We develop a new data-driven immuno-epidemiological model with distributed infectivity, recovery and death rates determined from the epidemiological, clinical and experimental data. Immunity in the population is taken into account through the time-dependent number of vaccinated people with different numbers of doses and through the acquired immunity for recovered individuals. The model is validated with the available data. We show that for the first time from the beginning of pandemic COVID-19 some countries reached collective immunity. However, the epidemic continues because of the emergence of new variant BA.2 with a larger immunity escape or disease transmission rate than the previous BA.1 variant. Large epidemic outbreaks can be expected several months later due to immunity waning. These outbreaks can be restrained by an intensive booster vaccination.
{"title":"Immuno-epidemiological model-based prediction of further COVID-19 epidemic outbreaks due to immunity waning","authors":"Samiran Ghosh, M. Banerjee, V. Volpert","doi":"10.1051/mmnp/2022017","DOIUrl":"https://doi.org/10.1051/mmnp/2022017","url":null,"abstract":"We develop a new data-driven immuno-epidemiological model with distributed infectivity, recovery and death rates determined from the epidemiological, clinical and experimental data. Immunity in the population is taken into account through the time-dependent number of vaccinated people with different numbers of doses and through the acquired immunity for recovered individuals. The model is validated with the available data. We show that for the first time from the beginning of pandemic COVID-19 some countries reached collective immunity. However, the epidemic continues because of the emergence of new variant BA.2 with a larger immunity escape or disease transmission rate than the previous BA.1 variant. Large epidemic outbreaks can be expected several months later due to immunity waning. These outbreaks can be restrained by an intensive booster vaccination.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42895290","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}
Alejandro BANDERA MORENO, Macarena Gómez-Mármol, S. Fernández-García, A. Vidal
In [16], the authors analyzed the synchronization features between two identical 3D slow-fast oscillators, symmetrically coupled, built as an extension of the FitzHugh–Nagumo dynamics generating Mixed-Mode Oscillations. The third variable, which is slow, represents the intracellular calcium concentration in neurons. Here, we consider an extension of this model in two directions. First, we consider heterogeneity among cells and analyze the coupling of two oscillators with different values for one parameter tuning the intrinsic frequency. We identify new patterns of antiphasic synchronization, with non-trivial signatures and that exhibit a Devil’s Staircase phenomenon in transitions. Second, we introduce a network of N cells divided into two clusters: the coupling between neurons in each cluster is excitatory, while between the two clusters is inhibitory. Such system models the interactions between neurons tending to synchronization in two subpopulations inhibiting each other, like ipsi- and contra-lateral motoneurons assemblies. To perform the numerical simulations when N is large, as an initial step towards the network analysis, we consider Reduced Order Models to save computational costs. We present the numerical reduction results in a network of 100 cells. To validate the numerical reduction method, we compare the outputs and CPU times obtained in different cases.
{"title":"A MULTIPLE TIMESCALE NETWORK MODEL OF INTRACELLULAR\u0000CALCIUM CONCENTRATIONS IN COUPLED NEURONS: INSIGHTS FROM\u0000ROM SIMULATIONS.","authors":"Alejandro BANDERA MORENO, Macarena Gómez-Mármol, S. Fernández-García, A. Vidal","doi":"10.1051/mmnp/2022016","DOIUrl":"https://doi.org/10.1051/mmnp/2022016","url":null,"abstract":"In [16], the authors analyzed the synchronization features between two identical 3D slow-fast oscillators, symmetrically coupled, built as an extension of the FitzHugh–Nagumo dynamics generating Mixed-Mode Oscillations. The third variable, which is slow, represents the intracellular calcium concentration in neurons. Here, we consider an extension of this model in two directions. First, we consider heterogeneity among cells and analyze the coupling of two oscillators with different values for one parameter tuning the intrinsic frequency. We identify new patterns of antiphasic synchronization, with non-trivial signatures and that exhibit a Devil’s Staircase phenomenon in transitions. Second, we introduce a network of N cells divided into two clusters: the coupling between neurons in each cluster is excitatory, while between the two clusters is inhibitory. Such system models the interactions between neurons tending to synchronization in two subpopulations inhibiting each other, like ipsi- and contra-lateral motoneurons assemblies. To perform the numerical simulations when N is large, as an initial step towards the network analysis, we consider Reduced Order Models to save computational costs. We present the numerical reduction results in a network of 100 cells. To validate the numerical reduction method, we compare the outputs and CPU times obtained in different cases.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41945418","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}
Several years ago, a new paradigm of cancer perception emerged, considering a tumor not as a senseless heap of cells but as a self-organizing heterogeneous tissue of cancer cells that collectively fight for survival. It implies that the architectural forms that a tumor takes during its growth are not occasional but are a synergistic response of a group of cancer cells in competition for the organism’s resources. In this work, we generate various patterns of a two-dimensional tumor using our previously developed individual-based model mimicking carcinoma features. Every cell is represented by a polygon dynamically changing its form and size. The dynamics of tissue are governed by the elastic potential energy. We numerically obtain various patterns of carcinoma and estimate empirical spatial entropy and complexity measures applying the approach based on the fast finite shearlet transform. We show how the complexity of growing carcinoma changes over time and depending on the values of the cell intercalation parameters. In each case, we give a rational explanation of why this form is beneficial to the tumor. Our results show that one can use complexity measurements for quantitative classification of tumors obtained in silico , which potentially could find its application in practice.
