The goal of this research is to conduct a theoretical investigation about the effect of the electroosmotic forces on the swimming of sperms throughout the cervical canal. To imitate male semen with self-propulsive spermatozoa, a hyperbolic tangent fluid is used as the base liquid. Swimming sperms move inside a ciliated cervical canal and peristalsis occurs due to the ciliated walls. The perturbation method is used to solve the controlling partial differential set of equations analytically. Due to self-propulsion of swimmers and long wavelength assumption, a creeping flow protocol is used throughout the stream. The stream pattern, velocity distribution, and pressure gradient (above and below the swimming sheet) solutions are produced and displayed with the relevant parameters. The outcomes of this manuscript show that the rheological parameters of hyperbolic tangent fluid are more appropriate to simulate and discuss the motility of cervical fluid. Moreover, the motility of mucus velocity is more applicable for small values of power law index n at the upper swimming sheet of propulsive spermatozoa. In addition, the mucus velocity increases in both region (upper and lower region of swimming sheet) with an increase of the electroosmotic parameter and Helmholtz-Smoluchowski velocity .
{"title":"On Behavioral Response of Ciliated Cervical Canal on the Development of Electroosmotic Forces in Spermatic Fluid","authors":"S. Abdelsalam, A. Z. Zaher","doi":"10.1051/mmnp/2022030","DOIUrl":"https://doi.org/10.1051/mmnp/2022030","url":null,"abstract":"The goal of this research is to conduct a theoretical investigation about the effect of the electroosmotic forces on the swimming of sperms throughout the cervical canal. To imitate male semen with self-propulsive spermatozoa, a hyperbolic tangent fluid is used as the base liquid. Swimming sperms move inside a ciliated cervical canal and peristalsis occurs due to the ciliated walls. The perturbation method is used to solve the controlling partial differential set of equations analytically. Due to self-propulsion of swimmers and long wavelength assumption, a creeping flow protocol is used throughout the stream. The stream pattern, velocity distribution, and pressure gradient (above and below the swimming sheet) solutions are produced and displayed with the relevant parameters. The outcomes of this manuscript show that the rheological parameters of hyperbolic tangent fluid are more appropriate to simulate and discuss the motility of cervical fluid. Moreover, the motility of mucus velocity is more applicable for small values of power law index n at the upper swimming sheet of propulsive spermatozoa. In addition, the mucus velocity increases in both region (upper and lower region of swimming sheet) with an increase of the electroosmotic parameter and Helmholtz-Smoluchowski velocity .","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44625749","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}
Analysis of longitudinal vibration in a nanorod is an important subject in science and engineering due to its vast application in nanotechnology. This paper introduces a port-Hamiltonian formulation for the longitudinal vibrations in a nanorod, which shows that this model is essentially hyperbolic. Furthermore, it investigates the spectral properties of the associated system operator. Standard distributed control and feedback are shown not to be controllable nor stabilizing.
{"title":"Nonlocal longitudinal vibration in a nanorod, a system theoretic analysis","authors":"Hanif Heidari, H. Zwart","doi":"10.1051/mmnp/2022028","DOIUrl":"https://doi.org/10.1051/mmnp/2022028","url":null,"abstract":"Analysis of longitudinal vibration in a nanorod is an important subject in science and engineering due to its vast application in nanotechnology. This paper introduces a port-Hamiltonian formulation for the longitudinal vibrations in a nanorod, which shows that this model is essentially hyperbolic. Furthermore, it investigates the spectral properties of the associated system operator. Standard distributed control and feedback are shown not to be controllable nor stabilizing.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43551718","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}
Ana P. Lemos-Paião, H. Maurer, Cristiana J. Silva, Delfim F. M. Torres
We improve a recent mathematical model for cholera by adding a time delay that represents the time between the instant at which an individual becomes infected and the instant at which he begins to have symptoms of cholera disease. We prove that the delayed cholera model is biologically meaningful and analyze the local asymptotic stability of the equilibrium points for positive time delays. An optimal control problem is proposed and analyzed, where the goal is to obtain optimal treatment strategies, through quarantine, that minimize the number of infective individuals and the bacterial concentration, as well as treatment costs. Necessary optimality conditions are applied to the delayed optimal control problem, with a $L^1$ type cost functional. We show that the delayed cholera model fits better the cholera outbreak that occurred in the Department of Artibonite -- Haiti, from 1 November 2010 to 1 May 2011, than the non delayed model. Considering the data of the cholera outbreak in Haiti, we solve numerically the delayed optimal control problem and propose solutions for the outbreak control and eradication.
