Pub Date : 2019-01-23DOI: 10.11145/J.BIOMATH.2019.01.026
J. Welker, M. Martcheva
Leishmaniasis is a neglected and emerging disease prevalent in Mediterranean and tropical climates. As such, the study and development of new models are of increasing importance. We introduce a new immuno-epidemiological model of visceral leishmaniasis in dogs. The within-host system is based on previously collected and published data, showing the movement and proliferation of the parasite in the skin and the bone-marrow, as well as the IgG response. The between-host system structures the infected individuals in time-since-infection and is of vector-host type. The within-host system has a parasite-free equilibrium and at least one endemic equilibrium, consistent with the fact that infected dogs do not recover without treatment. We compute the basic reproduction number R0 of the immuno-epidemiological model and provide the existence and stability results of the population-level disease-free equilibrium. Additionally, we prove existence of an unique endemic equilibrium when R0 > 1, and evidence of backward bifurcation and existence of multiple endemic equilibria when R0 < 1.
{"title":"A novel multi-scale immuno-epidemiological model of visceral leishmaniasis in dogs","authors":"J. Welker, M. Martcheva","doi":"10.11145/J.BIOMATH.2019.01.026","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2019.01.026","url":null,"abstract":"Leishmaniasis is a neglected and emerging disease prevalent in Mediterranean and tropical climates. As such, the study and development of new models are of increasing importance. We introduce a new immuno-epidemiological model of visceral leishmaniasis in dogs. The within-host system is based on previously collected and published data, showing the movement and proliferation of the parasite in the skin and the bone-marrow, as well as the IgG response. The between-host system structures the infected individuals in time-since-infection and is of vector-host type. The within-host system has a parasite-free equilibrium and at least one endemic equilibrium, consistent with the fact that infected dogs do not recover without treatment. We compute the basic reproduction number R0 of the immuno-epidemiological model and provide the existence and stability results of the population-level disease-free equilibrium. Additionally, we prove existence of an unique endemic equilibrium when R0 > 1, and evidence of backward bifurcation and existence of multiple endemic equilibria when R0 < 1.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41267775","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}
Pub Date : 2019-01-23DOI: 10.11145/J.BIOMATH.2019.01.029
R. Anguelov, R. Bekker, Y. Dumont
Crop host-pathogen interaction have been a main issue for decades, in particular for food security. In this paper, we focus on the modeling and long term behavior of soil-borne pathogens. We first develop a new compartmental temporal model, which exhibits bi-stable asymptotical dynamics. To investigate the long term behavior, we use LaSalle Invariance Principle to derive sufficient conditions for global asymptotic stability of the pathogen free equilibrium and monotone dynamical systems theory to provide sufficient conditions for permanence of the system. Finally, we develop a partially degenerate reaction diffusion system, providing a numerical exploration based on the results obtained for the temporal system. We show that a traveling wave solution may exist where the speed of the wave follows a power law.
{"title":"Bi-stable dynamics of a host-pathogen model","authors":"R. Anguelov, R. Bekker, Y. Dumont","doi":"10.11145/J.BIOMATH.2019.01.029","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2019.01.029","url":null,"abstract":"Crop host-pathogen interaction have been a main issue for decades, in particular for food security. In this paper, we focus on the modeling and long term behavior of soil-borne pathogens. We first develop a new compartmental temporal model, which exhibits bi-stable asymptotical dynamics. To investigate the long term behavior, we use LaSalle Invariance Principle to derive sufficient conditions for global asymptotic stability of the pathogen free equilibrium and monotone dynamical systems theory to provide sufficient conditions for permanence of the system. Finally, we develop a partially degenerate reaction diffusion system, providing a numerical exploration based on the results obtained for the temporal system. We show that a traveling wave solution may exist where the speed of the wave follows a power law.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41999100","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}
Pub Date : 2019-01-01Epub Date: 2019-10-15DOI: 10.11145/j.biomath.2019.10.037
Boseung Choi, Sydney Busch, Dieudonné Kazadi, Benoit Ilunga, Emile Okitolonda, Yi Dai, Robert Lumpkin, Omar Saucedo, Wasiur R KhudaBukhsh, Joseph Tien, Marcel Yotebieng, Eben Kenah, Grzegorz A Rempala
We describe two approaches to modeling data from a small to moderate-sized epidemic outbreak. The first approach is based on a branching process approximation and direct analysis of the transmission network, whereas the second one is based on a survival model derived from the classical SIR equations with no explicit transmission information. We compare these approaches using data from a 2012 outbreak of Ebola virus disease caused by Bundibugyo ebolavirus in city of Isiro, Democratic Republic of the Congo. The branching process model allows for a direct comparison of disease transmission across different environments, such as the general community or the Ebola treatment unit. However, the survival model appears to yield parameter estimates with more accuracy and better precision in some circumstances.