{"title":"Study of architectural forms of invasive carcinoma based on the measurement of pattern complexity","authors":"D. Bratsun, I. Krasnyakov","doi":"10.1051/mmnp/2022013","DOIUrl":"https://doi.org/10.1051/mmnp/2022013","url":null,"abstract":"Several years ago, a new paradigm of cancer perception emerged, considering a tumor not as a senseless heap of cells but as a self-organizing heterogeneous tissue of cancer cells that collectively fight for survival. It implies that the architectural forms that a tumor takes during its growth are not occasional but are a synergistic response of a group of cancer cells in competition for the organism’s resources. In this work, we generate various patterns of a two-dimensional tumor using our previously developed individual-based model mimicking carcinoma features. Every cell is represented by a polygon dynamically changing its form and size. The dynamics of tissue are governed by the elastic potential energy. We numerically obtain various patterns of carcinoma and estimate empirical spatial entropy and complexity measures applying the approach based on the fast finite shearlet transform. We show how the complexity of growing carcinoma changes over time and depending on the values of the cell intercalation parameters. In each case, we give a rational explanation of why this form is beneficial to the tumor. Our results show that one can use complexity measurements for quantitative classification of tumors obtained in silico , which potentially could find its application in practice.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49206254","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}
S. S. Chaharborj, Jalal Hassanzadeh Asl, Babak Mohammadi
Many researchers began doing studies about pandemic COVID-19 which began to spread from Wuhan, China in 2019 to all around the world and so far, numerous researches have been done around the world to control this contagious disease. In this paper, we proposed mathematical model to study the spreading of pandemic COVID-19. This paper is aimed to study the vaccination effect in the control of the disease propagation rate. Another goal of this paper is to find the maximum number of susceptible people, minimum number of infected people, and the best value for number of vaccination people. The Jacobin matrix was obtained in the virus absenteeism equilibrium point for the proposed dynamical system. The spectral radius method was applied to find the analytical formula for the reproductive number. Reproductive number is one of the most benefit and important tools to study of epidemic model’s stability and unstability. In the following, by adding a controller to the model and also using the optimal control strategy, model performance was improved. To validate of the proposed models with controller and without controller we use the real data of Covid-19 from 4 Jan, 2021 up to 14 June, 2021 in Iran.
