A system of two ordinary differential equations is proposed to model chemically-mediated interactions between plants and herbivores by incorporating a toxin-modifiednumerical response. This numerical response accounts for the reduction in the her-bivore's growth and reproduction due to chemical defenses from plants. It is shownthat the system exhibits very rich dynamics including saddle-node bifurcations, Hopfbifurcations, homoclinic bifurcations and co-dimension 2 bifurcations. Numerical sim-ulations are presented to illustrate the occurrence of multitype bistability, limit cycles,homoclinic orbits and heteroclinic orbits. We also discuss the ecological implicationsof the resulting dynamics.
{"title":"Dynamics of a plant-herbivore model with a chemically-mediated numerical response","authors":"Lin Wang, James Watmough, Fang Yu","doi":"10.5206/mase/11067","DOIUrl":"https://doi.org/10.5206/mase/11067","url":null,"abstract":"A system of two ordinary differential equations is proposed to model chemically-mediated interactions between plants and herbivores by incorporating a toxin-modifiednumerical response. This numerical response accounts for the reduction in the her-bivore's growth and reproduction due to chemical defenses from plants. It is shownthat the system exhibits very rich dynamics including saddle-node bifurcations, Hopfbifurcations, homoclinic bifurcations and co-dimension 2 bifurcations. Numerical sim-ulations are presented to illustrate the occurrence of multitype bistability, limit cycles,homoclinic orbits and heteroclinic orbits. We also discuss the ecological implicationsof the resulting dynamics.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70664469","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 order to determine the effectiveness of non-pharmaceutical interventions on an epidemic, we develop an agent-based model that simulates the spread of an infectious disease in a small community and its emerging phenomena. We vary parameters such as initial population, initial infected, infection rate, recovery rate, death rate, and asymptomatic rates, as inputs. Our simulations show that (i) random mass testing decreases the number of deaths, infections and time duration; (ii) as well as quarantines; (iii) social distancing lengthen outbreak period to an extent and helps flatten the epidemic curve; and (iv) the most effective combination of NPIs to minimize death, infection and duration is no mass testing, no social distancing and a total lockdown. Results of this study can aid decision makers in their policies to be implemented to have an optimal output.
{"title":"Determining the effectiveness of practicing non-pharmaceutical interventions in improving virus control in a pandemic using agent-based modelling","authors":"C. A. Buhat, S. Villanueva","doi":"10.5206/mase/10876","DOIUrl":"https://doi.org/10.5206/mase/10876","url":null,"abstract":"In order to determine the effectiveness of non-pharmaceutical interventions on an epidemic, we develop an agent-based model that simulates the spread of an infectious disease in a small community and its emerging phenomena. We vary parameters such as initial population, initial infected, infection rate, recovery rate, death rate, and asymptomatic rates, as inputs. Our simulations show that (i) random mass testing decreases the number of deaths, infections and time duration; (ii) as well as quarantines; (iii) social distancing lengthen outbreak period to an extent and helps flatten the epidemic curve; and (iv) the most effective combination of NPIs to minimize death, infection and duration is no mass testing, no social distancing and a total lockdown. Results of this study can aid decision makers in their policies to be implemented to have an optimal output.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48943517","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}
Ordinary differential equations models have a wide variety of applications in the fields of mathematics, statistics, and the sciences. Though they are widely used, these models are sometimes viewed as inflexible with respect to the incorporation of time delays. The Generalized Linear Chain Trick (GLCT) serves as a way for modelers to incorporate much more flexible delay or dwell time distribution assumptions than the usual exponential and Erlang distributions. In this paper we demonstrate how the GLCT can be used to generate new ODE models by generalizing or approximating existing models to yield much more general ODEs with phase-type distributed delays or dwell times.