我们介绍了对中小规模疫情数据建模的两种方法。第一种方法基于分支过程近似和对传播网络的直接分析，而第二种方法则基于由经典 SIR 方程推导出的生存模型，没有明确的传播信息。我们利用 2012 年在刚果民主共和国伊西罗市爆发的由本迪布吉埃博拉病毒引起的埃博拉病毒病的数据对这两种方法进行了比较。分支过程模型可直接比较疾病在不同环境中的传播情况，如普通社区或埃博拉治疗单位。不过，在某些情况下，生存模型似乎能得出更准确、更精确的参数估计。
{"title":"Modeling outbreak data: Analysis of a 2012 Ebola virus disease epidemic in DRC.","authors":"Boseung Choi, Sydney Busch, Dieudonné Kazadi, Benoit Ilunga, Emile Okitolonda, Yi Dai, Robert Lumpkin, Omar Saucedo, Wasiur R KhudaBukhsh, Joseph Tien, Marcel Yotebieng, Eben Kenah, Grzegorz A Rempala","doi":"10.11145/j.biomath.2019.10.037","DOIUrl":"10.11145/j.biomath.2019.10.037","url":null,"abstract":"<p><p>We describe two approaches to modeling data from a small to moderate-sized epidemic outbreak. The first approach is based on a branching process approximation and direct analysis of the transmission network, whereas the second one is based on a survival model derived from the classical SIR equations with no explicit transmission information. We compare these approaches using data from a 2012 outbreak of Ebola virus disease caused by <i>Bundibugyo ebolavirus</i> in city of Isiro, Democratic Republic of the Congo. The branching process model allows for a direct comparison of disease transmission across different environments, such as the general community or the Ebola treatment unit. However, the survival model appears to yield parameter estimates with more accuracy and better precision in some circumstances.</p>","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7665115/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38606788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-20DOI: 10.11145/J.BIOMATH.2018.12.167
V. Yatat, Alexis Tamen Tchuinte, Y. Dumont, P. Couteron
The savanna biome encompasses a variety of vegetation physiognomies that traduce complex dynamical responses of plants to the rainfall gradients leading from tropical forests to hot deserts. Such responses are shaped by interactions between woody and grassy plants that can be either direct, disturbance-mediated or both. There has been increasing evidence that several vegetation physiognomies, sometimes highly contrasted, may durably coexist under similar rainfall conditions suggesting multi-stability or at least not abrupt transitions. These fascinating questions have triggered burgeoning modelling efforts which have, however, not yet delivered an integrated picture liable to furnish sensible predictions of potential vegetation at broad scales. In this paper, we will recall the key ecological processes and resulting vegetation dynamics that models should take into account. We will also present the main modelling options present in the literature and advocate the use of minimalistic models, capturing only the essential processes while retaining sufficient mathematical tractability and restricting themselves to a minimal set of parameters assessable from the overall literature.
