In this work we propose a hybrid model of cell population dynamics, where cells are considered as discrete elements whose dynamics depending on the intracellular and extracellular regulation. The model takes into account different cell types which include undifferentiated cells and two types of differentiated cells. We use a simulation algorithm based on the dynamical systems approach on the one hand, and the multi-agent approach on the other hand. Both approaches have been implemented using NetLogo and Python. We discuss cell choice between two types of differentiated cells and analyze the coexistence of cell lineages.
{"title":"Multi-scale hybrid and agent-based modeling of cell differentiation","authors":"M. Benmir, K. Bellaj, S. Boujena, V. Volpert","doi":"10.23939/mmc2023.03.617","DOIUrl":"https://doi.org/10.23939/mmc2023.03.617","url":null,"abstract":"In this work we propose a hybrid model of cell population dynamics, where cells are considered as discrete elements whose dynamics depending on the intracellular and extracellular regulation. The model takes into account different cell types which include undifferentiated cells and two types of differentiated cells. We use a simulation algorithm based on the dynamical systems approach on the one hand, and the multi-agent approach on the other hand. Both approaches have been implemented using NetLogo and Python. We discuss cell choice between two types of differentiated cells and analyze the coexistence of cell lineages.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68768864","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 Allee effect is an important phenomena in the context of ecology characterized by a correlation between population density and the mean individual fitness of a population. In this work, we examine the influences of Allee effect on the dynamics of a delayed prey–predator model with Hattaf–Yousfi functional response. We first prove that the proposed model with Allee effect is mathematically and ecologically well-posed. Moreover, we study the stability of equilibriums and discuss the local existence of Hopf bifurcation.
{"title":"Stability analysis and Hopf bifurcation of a delayed prey–predator model with Hattaf–Yousfi functional response and Allee effect","authors":"S. Bouziane, E. Lotfi, K. Hattaf, N. Yousfi","doi":"10.23939/mmc2023.03.668","DOIUrl":"https://doi.org/10.23939/mmc2023.03.668","url":null,"abstract":"The Allee effect is an important phenomena in the context of ecology characterized by a correlation between population density and the mean individual fitness of a population. In this work, we examine the influences of Allee effect on the dynamics of a delayed prey–predator model with Hattaf–Yousfi functional response. We first prove that the proposed model with Allee effect is mathematically and ecologically well-posed. Moreover, we study the stability of equilibriums and discuss the local existence of Hopf bifurcation.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68768917","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 article, we propose a discrete mathematical model which describes the propagation of the drug phenomenon in a human population. The population is unscrewed in five compartments: "S" People likely to become drug addicts, "M" Moderate drug addicts, "H" Heavy drug addicts, "T" People receiving drug addiction treatment, "R" The recovered people who have completely abstained from drug addiction. Our goal is to find a better strategy to reduce the number of heavy addicts and to maximize the number of people receiving full treatment. The tools of optimal control theory were used in this study, in particular the Pontryagin maximum principle.
{"title":"Modeling and mathematical analysis of drug addiction with the study of the effect of psychological and biological treatment","authors":"E. M. Moumine, O. Balatif, M. Rachik","doi":"10.23939/mmc2023.03.935","DOIUrl":"https://doi.org/10.23939/mmc2023.03.935","url":null,"abstract":"In this article, we propose a discrete mathematical model which describes the propagation of the drug phenomenon in a human population. The population is unscrewed in five compartments: \"S\" People likely to become drug addicts, \"M\" Moderate drug addicts, \"H\" Heavy drug addicts, \"T\" People receiving drug addiction treatment, \"R\" The recovered people who have completely abstained from drug addiction. Our goal is to find a better strategy to reduce the number of heavy addicts and to maximize the number of people receiving full treatment. The tools of optimal control theory were used in this study, in particular the Pontryagin maximum principle.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769646","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 paper proposes the homogenization for a stratified viscoelastic media with free edge. We consider the effect of two-dimensional periodically stratified slab over a semi-infinite viscoelastic ground on the propagation of shear waves hitting the interface. Within the harmonic regime, the second order homogenization and matched-asymptotic expansions method is employed to derive an equivalent anisotropic slab associated with effective boundary and jump conditions for the displacement and the normal stress across an interface. The reflection coefficients and the displacement fields are obtained in closed forms and their validity is inspected by comparison with direct numerics in the case of layers associated with Neumann boundary conditions.