{"title":"Optimal Control Strategy to Control Pandemic COVID-19 Using MSI_LI_HR_V Model","authors":"S. S. Chaharborj, Jalal Hassanzadeh Asl, Babak Mohammadi","doi":"10.1051/mmnp/2022015","DOIUrl":"https://doi.org/10.1051/mmnp/2022015","url":null,"abstract":"Many researchers began doing studies about pandemic COVID-19 which began to spread from Wuhan, China in 2019 to all around the world and so far, numerous researches have been done around the world to control this contagious disease. In this paper, we proposed mathematical model to study the spreading of pandemic COVID-19. This paper is aimed to study the vaccination effect in the control of the disease propagation rate. Another goal of this paper is to find the maximum number of susceptible people, minimum number of infected people, and the best value for number of vaccination people. The Jacobin matrix was obtained in the virus absenteeism equilibrium point for the proposed dynamical system. The spectral radius method was applied to find the analytical formula for the reproductive number. Reproductive number is one of the most benefit and important tools to study of epidemic model’s stability and unstability. In the following, by adding a controller to the model and also using the optimal control strategy, model performance was improved. To validate of the proposed models with controller and without controller we use the real data of Covid-19 from 4 Jan, 2021 up to 14 June, 2021 in Iran.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46572690","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 explore the combined effect of the intrinsic noise and time delay on the spatial pattern formation within the framework of a multi-scale mobile lattice model mimicking two-dimensional epithelium tissues. Every cell is represented by an elastic polygon changing its form and size under pressure from the surrounding cells. The model includes the procedure of minimization of the potential energy of tissue. The protein fluctuations in the tissue are driven by transcription/translation processes in cells exchanging chemical and mechanical signals. Network architecture includes an autorepressor model with time-delayed negative feedback with the only gene defining oscillations. Simultaneously, the expressed protein of the autorepressor acts as a positive regulator of the signaling protein by activating its transcription. The signaling species is assumed to spread from one cell to the other by the diffusion mechanism. We provide both deterministic and stochastic descriptions. The numerical simulation of spatially-extended stochastic oscillations is performed using a generalized Gillespie algorithm. We developed this method earlier to account for the non-Markovian properties of random biochemical events with delay. Finally, we demonstrate that time delay, intrinsic noise, and spatial signaling can cause a system to develop the protein pattern even when its deterministic counterpart exhibits no pattern formation.
{"title":"Protein pattern formation induced by the joint effect of noise and delay in a multi-cellular system","authors":"D. Bratsun","doi":"10.1051/mmnp/2022011","DOIUrl":"https://doi.org/10.1051/mmnp/2022011","url":null,"abstract":"We explore the combined effect of the intrinsic noise and time delay on the spatial pattern formation within the framework of a multi-scale mobile lattice model mimicking two-dimensional epithelium tissues. Every cell is represented by an elastic polygon changing its form and size under pressure from the surrounding cells. The model includes the procedure of minimization of the potential energy of tissue. The protein fluctuations in the tissue are driven by transcription/translation processes in cells exchanging chemical and mechanical signals. Network architecture includes an autorepressor model with time-delayed negative feedback with the only gene defining oscillations. Simultaneously, the expressed protein of the autorepressor acts as a positive regulator of the signaling protein by activating its transcription. The signaling species is assumed to spread from one cell to the other by the diffusion mechanism. We provide both deterministic and stochastic descriptions. The numerical simulation of spatially-extended stochastic oscillations is performed using a generalized Gillespie algorithm. We developed this method earlier to account for the non-Markovian properties of random biochemical events with delay. Finally, we demonstrate that time delay, intrinsic noise, and spatial signaling can cause a system to develop the protein pattern even when its deterministic counterpart exhibits no pattern formation.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48087857","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}
This analysis is conducted for a theoretical examination of the fluid flow characteristics and heat transferred by the nanoparticle-enhanced drilling muds flowing through drilling pipes under various physical conditions. Here, an important type of drilling fluid called Aphron drilling fluid is under consideration which is very effective for drilling in depleted regions. The rheological characteristics of the drilling fluid are predicted by Herschel-Bulkley fluid model. The fluid flow is driven by peristaltic pumping which is further aided by electroosmosis. The zinc oxide nanoparticles are dispersed in the aphron drilling fluid to prepare the nanofluid. The administering set of equations are simplified under the lubrication approach and the closed-form solutions are obtained for velocity and pressure gradient force. However, numerical solutions are executed for the temperature of nanofluid through built-in routine bvp4c of MATLAB. Fluid flow characteristics are analyzed for variation in physical conditions through graphical results. The outcomes of this study reveal that velocity profile substantially rises for application of forwarding electric field and temperature profile significantly decays in this case. An increment in temperature difference raises the magnitude of the Nusselt number. Furthermore, the nanoparticle volume fraction contributes to fluid acceleration and thermal conductivity of the drilling fluid.
