In this paper we the study of dynamics of time since infection structured vector born model with the direct transmission. We use standard incidence term to model the new infections. We analyze the corresponding system of partial differential equation and obtain an explicit formula for the basic reproduction number ℜ0. The diseases-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number is less than one, ℜ0 < 1. Endemic equilibrium exists and is locally asymptotically stable when ℜ0 > 1. The disease will persist at the endemic equilibrium whenever the basic reproduction number is greater than one.
{"title":"Dynamics of a Vector-Borne model with direct transmission and age of infection","authors":"N. Tuncer, S. Giri","doi":"10.1051/MMNP/2021019","DOIUrl":"https://doi.org/10.1051/MMNP/2021019","url":null,"abstract":"In this paper we the study of dynamics of time since infection structured vector born model with the direct transmission. We use standard incidence term to model the new infections. We analyze the corresponding system of partial differential equation and obtain an explicit formula for the basic reproduction number ℜ0. The diseases-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number is less than one, ℜ0 < 1. Endemic equilibrium exists and is locally asymptotically stable when ℜ0 > 1. The disease will persist at the endemic equilibrium whenever the basic reproduction number is greater than one.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47345418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Clotilde Djuikem, F. Grognard, R. Wafo, S. Touzeau, S. Bowong
Coffee leaf rust (CLR) is one of the main diseases that affect coffee plantations worldwide. It is caused by the fungus Hemileia vastatrix. Damages induce severe yield losses (up to 70%). Its control mainly relies on cultural practices and fungicides, the latter having harmful ecological impact and important cost. Our goal is to understand the propagation of this fungus in order to propose a biocontrol solution, based on a mycoparasite that inhibits H. vastatrix reproduction. We develop and explore a spatio-temporal model that describes CLR propagation in a coffee plantation during the rainy and dry seasons. We show the existence of a solution and prove that there exists two threshold parameters, the dry and rainy basic reproduction numbers, that determine the stability of the equilibria for the dry and rainy season subsystems. To illustrate these theoretical results, numerical simulations are performed, using a non-standard finite method to integrate the pest model. We also numerically investigate the biocontrol impact. We determine its efficiency threshold in order to ensure CLR eradication.
{"title":"Modelling coffee leaf rust dynamics to control its spread","authors":"Clotilde Djuikem, F. Grognard, R. Wafo, S. Touzeau, S. Bowong","doi":"10.1051/MMNP/2021018","DOIUrl":"https://doi.org/10.1051/MMNP/2021018","url":null,"abstract":"Coffee leaf rust (CLR) is one of the main diseases that affect coffee plantations worldwide. It is caused by the fungus Hemileia vastatrix. Damages induce severe yield losses (up to 70%). Its control mainly relies on cultural practices and fungicides, the latter having harmful ecological impact and important cost. Our goal is to understand the propagation of this fungus in order to propose a biocontrol solution, based on a mycoparasite that inhibits H. vastatrix reproduction. We develop and explore a spatio-temporal model that describes CLR propagation in a coffee plantation during the rainy and dry seasons. We show the existence of a solution and prove that there exists two threshold parameters, the dry and rainy basic reproduction numbers, that determine the stability of the equilibria for the dry and rainy season subsystems. To illustrate these theoretical results, numerical simulations are performed, using a non-standard finite method to integrate the pest model. We also numerically investigate the biocontrol impact. We determine its efficiency threshold in order to ensure CLR eradication.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48767012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we investigate the non-constant stationary solutions of a general Gause-type predator-prey system with self- and cross-diffusions subject to the homogeneous Neumann boundary condition. In the system, the cross-diffusions are introduced in such a way that the prey runs away from the predator, while the predator moves away from a large group of preys. Firstly, we establish a priori estimate for the positive solutions. Secondly, we study the non-existence results of non-constant positive solutions. Finally, we consider the existence of non-constant positive solutions and discuss the Turing instability of the positive constant solution.