{"title":"A procedure for deriving new ODE models: Using the generalized linear chain trick to incorporate phase-type distributed delay and dwell time assumptions","authors":"P. Hurtado, Cameron Richards","doi":"10.5206/mase/10857","DOIUrl":"https://doi.org/10.5206/mase/10857","url":null,"abstract":"Ordinary differential equations models have a wide variety of applications in the fields of mathematics, statistics, and the sciences. Though they are widely used, these models are sometimes viewed as inflexible with respect to the incorporation of time delays. The Generalized Linear Chain Trick (GLCT) serves as a way for modelers to incorporate much more flexible delay or dwell time distribution assumptions than the usual exponential and Erlang distributions. In this paper we demonstrate how the GLCT can be used to generate new ODE models by generalizing or approximating existing models to yield much more general ODEs with phase-type distributed delays or dwell times.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70664420","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}
Preface: Thematic Issue in Mathematical Biology and Applied Evolutionary Equations
前言：数学生物学与应用进化方程专题
{"title":"Preface: Thematic Issue in Mathematical Biology and Applied Evolutionary Equations","authors":"N. Vaidya, Dhruba R. Adhikari","doi":"10.5206/mase/13502","DOIUrl":"https://doi.org/10.5206/mase/13502","url":null,"abstract":"Preface: Thematic Issue in Mathematical Biology and Applied Evolutionary Equations","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48065761","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 vadose zone is the portion of the subsurface above the water table and its pore space usually contains air and water. Due to the presence of infiltration, erosion, plant growth, microbiota, contaminant transport, aquifer recharge, and discharge to surface water, it is crucial to predict the transport rate of water and other substances within this zone. However, flow in the vadose zone has many complications as the parameters that control it are extremely sensitive to the saturation of the media, leading to a nonlinear problem. This flow is referred as unsaturated flow and is governed by Richards equation. Analytical solutions for this equation exists only for simplified cases, so most practical situations require a numerical solution. Nevertheless, the nonlinear nature of Richards equation introduces challenges that causes numerical solutions for this problem to be computationally expensive and, in some cases, unreliable. High order mimetic finite difference operators are discrete analogs of the continuous differential operators and have been extensively used in the fields of fluid and solid mechanics. In this work, we present a numerical approach involving high order mimetic operators along with a Newton root-finding algorithm for the treatment of the nonlinear component. Fully-implicit time discretization scheme is used to deal with the problem’s stiffness.
{"title":"High order mimetic difference simulation of unsaturated flow using Richards equation","authors":"Angel Boada Velazco, Johnny Corbino, J. Castillo","doi":"10.5206/mase/10874","DOIUrl":"https://doi.org/10.5206/mase/10874","url":null,"abstract":"The vadose zone is the portion of the subsurface above the water table and its pore space usually contains air and water. Due to the presence of infiltration, erosion, plant growth, microbiota, contaminant transport, aquifer recharge, and discharge to surface water, it is crucial to predict the transport rate of water and other substances within this zone. However, flow in the vadose zone has many complications as the parameters that control it are extremely sensitive to the saturation of the media, leading to a nonlinear problem. This flow is referred as unsaturated flow and is governed by Richards equation. Analytical solutions for this equation exists only for simplified cases, so most practical situations require a numerical solution. Nevertheless, the nonlinear nature of Richards equation introduces challenges that causes numerical solutions for this problem to be computationally expensive and, in some cases, unreliable. High order mimetic finite difference operators are discrete analogs of the continuous differential operators and have been extensively used in the fields of fluid and solid mechanics. In this work, we present a numerical approach involving high order mimetic operators along with a Newton root-finding algorithm for the treatment of the nonlinear component. Fully-implicit time discretization scheme is used to deal with the problem’s stiffness.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70664458","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 describe an empirical forecasting method for epidemic outbreaks. It is an iterative process to find possible parameter values for epidemic models to best fit real data. As a demonstration of principle, we used the logistic model, the simplest model in epidemiology, for an experiment of live forecasting. Short-term forecasts can last to 5 or more days with relative errors consistently kept blow 5%. The method should improve with more realistic models.