{"title":"A tribute to the use of minimalistic spatially-implicit models of savanna vegetation dynamics to address broad spatial scales in spite of scarce data","authors":"V. Yatat, Alexis Tamen Tchuinte, Y. Dumont, P. Couteron","doi":"10.11145/J.BIOMATH.2018.12.167","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2018.12.167","url":null,"abstract":"The savanna biome encompasses a variety of vegetation physiognomies that traduce complex dynamical responses of plants to the rainfall gradients leading from tropical forests to hot deserts. Such responses are shaped by interactions between woody and grassy plants that can be either direct, disturbance-mediated or both. There has been increasing evidence that several vegetation physiognomies, sometimes highly contrasted, may durably coexist under similar rainfall conditions suggesting multi-stability or at least not abrupt transitions. These fascinating questions have triggered burgeoning modelling efforts which have, however, not yet delivered an integrated picture liable to furnish sensible predictions of potential vegetation at broad scales. In this paper, we will recall the key ecological processes and resulting vegetation dynamics that models should take into account. We will also present the main modelling options present in the literature and advocate the use of minimalistic models, capturing only the essential processes while retaining sufficient mathematical tractability and restricting themselves to a minimal set of parameters assessable from the overall literature.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43235878","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}
Pub Date : 2018-12-19DOI: 10.11145/J.BIOMATH.2018.12.057
A. Adeniji, I. Fedotov, M. Shatalov
In this paper we undertake to consider the inverse problem of parameter identification of nonlinear system of ordinary differential equations for a specific case of complete information about solution of the Holling-Tanner model for finite number of points for the finite time interval. In this model the equations are nonlinearly dependent on the unknown parameters. By means of the proposed transformation the obtained equations become linearly dependent on new parameters functionally dependent on the original ones. This simplification is achieved by the fact that the new set of parameters becomes dependent and the corresponding constraint between the parameters is nonlinear. If the conventional approach based on introduction of the Lagrange multiplier is used this circumstance will result in a nonlinear system of equations. A novel algorithm of the problem solution is proposed in which only one nonlinear equation instead of the system of six nonlinear equations has to be solved. Differentiation and integration methods of the problem solution are implemented and it is shown that the integration method produces more accurate results and uses less number of points on the given time interval.
{"title":"Inverse problem of the Holling-Tanner model and its solution","authors":"A. Adeniji, I. Fedotov, M. Shatalov","doi":"10.11145/J.BIOMATH.2018.12.057","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2018.12.057","url":null,"abstract":"In this paper we undertake to consider the inverse problem of parameter identification of nonlinear system of ordinary differential equations for a specific case of complete information about solution of the Holling-Tanner model for finite number of points for the finite time interval. In this model the equations are nonlinearly dependent on the unknown parameters. By means of the proposed transformation the obtained equations become linearly dependent on new parameters functionally dependent on the original ones. This simplification is achieved by the fact that the new set of parameters becomes dependent and the corresponding constraint between the parameters is nonlinear. If the conventional approach based on introduction of the Lagrange multiplier is used this circumstance will result in a nonlinear system of equations. A novel algorithm of the problem solution is proposed in which only one nonlinear equation instead of the system of six nonlinear equations has to be solved. Differentiation and integration methods of the problem solution are implemented and it is shown that the integration method produces more accurate results and uses less number of points on the given time interval.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44979062","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}
Pub Date : 2018-12-18DOI: 10.11145/J.BIOMATH.2018.12.037
E. Peynaud
The time dependant advection-reaction-diffusion equation is used in the C-Root model to simulate root growth. This equation can also be applied in many others applications in life sciences. In this context the unknown is related to densities and one of the important property of the problem is that the solution is non-negative for positive initial conditions. One of the difficulty at the discrete level is to preserve the positivity of the approximated solution during the simulations. In this work we solved the model using Discontinuous Galerkin elements combined with an operator splitting technique. The DG method is briefly presented then we motivated the use of the operator splitting technique by doing some numerical experiments. Those experiments showed that the same time approximation scheme may not be suitable for all the operators of the model. We validated our implementation of the splitting technique in a simple test case. Then we performed a simulation of a plagiotropic root of Eucalyptus.