{"title":"A SIQRB delayed model for cholera and optimal control treatment","authors":"Ana P. Lemos-Paião, H. Maurer, Cristiana J. Silva, Delfim F. M. Torres","doi":"10.1051/mmnp/2022027","DOIUrl":"https://doi.org/10.1051/mmnp/2022027","url":null,"abstract":"We improve a recent mathematical model for cholera by adding a time delay that represents the time between the instant at which an individual becomes infected and the instant at which he begins to have symptoms of cholera disease. We prove that the delayed cholera model is biologically meaningful and analyze the local asymptotic stability of the equilibrium points for positive time delays. An optimal control problem is proposed and analyzed, where the goal is to obtain optimal treatment strategies, through quarantine, that minimize the number of infective individuals and the bacterial concentration, as well as treatment costs. Necessary optimality conditions are applied to the delayed optimal control problem, with a $L^1$ type cost functional. We show that the delayed cholera model fits better the cholera outbreak that occurred in the Department of Artibonite -- Haiti, from 1 November 2010 to 1 May 2011, than the non delayed model. Considering the data of the cholera outbreak in Haiti, we solve numerically the delayed optimal control problem and propose solutions for the outbreak control and eradication.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44850207","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 Sterile Insect Technique (SIT) is a classic vector control method that has been successfully applied to fight against diverse insect plagues since the 1950s . In recent years, this strategy has been used to control mosquito populations, in order to limit the spread of the diseases they transmit. In this paper, we consider a system of reaction-diffusion equations to model the mosquito population and study the effect of the release of sterile mosquito males. Then we propose to analyze the release in a limited area inside a wider area containing natural mosquito population. We are interested in protecting a mosquito free region from invasion by mosquitoes from an exterior domain by controlling the population in a release band at the border between the two regions: we construct a barrier blocking the invasion of mosquitoes from the exterior. We adapt the geometric method of Lewis and Keener in this framework and extend their main result to find relations on the size of the release region and the density of the released sterile males that allow us to block the invasion. Numerical simulations are also performed to illustrate our results.
{"title":"Wave blocking in a bistable system by local introduction of a population~: application to sterile insect techniques on mosquito populations\u0000p, li { white-space: pre-wrap; }","authors":"L. Almeida, J. Estrada, N. Vauchelet","doi":"10.1051/mmnp/2022026","DOIUrl":"https://doi.org/10.1051/mmnp/2022026","url":null,"abstract":"The Sterile Insect Technique (SIT) is a classic vector control method that has been successfully applied to fight against diverse insect plagues since the 1950s . In recent years, this strategy has been used to control mosquito populations, in order to limit the spread of the diseases they transmit. In this paper, we consider a system of reaction-diffusion equations to model the mosquito population and study the effect of the release of sterile mosquito males. Then we propose to analyze the release in a limited area inside a wider area containing natural mosquito population. We are interested in protecting a mosquito free region from invasion by mosquitoes from an exterior domain by controlling the population in a release band at the border between the two regions: we construct a barrier blocking the invasion of mosquitoes from the exterior. We adapt the geometric method of Lewis and Keener in this framework and extend their main result to find relations on the size of the release region and the density of the released sterile males that allow us to block the invasion. Numerical simulations are also performed to illustrate our results.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47675404","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 present study signifies the effect of distinct solids on the phase speed and attenuation of Rayleigh surface wave propagating on the boundary of composite porous matrix saturated with fluids. Secular equation depicting propagation of Rayleigh wave is obtained and solved numerically for obtaining phase speed and attenuation coefficient. Two different types of composite materials are considered for numerical study to analyze the effect of solids present in the structure. The study depicts that increase in rigidity of the composite increases the phase speed of the Rayleigh surface wave. Significant effect of the density and bulk modulus of fluid mixture present in the pores is also observed on the phase speed of the wave. The effect of porosity on the phase speed of the Rayleigh wave and the particle motion during the propagation of the wave is also analyzed.