{"title":"Mathematical Modeling of Aphron Drilling nanofluid Driven by Electroosmotically Modulated Peristalsis Through a Pipe","authors":"J. Akram, Noreen Sher Akbar","doi":"10.1051/mmnp/2022012","DOIUrl":"https://doi.org/10.1051/mmnp/2022012","url":null,"abstract":"This analysis is conducted for a theoretical examination of the fluid flow characteristics and heat transferred by the nanoparticle-enhanced drilling muds flowing through drilling pipes under various physical conditions. Here, an important type of drilling fluid called Aphron drilling fluid is under consideration which is very effective for drilling in depleted regions. The rheological characteristics of the drilling fluid are predicted by Herschel-Bulkley fluid model. The fluid flow is driven by peristaltic pumping which is further aided by electroosmosis. The zinc oxide nanoparticles are dispersed in the aphron drilling fluid to prepare the nanofluid. The administering set of equations are simplified under the lubrication approach and the closed-form solutions are obtained for velocity and pressure gradient force. However, numerical solutions are executed for the temperature of nanofluid through built-in routine bvp4c of MATLAB. Fluid flow characteristics are analyzed for variation in physical conditions through graphical results. The outcomes of this study reveal that velocity profile substantially rises for application of forwarding electric field and temperature profile significantly decays in this case. An increment in temperature difference raises the magnitude of the Nusselt number. Furthermore, the nanoparticle volume fraction contributes to fluid acceleration and thermal conductivity of the drilling fluid.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44054473","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}
Raúl Felipe-Sosa, A. Fraguela-Collar, Yofre H. Garc'ia G'omez
In this paper, we investigate the convergence of the Faedo - Galerkin approximations, in a strong sense, to a strong T-periodic solution of the torso-coupled bidomain model where $T$ is the period of activation of the inner wall of heart. First, we define the torso-coupled bi-domain operator and prove some of its more important properties for our work. After, we define the abstract evolution system of equations associated with torso-coupled bidomain model and give the definition of strong solution. We prove that the Faedo - Galerkin's approximations have the regularity of a strong solution, and we find that some restrictions can be imposed over the initial conditions, so that this sequence of Faedo - Galerkin fully converge to a strong solution of the Cauchy problem. Finally, this results are used for showing the existence a strong $T$ -periodic solution.
{"title":"On the strong convergence of the Faedo-Galerkin approximations to a strong T-periodic solution of the torso-coupled bi-domain model","authors":"Raúl Felipe-Sosa, A. Fraguela-Collar, Yofre H. Garc'ia G'omez","doi":"10.1051/mmnp/2023012","DOIUrl":"https://doi.org/10.1051/mmnp/2023012","url":null,"abstract":"In this paper, we investigate the convergence of the Faedo - Galerkin approximations, in a strong sense, to a strong T-periodic solution of the torso-coupled bidomain model where $T$ is the period of activation of the inner wall of heart. First, we define the torso-coupled bi-domain operator and prove some of its more important properties for our work. After, we define the abstract evolution system of equations associated with torso-coupled bidomain model and give the definition of strong solution. We prove that the Faedo - Galerkin's approximations have the regularity of a strong solution, and we find that some restrictions can be imposed over the initial conditions, so that this sequence of Faedo - Galerkin fully converge to a strong solution of the Cauchy problem. Finally, this results are used for showing the existence a strong $T$ -periodic solution.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44513409","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 phenomena of concentration and cavitation are identified and analyzed by studying the vanishing pressure limit of solutions to the 3×3 isentropic compressible Euler equations for generalized Chaplygin gas (GCG) with a small parameter. It is rigorously proved that, any Riemann solution containing two shocks and possibly one-contact-discontinuity of the GCG equations converges to a delta-shock solution of the same system as the parameter decreases to a certain critical value. Moreover, as the parameter goes to zero, that is, the pressure vanishes, the limiting solution is just the delta-shock solution of the pressureless gas dynamics (PGD) model, and the intermediate density between the two shocks tends to a weighted δ -measure that forms the delta shock wave; any Riemann solution containing two rarefaction waves and possibly one contact-discontinuity tends to a two-contact-discontinuity solution of the PGD model, and the nonvacuum intermediate state in between tends to a vacuum state. Finally, some numerical results are presented to exhibit the processes of concentration and cavitation as the pressure decreases.
