were also incorporated. We investigated the local stability of the disease-free equilibrium using the Jacobian Matrix approach and the disease-endemic stability using the center manifold theorem. We also investigated the global","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69245848","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}
. We examine two prey and one predator models with Holling type I functional behaviours in this paper. To demonstrate the system’s permanence and boundedness, we used a discrete-time delay. Through the use of traditional mathematical techniques, the effects of random variations in the environment and time delay on the model’s stability are analytically examined. The stability and Hopf-Bifurcation for the competition model are also described and shown. A few numerical computations are provided to demonstrate the efficacy of the theoretical findings.
{"title":"Mathematical analysis of prey predator models with Holling type I functional responses and time delay","authors":"N. Sharmila, C. Gunasundari","doi":"10.28919/cmbn/8014","DOIUrl":"https://doi.org/10.28919/cmbn/8014","url":null,"abstract":". We examine two prey and one predator models with Holling type I functional behaviours in this paper. To demonstrate the system’s permanence and boundedness, we used a discrete-time delay. Through the use of traditional mathematical techniques, the effects of random variations in the environment and time delay on the model’s stability are analytically examined. The stability and Hopf-Bifurcation for the competition model are also described and shown. A few numerical computations are provided to demonstrate the efficacy of the theoretical findings.","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69245231","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}
: This article suggests and explores a three-species food chain model that includes fear effects, refuges depending on predators, and cannibalism at the second level. The Holling type II functional response determines food consumption between stages of the food chain. This study examined the long-term behavior and impacts of the suggested model's essential elements. The model's solution properties were studied. The existence and stability of every probable equilibrium point were examined. The persistence needs of the system have been determined. It was discovered what conditions could lead to local bifurcation at equilibrium points. Appropriate Lyapunov functions are utilized to investigate the overall dynamics of the system. To support the analytical conclusions, numerical simulations were done to validate the model's inferred long-term behavior and to comprehend the implications of the model's significant parameters
{"title":"Three-species food chain model with cannibalism in the second level","authors":"A. S. Abdulghafour, R. K. Naji","doi":"10.28919/cmbn/8009","DOIUrl":"https://doi.org/10.28919/cmbn/8009","url":null,"abstract":": This article suggests and explores a three-species food chain model that includes fear effects, refuges depending on predators, and cannibalism at the second level. The Holling type II functional response determines food consumption between stages of the food chain. This study examined the long-term behavior and impacts of the suggested model's essential elements. The model's solution properties were studied. The existence and stability of every probable equilibrium point were examined. The persistence needs of the system have been determined. It was discovered what conditions could lead to local bifurcation at equilibrium points. Appropriate Lyapunov functions are utilized to investigate the overall dynamics of the system. To support the analytical conclusions, numerical simulations were done to validate the model's inferred long-term behavior and to comprehend the implications of the model's significant parameters","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69245439","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 dynamics of the SIR epidemic model are examined in this paper with finite medical resources and variable supply efficiency are examined along with the implications of time delay. This work demonstrates the stability of endemic equilibrium as well as the incidence of backward bifurcation can be significantly impacted by the inclusion of time delay. The theoretical results are supported and supplemented with numerical simulations
{"title":"Dynamics of an SIR pandemic model using constrained medical resources with time delay","authors":"S. Jothika, M. Radhakrishnan","doi":"10.28919/cmbn/8119","DOIUrl":"https://doi.org/10.28919/cmbn/8119","url":null,"abstract":". The dynamics of the SIR epidemic model are examined in this paper with finite medical resources and variable supply efficiency are examined along with the implications of time delay. This work demonstrates the stability of endemic equilibrium as well as the incidence of backward bifurcation can be significantly impacted by the inclusion of time delay. The theoretical results are supported and supplemented with numerical simulations","PeriodicalId":44079,"journal":{"name":"Communications in Mathematical Biology and Neuroscience","volume":"1 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69246487","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}
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