{"title":"The effect of composite material on Rayleigh wave at free surface of composite matrix saturated by fluids.","authors":"A. Arora, N. Bala","doi":"10.1051/mmnp/2022025","DOIUrl":"https://doi.org/10.1051/mmnp/2022025","url":null,"abstract":"The present study signifies the effect of distinct solids on the phase speed and attenuation of Rayleigh surface wave propagating on the boundary of composite porous matrix saturated with fluids. Secular equation depicting propagation of Rayleigh wave is obtained and solved numerically for obtaining phase speed and attenuation coefficient. Two different types of composite materials are considered for numerical study to analyze the effect of solids present in the structure. The study depicts that increase in rigidity of the composite increases the phase speed of the Rayleigh surface wave. Significant effect of the density and bulk modulus of fluid mixture present in the pores is also observed on the phase speed of the wave. The effect of porosity on the phase speed of the Rayleigh wave and the particle motion during the propagation of the wave is also analyzed.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43113476","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}
Blood vessels exhibit highly nonlinear, anisotropic behaviour with numerous mechanical interactions. Since exact modelling of all involved effects would yield a computationally prohibitive procedure, a practical clinical simulation tool needs to account for a minimum threshold of relevant factors. In this study, we analyse needed modelling assumptions for a reliable simulation of the end-to-side anastomosis. The artery wall is modelled in a geometrically exact setting as a pre-stressed fibre-reinforced composite. The study focuses on the sensitivity analysis of post-anastomosis stress fields concerning the modelling assumptions. Toward that end, a set of full-scale finite element simulations is carried out for three sensitivity cases: (i) The post-operational stresses are estimated with and without taking the residual stresses into account. (ii) Different geometries of the cut in the recipient vessel are examined. (iii) The influence of errors in material stiffness identification on the post-operational stress field is estimated. The studied cases (i)---(iii) have shown a substantial impact of the considered modelling assumptions on the predictive capabilities of the simulation. Approaches to more accurate predictions of post-operational stress distribution are outlined, and a quest for more accurate experimental procedures is made. As a by-product, the occurrence of the pseudo-aneurysm is explained.
{"title":"Rational choice of modelling assumptions for simulation of blood vessel end-to-side anastomosis","authors":"I. I. Tagiltsev, D. Parshin, A. Shutov","doi":"10.1051/mmnp/2022022","DOIUrl":"https://doi.org/10.1051/mmnp/2022022","url":null,"abstract":"Blood vessels exhibit highly nonlinear, anisotropic behaviour with numerous mechanical interactions. Since exact modelling of all involved effects would yield a computationally prohibitive procedure, a practical clinical simulation tool needs to account for a minimum threshold of relevant factors. In this study, we analyse needed modelling assumptions for a reliable simulation of the end-to-side anastomosis. The artery wall is modelled in a geometrically exact setting as a pre-stressed fibre-reinforced composite. The study focuses on the sensitivity analysis of post-anastomosis stress fields concerning the modelling assumptions. Toward that end, a set of full-scale finite element simulations is carried out for three sensitivity cases: (i) The post-operational stresses are estimated with and without taking the residual stresses into account. (ii) Different geometries of the cut in the recipient vessel are examined. (iii) The influence of errors in material stiffness identification on the post-operational stress field is estimated. The studied cases (i)---(iii) have shown a substantial impact of the considered modelling assumptions on the predictive capabilities of the simulation. Approaches to more accurate predictions of post-operational stress distribution are outlined, and a quest for more accurate experimental procedures is made. As a by-product, the occurrence of the pseudo-aneurysm is explained.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49185666","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}
Abstract. We consider a class of biological models represented by a system composed of reaction-diffusion PDE coupled with difference equations (renewal equations) in $n$-dimensional space, with nonlocal dispersal terms and implicit time delays. The difference equation generally arises, by means of the method of characteristics, from an age-structured partial differential system. Using upper and lower solutions, we study the existence of monotonic planar traveling wave fronts connecting the extinction state to the uniform positive state. The corresponding minimum wave speed is also obtained. In addition, we investigate the effect of the parameters on this minimum wave speed and we give a detailed analysis of its asymptotic behavior.