{"title":"Concentration and cavitation in the vanishing pressure limit of solutions to a 3 × 3 generalized Chaplygin gas equations","authors":"Yu Zhang, S. Fan, Yanyan Zhang","doi":"10.1051/mmnp/2022009","DOIUrl":"https://doi.org/10.1051/mmnp/2022009","url":null,"abstract":"The phenomena of concentration and cavitation are identified and analyzed by studying the vanishing pressure limit of solutions to the 3×3 isentropic compressible Euler equations for generalized Chaplygin gas (GCG) with a small parameter. It is rigorously proved that, any Riemann solution containing two shocks and possibly one-contact-discontinuity of the GCG equations converges to a delta-shock solution of the same system as the parameter decreases to a certain critical value. Moreover, as the parameter goes to zero, that is, the pressure vanishes, the limiting solution is just the delta-shock solution of the pressureless gas dynamics (PGD) model, and the intermediate density between the two shocks tends to a weighted δ -measure that forms the delta shock wave; any Riemann solution containing two rarefaction waves and possibly one contact-discontinuity tends to a two-contact-discontinuity solution of the PGD model, and the nonvacuum intermediate state in between tends to a vacuum state. Finally, some numerical results are presented to exhibit the processes of concentration and cavitation as the pressure decreases.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48697441","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}
B. Reyné, Q. Richard, C. Selinger, Mircea T. Sofonea, R. Djidjou-Demasse, S. Alizon
The Covid-19 outbreak was followed by a huge amount of modelling studies in order to rapidly gain insights to implement the best public health policies. Most of these compartmental models involved ordinary differential equations (ODEs) systems. Such a formalism implicitly assumes that the time spent in each compartment does not depend on the time already spent in it, which is unrealistic. To overcome this “memoryless” issue, a widely used solution is to chain the number of compartments of a unique reality (e.g. have infected individual move between several compartments). This allows for greater heterogeneity, but also tends to make the whole model more difficult to apprehend and parameterize. We develop a non-Markovian alternative formalism based on partial differential equations (PDEs) instead of ODEs, which, by construction, provides a memory structure for each compartment. We apply our model to the French 2021 SARS-CoV-2 epidemic and we determine the major components that contributed to the Covid-19 hospital admissions. A global sensitivity analysis highlights a huge uncertainty attributable to the age-structured contact matrix. Our study shows the flexibility and robustness of PDE formalism to capture national COVID-19 dynamics and opens perspectives to study medium or long-term scenarios involving immune waning or virus evolution.
{"title":"Non-Markovian modelling highlights the importance of age structure on Covid-19 epidemiological dynamics","authors":"B. Reyné, Q. Richard, C. Selinger, Mircea T. Sofonea, R. Djidjou-Demasse, S. Alizon","doi":"10.1051/mmnp/2022008","DOIUrl":"https://doi.org/10.1051/mmnp/2022008","url":null,"abstract":"The Covid-19 outbreak was followed by a huge amount of modelling studies in order to rapidly gain insights to implement the best public health policies. Most of these compartmental models involved ordinary differential equations (ODEs) systems. Such a formalism implicitly assumes that the time spent in each compartment does not depend on the time already spent in it, which is unrealistic. To overcome this “memoryless” issue, a widely used solution is to chain the number of compartments of a unique reality (e.g. have infected individual move between several compartments). This allows for greater heterogeneity, but also tends to make the whole model more difficult to apprehend and parameterize. We develop a non-Markovian alternative formalism based on partial differential equations (PDEs) instead of ODEs, which, by construction, provides a memory structure for each compartment. We apply our model to the French 2021 SARS-CoV-2 epidemic and we determine the major components that contributed to the Covid-19 hospital admissions. A global sensitivity analysis highlights a huge uncertainty attributable to the age-structured contact matrix. Our study shows the flexibility and robustness of PDE formalism to capture national COVID-19 dynamics and opens perspectives to study medium or long-term scenarios involving immune waning or virus evolution.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43286414","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 explore the Darboux-dressing transformation of the coupled complex modified Korteweg-de Vries equation. Next, with the aid of an asymptotic expansion theory, we derive the concrete forms of three types of semi-rational solutions. In particular, the seed solution is related to the normalized distance and retarded time. Interestingly, we construct a kind of novel rogue wave called as curve rogue wave. More importantly, the kinetics of semi-rational solutions are discussed in detail. We hope that these results would shed more light on comprehending of the solutions occurring in multi-component coupled systems.
{"title":"Higher-order semi-rational solutions for the coupled complex modified Korteweg-de Vries equation","authors":"Yu Lou, Yi Zhang, Rusuo Ye","doi":"10.1051/mmnp/2022006","DOIUrl":"https://doi.org/10.1051/mmnp/2022006","url":null,"abstract":"We explore the Darboux-dressing transformation of the coupled complex modified Korteweg-de Vries equation. Next, with the aid of an asymptotic expansion theory, we derive the concrete forms of three types of semi-rational solutions. In particular, the seed solution is related to the normalized distance and retarded time. Interestingly, we construct a kind of novel rogue wave called as curve rogue wave. More importantly, the kinetics of semi-rational solutions are discussed in detail. We hope that these results would shed more light on comprehending of the solutions occurring in multi-component coupled systems.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44877464","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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