{"title":"Non-constant positive solutions of a general Gause-type predator-prey system with self- and cross-diffusions","authors":"Pan Xue, Yunfeng Jia, Cuiping Ren, Xingjun Li","doi":"10.1051/MMNP/2021017","DOIUrl":"https://doi.org/10.1051/MMNP/2021017","url":null,"abstract":"In this paper, we investigate the non-constant stationary solutions of a general Gause-type predator-prey system with self- and cross-diffusions subject to the homogeneous Neumann boundary condition. In the system, the cross-diffusions are introduced in such a way that the prey runs away from the predator, while the predator moves away from a large group of preys. Firstly, we establish a priori estimate for the positive solutions. Secondly, we study the non-existence results of non-constant positive solutions. Finally, we consider the existence of non-constant positive solutions and discuss the Turing instability of the positive constant solution.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41410357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we investigate a initial value problem for the Caputo time-fractional pseudo-parabolic equations with fractional Laplace operator of order 0 < ν ≤ 1 and the nonlinear memory source term. For 0 < ν < 1, the problem will be considered on a bounded domain of ℝd. By some Sobolev embeddings and the properties of the Mittag-Leffler function, we will give some results on the existence and the uniqueness of mild solution for problem (1.1) below. When ν = 1, we will introduce some Lp − Lq estimates, and based on them we derive the global existence of a mild solution in the whole space ℝd.
{"title":"Initial value problem for fractional Volterra integrodifferential pseudo-parabolic equations","authors":"N. Phuong, N. Tuan, Devendra Kumar, N. Tuan","doi":"10.1051/MMNP/2021015","DOIUrl":"https://doi.org/10.1051/MMNP/2021015","url":null,"abstract":"In this paper, we investigate a initial value problem for the Caputo time-fractional pseudo-parabolic equations with fractional Laplace operator of order 0 < ν ≤ 1 and the nonlinear memory source term. For 0 < ν < 1, the problem will be considered on a bounded domain of ℝd. By some Sobolev embeddings and the properties of the Mittag-Leffler function, we will give some results on the existence and the uniqueness of mild solution for problem (1.1) below. When ν = 1, we will introduce some Lp − Lq estimates, and based on them we derive the global existence of a mild solution in the whole space ℝd.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49609107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We give a brief review of several prominent fluid instabilities representing transitions driven by gravity, surface tension, thermal energy, and applied motion/acceleration. Strategies for controlling these instabilities, including their pattern formation properties, are discussed. The importance of gravity for many common fluid instabilities is emphasized and used to understand the sometimes dramatically different behavior of fluids in microgravity environments. This is illustrated in greater detail, using recent results, for the case of the frozen wave instability, which leads to large columnar structures in the absence of gravity. The development of these highly nonlinear states is often complex, but can be manipulated through an appropriate choice of forcing amplitude, container length and height, initial inclination of the surface, and other parameters affecting the nonlinear and inhomogeneous growth process. The increased opportunity for controlling fluids and their instabilities via small forcing or parameter changes in microgravity is noted.
{"title":"A review of fluid instabilities and control strategies with applications in microgravity","authors":"J. Porter, P. S. Sánchez, V. Shevtsova, V. Yasnou","doi":"10.1051/MMNP/2021020","DOIUrl":"https://doi.org/10.1051/MMNP/2021020","url":null,"abstract":"We give a brief review of several prominent fluid instabilities representing transitions driven by gravity, surface tension, thermal energy, and applied motion/acceleration. Strategies for controlling these instabilities, including their pattern formation properties, are discussed. The importance of gravity for many common fluid instabilities is emphasized and used to understand the sometimes dramatically different behavior of fluids in microgravity environments. This is illustrated in greater detail, using recent results, for the case of the frozen wave instability, which leads to large columnar structures in the absence of gravity. The development of these highly nonlinear states is often complex, but can be manipulated through an appropriate choice of forcing amplitude, container length and height, initial inclination of the surface, and other parameters affecting the nonlinear and inhomogeneous growth process. The increased opportunity for controlling fluids and their instabilities via small forcing or parameter changes in microgravity is noted.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49570461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The dynamics of a single red blood cell in shear flow is a fluid–structure interaction problem that yields a tremendous richness of behaviors, as a function of the parameters of the problem. A low shear rates, the deformations of the red blood cell remain small and low-order models have been developed, predicting the orientation of the cell and the membrane circulation along time. They reproduce the dynamics observed in experiments and in simulations, but they do not simplify the problem enough to enable simple interpretations of the phenomena. In a process of exploring the red blood cell dynamics at low shear rates, an existing model constituted of 5 nonlinear ordinary differential equations is rewritten using quaternions to parametrize the rotations of the red blood cell. Techniques from algebraic geometry are then used to determine the steady-state solutions of the problems. These solutions are relevant to a particular regime where the red blood cell reaches a constant inclination angle, with its membrane rotating around it, and referred to as frisbee motion. Comparing the numerical solutions of the model to the steady-state solutions allows a better understanding of the transition between the most emblematic motions of red blood cells, flipping and tank-treading.