{"title":"Homogenization of subwavelength free stratified edge of viscoelastic media including finite size effect","authors":"R. Belemou, A. Sbitti, J.-J. Marigo, A. Tsouli","doi":"10.23939/mmc2023.01.010","DOIUrl":"https://doi.org/10.23939/mmc2023.01.010","url":null,"abstract":"This paper proposes the homogenization for a stratified viscoelastic media with free edge. We consider the effect of two-dimensional periodically stratified slab over a semi-infinite viscoelastic ground on the propagation of shear waves hitting the interface. Within the harmonic regime, the second order homogenization and matched-asymptotic expansions method is employed to derive an equivalent anisotropic slab associated with effective boundary and jump conditions for the displacement and the normal stress across an interface. The reflection coefficients and the displacement fields are obtained in closed forms and their validity is inspected by comparison with direct numerics in the case of layers associated with Neumann boundary conditions.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134996612","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}
Modeling a dynamics of complex biologic disease such as cancer still present a complex dealing. So, we try in our case to study it by considering the system of normal cells, tumor cells and immune response as mathematical variables structured in fractional-order derivatives equations which express the dynamics of cancer's evolution under immunity of the body. We will analyze the stability of the formulated system at different equilibrium points. Numerical simulations are carried out to get more helpful and specific outcome about the variations of the cancer's dynamics.
{"title":"Fractional derivative model for tumor cells and immune system competition","authors":"M. Elkaf, K. Allali","doi":"10.23939/mmc2023.02.288","DOIUrl":"https://doi.org/10.23939/mmc2023.02.288","url":null,"abstract":"Modeling a dynamics of complex biologic disease such as cancer still present a complex dealing. So, we try in our case to study it by considering the system of normal cells, tumor cells and immune response as mathematical variables structured in fractional-order derivatives equations which express the dynamics of cancer's evolution under immunity of the body. We will analyze the stability of the formulated system at different equilibrium points. Numerical simulations are carried out to get more helpful and specific outcome about the variations of the cancer's dynamics.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136297913","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}
B. Gayvas, B. Markovych, A. Dmytruk, M. Havran, V. Dmytruk
The problem of conductive (contact) drying of a capillary-porous body in a steam-air (gas) environment by heat transfer to the material during its contact with the heated surfaces of the material is considered. A system of significantly nonlinear differential equations of heat and mass transfer to describe such a process is obtained. To solve the formulated problem of heat and mass transfer (without taking into account deformability), the method of solving nonlinear boundary value problems is applied in the form of an iterative process, at each step of which a linear boundary value problem is solved. The results of the application of the method are verified based on the popular numerical scheme used. They agree well. A numerical experiment is conducted for materials of three types of porosity. The results are presented graphically and tabularly. The regularities of contact drying of capillary-porous materials in a steam-air environment are deduced.
{"title":"Numerical modeling of heat and mass transfer processes in a capillary-porous body during contact drying","authors":"B. Gayvas, B. Markovych, A. Dmytruk, M. Havran, V. Dmytruk","doi":"10.23939/mmc2023.02.387","DOIUrl":"https://doi.org/10.23939/mmc2023.02.387","url":null,"abstract":"The problem of conductive (contact) drying of a capillary-porous body in a steam-air (gas) environment by heat transfer to the material during its contact with the heated surfaces of the material is considered. A system of significantly nonlinear differential equations of heat and mass transfer to describe such a process is obtained. To solve the formulated problem of heat and mass transfer (without taking into account deformability), the method of solving nonlinear boundary value problems is applied in the form of an iterative process, at each step of which a linear boundary value problem is solved. The results of the application of the method are verified based on the popular numerical scheme used. They agree well. A numerical experiment is conducted for materials of three types of porosity. The results are presented graphically and tabularly. The regularities of contact drying of capillary-porous materials in a steam-air environment are deduced.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68768545","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}
Smart greenhouses use Internet of Things (IoT) technology to monitor and control various factors that affect plant growth, such as soil humidity, indoor humidity, soil temperature, rain sensor, illumination, and indoor temperature. Sensors and actuators connected to an IoT network can collect data on these factors and use it to automate processes such as watering, heating, and ventilation. This can help optimize growing conditions and improve crop yield. To enable their vegetative growth and development, plants need the right amount of water at the right time. The objective of this work is to strictly control the different factors that affect the growth of greenhouse crops. Therefore, we need a non-linear prediction model to perform greenhouse crop irrigation prediction. During operation, the system receives the input commands via sensors and then predicts the next watering run. The irrigation is predicted using GRU, LSTM, and BLSTM and a comparison was made between the results of the three techniques, and the technique with the best result was selected.
{"title":"A drip irrigation prediction system in a greenhouse based on long short-term memory and connected objects","authors":"M. Ghazouani, M. Azzouazi, M. A. Lamhour","doi":"10.23939/mmc2023.02.524","DOIUrl":"https://doi.org/10.23939/mmc2023.02.524","url":null,"abstract":"Smart greenhouses use Internet of Things (IoT) technology to monitor and control various factors that affect plant growth, such as soil humidity, indoor humidity, soil temperature, rain sensor, illumination, and indoor temperature. Sensors and actuators connected to an IoT network can collect data on these factors and use it to automate processes such as watering, heating, and ventilation. This can help optimize growing conditions and improve crop yield. To enable their vegetative growth and development, plants need the right amount of water at the right time. The objective of this work is to strictly control the different factors that affect the growth of greenhouse crops. Therefore, we need a non-linear prediction model to perform greenhouse crop irrigation prediction. During operation, the system receives the input commands via sensors and then predicts the next watering run. The irrigation is predicted using GRU, LSTM, and BLSTM and a comparison was made between the results of the three techniques, and the technique with the best result was selected.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769005","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 are interested to the dynamic von Karman equations coupled with viscous damping and without rotational forces, (α=0) [Chueshov I., Lasiecka I. (2010)], this problem describes the buckling and flexible phenomenon of small nonlinear vibration of vertical displacement to the elastic plates. Our fundamental goal is to establish the existence and the uniqueness to the weak solution for the so-called global energy, under assumption F0∈H3+ϵ(ω). Finally for illustrate our theoretical results we use the finite difference method.