{"title":"An empirical forecasting method for epidemic outbreaks with application to Covid-19","authors":"Bo Deng","doi":"10.5206/mase/11101","DOIUrl":"https://doi.org/10.5206/mase/11101","url":null,"abstract":"In this paper we describe an empirical forecasting method for epidemic outbreaks. It is an iterative process to find possible parameter values for epidemic models to best fit real data. As a demonstration of principle, we used the logistic model, the simplest model in epidemiology, for an experiment of live forecasting. Short-term forecasts can last to 5 or more days with relative errors consistently kept blow 5%. The method should improve with more realistic models.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46098863","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}
Dylan Hull-Nye, Bhawna Malik, R. Keshavamurthy, E. J. Schwartz
The prevalence of end stage renal disease (ESRD) is rising among HIV-infected populations in several regions worldwide. We used an ordinary differential equation model of the dynamics of the AIDS and HIV+ ESRD populations to investigate the effect of antiretroviral therapy (ART) on the transient dynamics of the epidemic. We considered ART that blocks the entry to each population, by preventing individuals from joining the AIDS population and by reducing the development from AIDS to HIV+ ESRD, as well as the combined effects together. Numerical simulation of our model revealed that when levels of ART are below 100%, the prevalence of HIV+ ESRD drops, but then increases again due to the recovery in the AIDS population. The effect can be seen with ART acting to block entry into either population. We then examined the dip in HIV+ ESRD seen with ART analytically by calculating the minimum HIV+ ESRD level and the time to achieve this minimum. We also evaluated the length of time to reach the minimum and its dependence on ART parameters, both singly and in combination. We conclude that our model predicts that the drop in HIV+ ESRD prevalence seen after increased ART will be followed by an increase, unless ART is sufficiently high enough to eradicate HIV/AIDS.
{"title":"Transient dynamics of the renal disease epidemic among HIV-infected individuals","authors":"Dylan Hull-Nye, Bhawna Malik, R. Keshavamurthy, E. J. Schwartz","doi":"10.5206/mase/10852","DOIUrl":"https://doi.org/10.5206/mase/10852","url":null,"abstract":"The prevalence of end stage renal disease (ESRD) is rising among HIV-infected populations in several regions worldwide. We used an ordinary differential equation model of the dynamics of the AIDS and HIV+ ESRD populations to investigate the effect of antiretroviral therapy (ART) on the transient dynamics of the epidemic. We considered ART that blocks the entry to each population, by preventing individuals from joining the AIDS population and by reducing the development from AIDS to HIV+ ESRD, as well as the combined effects together. Numerical simulation of our model revealed that when levels of ART are below 100%, the prevalence of HIV+ ESRD drops, but then increases again due to the recovery in the AIDS population. The effect can be seen with ART acting to block entry into either population. We then examined the dip in HIV+ ESRD seen with ART analytically by calculating the minimum HIV+ ESRD level and the time to achieve this minimum. We also evaluated the length of time to reach the minimum and its dependence on ART parameters, both singly and in combination. We conclude that our model predicts that the drop in HIV+ ESRD prevalence seen after increased ART will be followed by an increase, unless ART is sufficiently high enough to eradicate HIV/AIDS.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41507192","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}
T. Bolger, Brydon Eastman, Madeleine Hill, G. Wolkowicz
A model of predator-prey interaction in a chemostat with Holling Type II functional and numerical response functions of the Monod or Michaelis-Menten form is considered. It is proved that local asymptotic stability of the coexistence equilibrium implies that it is globally asymptotically stable. It is also shown that when the coexistence equilibrium exists but is unstable, solutions converge to a unique, orbitally asymptotically stable periodic orbit. Thus the range of the dynamics of the chemostat predator-prey model is the same as for the analogous classical Rosenzweig-MacArthur predator-prey model with Holling Type II functional response. An extension that applies to other functional rsponses is also given.