{"title":"Mathematical Modelling of Natural Phenomena","authors":"M. Adimy, Abdennasser Chekroun, B. Kazmierczak","doi":"10.1051/mmnp/2022021","DOIUrl":"https://doi.org/10.1051/mmnp/2022021","url":null,"abstract":"Abstract. We consider a class of biological models represented by a system composed of reaction-diffusion PDE coupled with difference equations (renewal equations) in $n$-dimensional space, with nonlocal dispersal terms and implicit time delays. The difference equation generally arises, by means of the method of characteristics, from an age-structured partial differential system. Using upper and lower solutions, we study the existence of monotonic planar traveling wave fronts connecting the extinction state to the uniform positive state. The corresponding minimum wave speed is also obtained. In addition, we investigate the effect of the parameters on this minimum wave speed and we give a detailed analysis of its asymptotic behavior.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45461168","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}
Numerical study is devoted to the spatial transformations of a radially symmetric flow in the liquid, filling a shallow cylindrical cavity covered partially by a solid non-deformable film. The upper part of liquid has a free surface in the center of which a beam of light produces the hot dot. The heating generates a divergent thermocapillary motion along the free surface after that the liquid flows under the immovable solid film. The edge of this film induces the perturbations into the current. At definite values of heat generation these perturbations begin to increase and cause the radial flow symmetry breakdown that visually leads to the origin of the vorticity in azimuthal plane. Three-dimensional calculations have been fulfilled on the base of interfacial hydrodynamics equations using mathematical package “Comsol Multiphysics”. The motion in azimuthal direction becomes more evident with the growth of heating intensity. There is a predominantly radial flow in the region with the free surface. At the same time, the vortices with azimuthal component of velocity are observed under the film. As in experiment, the proportion of free surface area to the covered one determines the number of vortices in azimuthal plane.
{"title":"Structural changes of a radially symmetric thermocapillary flow in the shallow cavity partially covered by a solid film","authors":"V. Demin, M. Petukhov","doi":"10.1051/mmnp/2022019","DOIUrl":"https://doi.org/10.1051/mmnp/2022019","url":null,"abstract":"Numerical study is devoted to the spatial transformations of a radially symmetric flow in the liquid, filling a shallow cylindrical cavity covered partially by a solid non-deformable film. The upper part of liquid has a free surface in the center of which a beam of light produces the hot dot. The heating generates a divergent thermocapillary motion along the free surface after that the liquid flows under the immovable solid film. The edge of this film induces the perturbations into the current. At definite values of heat generation these perturbations begin to increase and cause the radial flow symmetry breakdown that visually leads to the origin of the vorticity in azimuthal plane. Three-dimensional calculations have been fulfilled on the base of interfacial hydrodynamics equations using mathematical package “Comsol Multiphysics”. The motion in azimuthal direction becomes more evident with the growth of heating intensity. There is a predominantly radial flow in the region with the free surface. At the same time, the vortices with azimuthal component of velocity are observed under the film. As in experiment, the proportion of free surface area to the covered one determines the number of vortices in azimuthal plane.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46162963","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}
V. Bobrovskiy, J. Galvis, A. Kaplin, A. Sinitsyn, Marco Tognoli, P. Trucco
In the study, we address the mathematical problem of proton migration in the Earth’s mantle and suggest a prototype for exploring the Earth’s interior to map the effects of superionic proton conduction. The problem can be mathematically solved by deriving the self-consistent electromagnetic field potential U(x,t) and then reconstructing the distribution function f(x, v, t). Reducing the Vlasov-Maxwell system of equations to non-linear sh-Gordon hyperbolic and transport equations, the propagation of a non-linear wavefront within the domain and transport of the boundary conditions in the form of a non-linear wave are examined. By computing a 3D model and through Fourier-analysis, the spatial and electrical characteristics of potential U(x, t) are investigated. The numerical results are compared to the Fourier transformed quantities of the potential (V) obtained through field observations of the electric potential (Kuznetsov method). The non-stationary solutions for the forced oscillation of two-component system, and therefore, the oscillatory strengths of two types of charged particles can be usefully addressed by the proposed mathematical model. Moreover, the model, along with data analysis of the electric potential observations and probabilistic seismic hazard maps, can be used to develop an advanced seismic risk metric.