{"title":"Dynamic von Karman equations with viscous damping","authors":"B. El-Aqqad, J. Oudaani, A. El Mouatasim","doi":"10.23939/mmc2023.03.816","DOIUrl":"https://doi.org/10.23939/mmc2023.03.816","url":null,"abstract":"In this paper we are interested to the dynamic von Karman equations coupled with viscous damping and without rotational forces, (α=0) [Chueshov I., Lasiecka I. (2010)], this problem describes the buckling and flexible phenomenon of small nonlinear vibration of vertical displacement to the elastic plates. Our fundamental goal is to establish the existence and the uniqueness to the weak solution for the so-called global energy, under assumption F0∈H3+ϵ(ω). Finally for illustrate our theoretical results we use the finite difference method.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769410","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 suggest a new model for establishing a numerical study related to a European options pricing problem where assets' prices can be described by a stochastic equation with a discontinuous sample path (Slow Growth Volatility with Jump SGVJ model) which uses a non-standard volatility. A special attention is given to characteristics of the proposed model represented by its non-standard volatility defined by the parameters α and β. The mathematical modeling in the presence of jump shows that one has to resort to a degenerate partial integro-differential equation (PIDE) which the resolution of this one gives a price of the European option as a function of time, price of the underlying asset and the instantaneous volatility. However, in general, an exact or closed solution to this problem is not available. For this reason we approximate it using a finite difference method. At the end of the paper, we present some numerical and comparison results with some classical models known in the literature.
{"title":"European option pricing under model involving slow growth volatility with jump","authors":"E. Aatif, A. El Mouatasim","doi":"10.23939/mmc2023.03.889","DOIUrl":"https://doi.org/10.23939/mmc2023.03.889","url":null,"abstract":"In this paper, we suggest a new model for establishing a numerical study related to a European options pricing problem where assets' prices can be described by a stochastic equation with a discontinuous sample path (Slow Growth Volatility with Jump SGVJ model) which uses a non-standard volatility. A special attention is given to characteristics of the proposed model represented by its non-standard volatility defined by the parameters α and β. The mathematical modeling in the presence of jump shows that one has to resort to a degenerate partial integro-differential equation (PIDE) which the resolution of this one gives a price of the European option as a function of time, price of the underlying asset and the instantaneous volatility. However, in general, an exact or closed solution to this problem is not available. For this reason we approximate it using a finite difference method. At the end of the paper, we present some numerical and comparison results with some classical models known in the literature.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769526","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. El Mansouri, I. Smouni, B. Khajji, A. Labzai, M. Belam
In this study, we propose a discrete time mathematical model (SEIQR) that describes the dynamics of monkeypox within a human population. The studied population is divided into five compartments: susceptible (S), exposed (E), infected (I), quarantined (Q), and recovered (R). Also, we propose an optimal strategy to fight against the spread of this epidemic. In this sense we use three controls which represent: 1) the awarness of vulnerable people through the media, civil society and education; 2) the quarantine of infected persons at home or, if required, in hospital; 3) encouraging of vaccination of susceptible persons. To characterize these optimal controls, we apply the Pontryagin's maximum principle. The optimality system is solved numerically using Matlab. Therefore, the obtained results confirm the effectiveness of the proposed optimization approach.
{"title":"Mathematical modeling and optimal control strategy for the monkeypox epidemic","authors":"A. El Mansouri, I. Smouni, B. Khajji, A. Labzai, M. Belam","doi":"10.23939/mmc2023.03.944","DOIUrl":"https://doi.org/10.23939/mmc2023.03.944","url":null,"abstract":"In this study, we propose a discrete time mathematical model (SEIQR) that describes the dynamics of monkeypox within a human population. The studied population is divided into five compartments: susceptible (S), exposed (E), infected (I), quarantined (Q), and recovered (R). Also, we propose an optimal strategy to fight against the spread of this epidemic. In this sense we use three controls which represent: 1) the awarness of vulnerable people through the media, civil society and education; 2) the quarantine of infected persons at home or, if required, in hospital; 3) encouraging of vaccination of susceptible persons. To characterize these optimal controls, we apply the Pontryagin's maximum principle. The optimality system is solved numerically using Matlab. Therefore, the obtained results confirm the effectiveness of the proposed optimization approach.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769658","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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