{"title":"Simulation of a time dependent advection-reaction-diffusion problem using operator splitting and discontinuous Galerkin methods with application to plant root growth","authors":"E. Peynaud","doi":"10.11145/J.BIOMATH.2018.12.037","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2018.12.037","url":null,"abstract":"The time dependant advection-reaction-diffusion equation is used in the C-Root model to simulate root growth. This equation can also be applied in many others applications in life sciences. In this context the unknown is related to densities and one of the important property of the problem is that the solution is non-negative for positive initial conditions. One of the difficulty at the discrete level is to preserve the positivity of the approximated solution during the simulations. In this work we solved the model using Discontinuous Galerkin elements combined with an operator splitting technique. The DG method is briefly presented then we motivated the use of the operator splitting technique by doing some numerical experiments. Those experiments showed that the same time approximation scheme may not be suitable for all the operators of the model. We validated our implementation of the splitting technique in a simple test case. Then we performed a simulation of a plagiotropic root of Eucalyptus.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42306555","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}
Pub Date : 2018-10-27DOI: 10.11145/J.BIOMATH.2018.10.197
B. Roth
The mechanical bidomain model is a mathematical description of biological tissue that focuses on mechanotransduction. The model’s fundamental hypothesis is that differences in the intracellular and extracellular displacements activate integrins, causing a cascade of biological effects. This paper presents analytical solutions of the bidomain equations for an extracellular point force. The intra- and extracellular spaces are incompressible, isotropic, and coupled. The expressions for the intra- and extracellular displacements each contain three terms: a monodomain term that is identical in the two spaces, and two bidomain terms, one of which decays exponentially. Near the origin the intracellular displacement remains finite and the extracellular displacement diverges. Far from the origin the monodomain displacement decays in inverse proportion to the distance, the strain decays as the distance squared, and the difference between the intra- and extracellular displacements decays as the distance cubed. These predictions could be tested by applying a force to a magnetic nanoparticle embedded in the extracellular matrix and recording the mechanotransduction response.
{"title":"Mechanotransduction caused by a point force in the extracellular space","authors":"B. Roth","doi":"10.11145/J.BIOMATH.2018.10.197","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2018.10.197","url":null,"abstract":"The mechanical bidomain model is a mathematical description of biological tissue that focuses on mechanotransduction. The model’s fundamental hypothesis is that differences in the intracellular and extracellular displacements activate integrins, causing a cascade of biological effects. This paper presents analytical solutions of the bidomain equations for an extracellular point force. The intra- and extracellular spaces are incompressible, isotropic, and coupled. The expressions for the intra- and extracellular displacements each contain three terms: a monodomain term that is identical in the two spaces, and two bidomain terms, one of which decays exponentially. Near the origin the intracellular displacement remains finite and the extracellular displacement diverges. Far from the origin the monodomain displacement decays in inverse proportion to the distance, the strain decays as the distance squared, and the difference between the intra- and extracellular displacements decays as the distance cubed. These predictions could be tested by applying a force to a magnetic nanoparticle embedded in the extracellular matrix and recording the mechanotransduction response.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47482328","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}
Pub Date : 2018-09-20DOI: 10.11145/J.BIOMATH.2018.11.097
Nikolaos Sfakianakis, D. Peurichard, Aaron Brunk, C. Schmeiser
We extend the live-cell motility Filament Based Lamellipodium Model (FBLM) to incorporate the forces exerted on the lamellipodium of the cells due to cell-cell collision and cadherin induced cell-cell adhesion. We take into account the nature of these forces via physical and biological constraints and modelling assumptions. We investigate the effect these new components have in the migration and morphology of the cells through particular experiments. We exhibit moreover the similarities between our simulated cells and HeLa cancer cells.