{"title":"Mathematical modelling of proton migration in Earth mantle","authors":"V. Bobrovskiy, J. Galvis, A. Kaplin, A. Sinitsyn, Marco Tognoli, P. Trucco","doi":"10.1051/mmnp/2022018","DOIUrl":"https://doi.org/10.1051/mmnp/2022018","url":null,"abstract":"In the study, we address the mathematical problem of proton migration in the Earth’s\u0000mantle and suggest a prototype for exploring the Earth’s interior to map the effects of superionic\u0000proton conduction. The problem can be mathematically solved by deriving the self-consistent electromagnetic field potential U(x,t) and then reconstructing the distribution function f(x, v, t). Reducing the Vlasov-Maxwell system of equations to non-linear sh-Gordon hyperbolic and transport equations, the propagation of a non-linear wavefront within the domain and transport of the boundary conditions in the form of a non-linear wave are examined. By computing a 3D model and through Fourier-analysis, the spatial and electrical characteristics of potential U(x, t) are investigated. The numerical results are compared to the Fourier transformed quantities of the potential (V) obtained through field observations of the electric potential (Kuznetsov method). The non-stationary solutions for the forced oscillation of two-component system, and therefore, the oscillatory strengths of two types of charged particles can be usefully addressed by the proposed mathematical model. Moreover, the model, along with data analysis of the electric potential observations and probabilistic seismic hazard maps, can be used to develop an advanced seismic risk metric.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45420879","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 use of epidemic modelling in connection with spread of diseases plays an important role in understanding dynamics and providing forecasts for informed analysis and decision-making. In this regard, it is crucial to quantify the effects of uncertainty in the modelling and in model-based predictions to trustfully communicate results and limitations. We propose to do efficient uncertainty quantification in compartmental epidemic models using the generalized Polynomial Chaos (gPC) framework. This framework uses a suitable polynomial basis that can be tailored to the underlying distribution for the parameter uncertainty to do forward propagation through efficient sampling via a mathematical model to quantify the effect on the output. By evaluating the model in a small number of selected points, gPC provides illuminating statistics and sensitivity analysis at a low computational cost. Through two particular case studies based on Danish data for the spread of Covid-19, we demonstrate the applicability of the technique. The test cases consider epidemic peak time estimation and the dynamics between superspreading and partial lockdown measures. The computational results show the efficiency and feasibility of the uncertainty quantification techniques based on gPC, and highlight the relevance of computational uncertainty quantification in epidemic modelling.
{"title":"Efficient Uncertainty Quantification and Variance-Based Sensitivity Analysis in Epidemic Modelling using Polynomial Chaos","authors":"Bjørn Jensen, A. Engsig-Karup, Kim Knudsen","doi":"10.1051/mmnp/2022014","DOIUrl":"https://doi.org/10.1051/mmnp/2022014","url":null,"abstract":"The use of epidemic modelling in connection with spread of diseases plays an important role in understanding dynamics and providing forecasts for informed analysis and decision-making. In this regard, it is crucial to quantify the effects of uncertainty in the modelling and in model-based predictions to trustfully communicate results and limitations. We propose to do efficient uncertainty quantification in compartmental epidemic models using the generalized Polynomial Chaos (gPC) framework. This framework uses a suitable polynomial basis that can be tailored to the underlying distribution for the parameter uncertainty to do forward propagation through efficient sampling via a mathematical model to quantify the effect on the output. By evaluating the model in a small number of selected points, gPC provides illuminating statistics and sensitivity analysis at a low computational cost. Through two particular case studies based on Danish data for the spread of Covid-19, we demonstrate the applicability of the technique. The test cases consider epidemic peak time estimation and the dynamics between superspreading and partial lockdown measures. The computational results show the efficiency and feasibility of the uncertainty quantification techniques based on gPC, and highlight the relevance of computational uncertainty quantification in epidemic modelling.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.2,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41974327","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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