{"title":"A Predator-Prey model in the chemostat with Holling Type II response function","authors":"T. Bolger, Brydon Eastman, Madeleine Hill, G. Wolkowicz","doi":"10.5206/mase/10842","DOIUrl":"https://doi.org/10.5206/mase/10842","url":null,"abstract":"A model of predator-prey interaction in a chemostat with Holling Type II functional and numerical response functions of the Monod or Michaelis-Menten form is considered. It is proved that local asymptotic stability of the coexistence equilibrium implies that it is globally asymptotically stable. It is also shown that when the coexistence equilibrium exists but is unstable, solutions converge to a unique, orbitally asymptotically stable periodic orbit. Thus the range of the dynamics of the chemostat predator-prey model is the same as for the analogous classical Rosenzweig-MacArthur predator-prey model with Holling Type II functional response. An extension that applies to other functional rsponses is also given.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44277612","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 give a review of the recent progress on the focusing generalized Hartree equation, which is a nonlinear Schrodinger-type equation with the nonlocal nonlinearity, expressed as a convolution with the Riesz potential. We describe the local well-posedness in H1 and Hs settings, discuss the extension to the global existence and scattering, or finite time blow-up. We point out different techniques used to obtain the above results, and then show the numerical investigations of the stable blow-up in the L2 -critical setting. We finish by showing known analytical results about the stable blow-up dynamics in the L2 -critical setting.
{"title":"On the focusing generalized Hartree equation","authors":"A. Arora, S. Roudenko, Kai Yang","doi":"10.5206/mase/10855","DOIUrl":"https://doi.org/10.5206/mase/10855","url":null,"abstract":"In this paper we give a review of the recent progress on the focusing generalized Hartree equation, which is a nonlinear Schrodinger-type equation with the nonlocal nonlinearity, expressed as a convolution with the Riesz potential. We describe the local well-posedness in H1 and Hs settings, discuss the extension to the global existence and scattering, or finite time blow-up. We point out different techniques used to obtain the above results, and then show the numerical investigations of the stable blow-up in the L2 -critical setting. We finish by showing known analytical results about the stable blow-up dynamics in the L2 -critical setting.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42080027","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 many developing countries, including Nepal, rabies epidemics constitute a serious public health concern, partly because of limited resources for proper implementation of control measures. In this study, we develop an extended model by incorporating various controls into the transmission dynamics model with both dog and jackal vectors. We apply the optimal control theory on the developed model system to identify optimal control strategy for mitigating rabies burden in Nepal with limited resources. Among the potential control strategies, human vaccination, dog vaccination, dog culling, dog sterilization, and jackal vaccination, considered in this study, our results show that a combination of dog vaccination and dog culling is the most effective strategy to control rabies in Nepal. Our optimal control solutions provide the strategy for optimal implementation of these controls to suppress rabies prevalence among dogs and jackals of Nepal using a minimum cost associated with controls. We found that given limited resources, implementing controls in a time-dependent manner with a higher level at the beginning of the outbreaks and reducing them during later part of the epidemics can provide maximum benefits.
{"title":"Controlling rabies epidemics in Nepal with limited resources: optimal control theory approach","authors":"Buddhi Pantha, H. Joshi, N. Vaidya","doi":"10.5206/mase/10847","DOIUrl":"https://doi.org/10.5206/mase/10847","url":null,"abstract":"In many developing countries, including Nepal, rabies epidemics constitute a serious public health concern, partly because of limited resources for proper implementation of control measures. In this study, we develop an extended model by incorporating various controls into the transmission dynamics model with both dog and jackal vectors. We apply the optimal control theory on the developed model system to identify optimal control strategy for mitigating rabies burden in Nepal with limited resources. Among the potential control strategies, human vaccination, dog vaccination, dog culling, dog sterilization, and jackal vaccination, considered in this study, our results show that a combination of dog vaccination and dog culling is the most effective strategy to control rabies in Nepal. Our optimal control solutions provide the strategy for optimal implementation of these controls to suppress rabies prevalence among dogs and jackals of Nepal using a minimum cost associated with controls. We found that given limited resources, implementing controls in a time-dependent manner with a higher level at the beginning of the outbreaks and reducing them during later part of the epidemics can provide maximum benefits.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45918845","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：