{"title":"A theoretical investigation of the frisbee motion of red blood cells in shear flow","authors":"T. Mignon, S. Mendez","doi":"10.1051/MMNP/2021014","DOIUrl":"https://doi.org/10.1051/MMNP/2021014","url":null,"abstract":"The dynamics of a single red blood cell in shear flow is a fluid–structure interaction problem that yields a tremendous richness of behaviors, as a function of the parameters of the problem. A low shear rates, the deformations of the red blood cell remain small and low-order models have been developed, predicting the orientation of the cell and the membrane circulation along time. They reproduce the dynamics observed in experiments and in simulations, but they do not simplify the problem enough to enable simple interpretations of the phenomena. In a process of exploring the red blood cell dynamics at low shear rates, an existing model constituted of 5 nonlinear ordinary differential equations is rewritten using quaternions to parametrize the rotations of the red blood cell. Techniques from algebraic geometry are then used to determine the steady-state solutions of the problems. These solutions are relevant to a particular regime where the red blood cell reaches a constant inclination angle, with its membrane rotating around it, and referred to as frisbee motion. Comparing the numerical solutions of the model to the steady-state solutions allows a better understanding of the transition between the most emblematic motions of red blood cells, flipping and tank-treading.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42183681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Domoshnitsky, S. Levi, Ron Hay Kappel, E. Litsyn, R. Yavich
In this paper the exponential stability of linear neutral second order differential equations is studied. In contrast with many other works, coefficients and delays in our equations can be variable. The neutral term makes this object essentially more complicated for the study. A new method for the study of stability of neutral equation based on an idea of the Azbelev W-transform has been proposed. An application to stabilization in a model of human balancing has been described. New stability tests in explicit form are proposed.
{"title":"Stability of neutral delay differential equations with applications in a model of human balancing","authors":"A. Domoshnitsky, S. Levi, Ron Hay Kappel, E. Litsyn, R. Yavich","doi":"10.1051/MMNP/2021008","DOIUrl":"https://doi.org/10.1051/MMNP/2021008","url":null,"abstract":"In this paper the exponential stability of linear neutral second order differential equations is studied. In contrast with many other works, coefficients and delays in our equations can be variable. The neutral term makes this object essentially more complicated for the study. A new method for the study of stability of neutral equation based on an idea of the Azbelev W-transform has been proposed. An application to stabilization in a model of human balancing has been described. New stability tests in explicit form are proposed.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47602566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
H. Rezazadeh, M. Younis, Shafqat-ur-Rehman, M. Eslami, M. Bilal, U. Younas
In this research work, we successfully construct various kinds of exact traveling wave solutions such as trigonometric like, singular and periodic wave solutions as well as hyperbolic solutions to the (2+1)-dimensional Chiral nonlinear Schröginger equation (CNLSE) which is used as a governing equation to discuss the wave in the quantum field theory. The mechanisms which are used to obtain these solutions are extended rational sine-cosine/sinh-cosh and the constraint conditions for the existence of valid solutions are also given. The attained results exhibit that the proposed techniques are a significant addition for exploring several types of nonlinear partial differential equations in applied sciences. Moreover, 3D, 2D-polar and contour profiles are depicted for showing the physical behavior of the reported solutions by setting suitable values of unknown parameters.