{"title":"Modelling cell-cell collision and adhesion with the filament based lamellipodium model","authors":"Nikolaos Sfakianakis, D. Peurichard, Aaron Brunk, C. Schmeiser","doi":"10.11145/J.BIOMATH.2018.11.097","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2018.11.097","url":null,"abstract":"We extend the live-cell motility Filament Based Lamellipodium Model (FBLM) to incorporate the forces exerted on the lamellipodium of the cells due to cell-cell collision and cadherin induced cell-cell adhesion. We take into account the nature of these forces via physical and biological constraints and modelling assumptions. We investigate the effect these new components have in the migration and morphology of the cells through particular experiments. We exhibit moreover the similarities between our simulated cells and HeLa cancer cells.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47297853","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}
Pub Date : 2018-08-14DOI: 10.11145/J.BIOMATH.2018.07.317
R. Anguelov, N. Kyurkchiev, S. Markov
The paper considers the sigmoid function definedthrough the hyper-log-logistic model introduced by Blumberg. We study the Hausdorff distance of this sigmoid to the Heaviside function, which characterises the shape of switching from 0 to 1. Estimates of the Hausdorff distance in terms of the intrinsic growth rate are derived. We construct a family of recurrence generated sigmoidal functions based on the hyper-log-logistic function. Numerical illustrations are provided.
{"title":"Some properties of the Blumberg's hyper-log-logistic curve","authors":"R. Anguelov, N. Kyurkchiev, S. Markov","doi":"10.11145/J.BIOMATH.2018.07.317","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2018.07.317","url":null,"abstract":"The paper considers the sigmoid function definedthrough the hyper-log-logistic model introduced by Blumberg. We study the Hausdorff distance of this sigmoid to the Heaviside function, which characterises the shape of switching from 0 to 1. Estimates of the Hausdorff distance in terms of the intrinsic growth rate are derived. We construct a family of recurrence generated sigmoidal functions based on the hyper-log-logistic function. Numerical illustrations are provided.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47960402","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}
Pub Date : 2018-08-07DOI: 10.11145/J.BIOMATH.2018.07.219
P. T. Mouofo, J. Tewa, S. Bowong
The Hepatitis delta virus (HDV) is a defect RNA virus that requires the presence of the hepatitis B virus (HBV) for cellular infection. A co-infection may result in a more severe acute disease and a higher risk of developing acute liver failure compared with those infected with HBV alone. At the present time, there has been very little to the modeling of HDV. The derivation and analysis of such a mathematical model poses difficulty as it requires the inclusion of (HBV). In this paper, a within-host model for the co-interaction of HDV and HBV is presented and rigorously analyzed. We calculate the basic reproduction number (Ro), the disease-free equilibrium, boundary equilibrium, which we define as the existence of one disease along with the complete eradication of the other disease, and the co-infection equilibrium. We determine stability criteria for the disease-free and boundary equilibrium. We also use the optimal control theory to assess the disease control. Numerical simulations have been presented to illustrate analytical results.
{"title":"Modelling and analysis of a within-host model of hepatitis B and D co-infections","authors":"P. T. Mouofo, J. Tewa, S. Bowong","doi":"10.11145/J.BIOMATH.2018.07.219","DOIUrl":"https://doi.org/10.11145/J.BIOMATH.2018.07.219","url":null,"abstract":"The Hepatitis delta virus (HDV) is a defect RNA virus that requires the presence of the hepatitis B virus (HBV) for cellular infection. A co-infection may result in a more severe acute disease and a higher risk of developing acute liver failure compared with those infected with HBV alone. At the present time, there has been very little to the modeling of HDV. The derivation and analysis of such a mathematical model poses difficulty as it requires the inclusion of (HBV). In this paper, a within-host model for the co-interaction of HDV and HBV is presented and rigorously analyzed. We calculate the basic reproduction number (Ro), the disease-free equilibrium, boundary equilibrium, which we define as the existence of one disease along with the complete eradication of the other disease, and the co-infection equilibrium. We determine stability criteria for the disease-free and boundary equilibrium. We also use the optimal control theory to assess the disease control. Numerical simulations have been presented to illustrate analytical results.","PeriodicalId":52247,"journal":{"name":"Biomath","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48649005","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：