{"title":"New exact traveling wave solutions to the (2+1)-dimensional Chiral nonlinear Schrödinger equation","authors":"H. Rezazadeh, M. Younis, Shafqat-ur-Rehman, M. Eslami, M. Bilal, U. Younas","doi":"10.1051/MMNP/2021001","DOIUrl":"https://doi.org/10.1051/MMNP/2021001","url":null,"abstract":"In this research work, we successfully construct various kinds of exact traveling wave solutions such as trigonometric like, singular and periodic wave solutions as well as hyperbolic solutions to the (2+1)-dimensional Chiral nonlinear Schröginger equation (CNLSE) which is used as a governing equation to discuss the wave in the quantum field theory. The mechanisms which are used to obtain these solutions are extended rational sine-cosine/sinh-cosh and the constraint conditions for the existence of valid solutions are also given. The attained results exhibit that the proposed techniques are a significant addition for exploring several types of nonlinear partial differential equations in applied sciences. Moreover, 3D, 2D-polar and contour profiles are depicted for showing the physical behavior of the reported solutions by setting suitable values of unknown parameters.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46320208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. Bisen, Faheem Farooq, Manaeil Hasan, Akhil Patel, J. Rychtář, Dewey T. Taylor
We consider kleptoparasitic interactions between two individuals – the Owner and the Intruder – and model the situation as a sequential game in an extensive form. The Owner is in possession of a resource when another individual, the Intruder, comes along and may try to steal it. If the Intruder makes such a stealing attempt, the Owner has to decide whether to defend the resource; if the Owner defends, the Intruder can withdraw or continue with the stealing attempt. The individuals may value the resource differently and we distinguish three information cases: (a) both individuals know resource values to both of them, (b) individuals know only their own valuation, (c) individuals do not know the value at all. We solve the game in all three cases. We identify scenarios when it is beneficial for the individuals to know as much information as possible. We also identify several scenarios where knowing less seems better as well as show that an individual may not benefit from their opponent knowing less. Finally, we consider the same kind of interactions but without the option for the Intruder to withdraw. We find that, surprisingly, the Intruder typically fares better in that case.
{"title":"Owner-Intruder contests with information asymmetry","authors":"J. Bisen, Faheem Farooq, Manaeil Hasan, Akhil Patel, J. Rychtář, Dewey T. Taylor","doi":"10.1051/MMNP/2021006","DOIUrl":"https://doi.org/10.1051/MMNP/2021006","url":null,"abstract":"We consider kleptoparasitic interactions between two individuals – the Owner and the Intruder – and model the situation as a sequential game in an extensive form. The Owner is in possession of a resource when another individual, the Intruder, comes along and may try to steal it. If the Intruder makes such a stealing attempt, the Owner has to decide whether to defend the resource; if the Owner defends, the Intruder can withdraw or continue with the stealing attempt. The individuals may value the resource differently and we distinguish three information cases: (a) both individuals know resource values to both of them, (b) individuals know only their own valuation, (c) individuals do not know the value at all. We solve the game in all three cases. We identify scenarios when it is beneficial for the individuals to know as much information as possible. We also identify several scenarios where knowing less seems better as well as show that an individual may not benefit from their opponent knowing less. Finally, we consider the same kind of interactions but without the option for the Intruder to withdraw. We find that, surprisingly, the Intruder typically fares better in that case.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57784259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, by using the new concepts of monotonicity, pseudomonotonicity and hemicontinuity associated with the considered curvilinear integral functional, we investigate the well-posedness and well-posedness in generalized sense for a class of controlled variational inequality problems. More precisely, by introducing the approximating solution set of the considered class of controlled variational inequality problems, we formulate and prove some characterization results on well-posedness and well-posedness in generalized sense. Also, the theoretical developments presented in the paper are accompanied by illustrative examples.
{"title":"On well-posedness associated with a class of controlled variational inequalities","authors":"Savin Treanțǎ, Shalini Jha","doi":"10.1051/mmnp/2021046","DOIUrl":"https://doi.org/10.1051/mmnp/2021046","url":null,"abstract":"In this paper, by using the new concepts of monotonicity, pseudomonotonicity and hemicontinuity associated with the considered curvilinear integral functional, we investigate the well-posedness and well-posedness in generalized sense for a class of controlled variational inequality problems. More precisely, by introducing the approximating solution set of the considered class of controlled variational inequality problems, we formulate and prove some characterization results on well-posedness and well-posedness in generalized sense. Also, the theoretical developments presented in the paper are accompanied by illustrative examples.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57785874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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