Maria Carme Calderer, Duvan Henao, Manuel A. Sánchez, Ronald A. Siegel, Sichen Song
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1766-1791, August 2024. Abstract. This article presents a numerical scheme for the variational model formulated by Calderer et al. [J. Elast., 141 (2020), pp. 51–73] for the debonding of a hydrogel film from a rigid substrate upon exposure to solvent, in the two-dimensional case of a film placed between two parallel walls. It builds upon the scheme introduced by Song et al. [J. Elast., 153 (2023), pp. 651–679] for completely bonded gels, which fails to be robust in the case of gels that are already debonded. The new scheme is used to compute the energy release rate function, based on which predictions are offered for the threshold thickness below which the gel/substrate system is stable against debonding. This study, in turn, makes it possible to validate a theoretical estimate for the energy release rate obtained in the cited works, which is based on a thin-film asymptotic analysis and which, due to its explicit nature, is potentially valuable in medical device development. An existence theorem and rigorous justifications of some approximations made in our numerical scheme are also provided.
{"title":"A Numerical Scheme and Validation of the Asymptotic Energy Release Rate Formula for a 2D Gel Thin-Film Debonding Problem","authors":"Maria Carme Calderer, Duvan Henao, Manuel A. Sánchez, Ronald A. Siegel, Sichen Song","doi":"10.1137/23m1579042","DOIUrl":"https://doi.org/10.1137/23m1579042","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1766-1791, August 2024. <br/> Abstract. This article presents a numerical scheme for the variational model formulated by Calderer et al. [J. Elast., 141 (2020), pp. 51–73] for the debonding of a hydrogel film from a rigid substrate upon exposure to solvent, in the two-dimensional case of a film placed between two parallel walls. It builds upon the scheme introduced by Song et al. [J. Elast., 153 (2023), pp. 651–679] for completely bonded gels, which fails to be robust in the case of gels that are already debonded. The new scheme is used to compute the energy release rate function, based on which predictions are offered for the threshold thickness below which the gel/substrate system is stable against debonding. This study, in turn, makes it possible to validate a theoretical estimate for the energy release rate obtained in the cited works, which is based on a thin-film asymptotic analysis and which, due to its explicit nature, is potentially valuable in medical device development. An existence theorem and rigorous justifications of some approximations made in our numerical scheme are also provided.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"24 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219287","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1742-1765, August 2024. Abstract. This paper is devoted to the study of the global dynamics for a large class of reaction-diffusion systems with a time-varying domain. By appealing to the theories of asymptotically autonomous and periodic semiflows, we establish the threshold-type results on the long-time behavior of solutions for such a system in the cases of asymptotically bounded and periodic domains, respectively. To investigate the model system in the case of asymptotically unbounded domain, we first prove the global attractivity for nonautonomous reaction-diffusion systems with asymptotically vanishing diffusion coefficients via the method of sub- and supersolutions and then use the comparison arguments to obtain the threshold dynamics. We also apply these analytical results to a reaction-diffusion model of dengue fever transmission to investigate the effect of time-varying domain on the basic reproduction number. It turns out that the basic reproduction numbers with dengue fever transmission for the asymptotically bounded and unbounded domains are always less than that for the spatially homogeneous case, and under appropriate conditions, the basic reproduction numbers for asymptotically bounded and periodic domains are larger than or equal to that for the stationary bounded domain.
{"title":"Global Dynamics of Reaction-Diffusion Systems with a Time-Varying Domain","authors":"King-Yeung Lam, Xiao-Qiang Zhao, Min Zhu","doi":"10.1137/23m1582990","DOIUrl":"https://doi.org/10.1137/23m1582990","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1742-1765, August 2024. <br/> Abstract. This paper is devoted to the study of the global dynamics for a large class of reaction-diffusion systems with a time-varying domain. By appealing to the theories of asymptotically autonomous and periodic semiflows, we establish the threshold-type results on the long-time behavior of solutions for such a system in the cases of asymptotically bounded and periodic domains, respectively. To investigate the model system in the case of asymptotically unbounded domain, we first prove the global attractivity for nonautonomous reaction-diffusion systems with asymptotically vanishing diffusion coefficients via the method of sub- and supersolutions and then use the comparison arguments to obtain the threshold dynamics. We also apply these analytical results to a reaction-diffusion model of dengue fever transmission to investigate the effect of time-varying domain on the basic reproduction number. It turns out that the basic reproduction numbers with dengue fever transmission for the asymptotically bounded and unbounded domains are always less than that for the spatially homogeneous case, and under appropriate conditions, the basic reproduction numbers for asymptotically bounded and periodic domains are larger than or equal to that for the stationary bounded domain.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"111 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219288","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1718-1741, August 2024. Abstract. This work considers the optimization of electrode positions in head imaging by electrical impedance tomography. The study is motivated by maximizing the sensitivity of electrode measurements to conductivity changes when monitoring the condition of a stroke patient, which justifies adopting a linearized version of the complete electrode model as the forward model. The algorithm is based on finding a (locally) A-optimal measurement configuration via gradient descent with respect to the electrode positions. The efficient computation of the needed derivatives of the complete electrode model is one of the focal points. Two algorithms are introduced and numerically tested on a three-layer head model. The first one assumes a region of interest and a Gaussian prior for the conductivity in the brain, and it can be run offline, i.e., prior to taking any measurements. The second algorithm first computes a reconstruction of the conductivity anomaly caused by the stroke with an initial electrode configuration by combining lagged diffusivity iteration with sequential linearizations, which can be interpreted to produce an approximate Gaussian probability density for the conductivity perturbation. It then resorts to the first algorithm to find new, more informative positions for the available electrodes with the constructed density as the prior.
{"title":"Bayesian Experimental Design for Head Imaging by Electrical Impedance Tomography","authors":"N. Hyvönen, A. Jääskeläinen, R. Maity, A. Vavilov","doi":"10.1137/23m1624634","DOIUrl":"https://doi.org/10.1137/23m1624634","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1718-1741, August 2024. <br/> Abstract. This work considers the optimization of electrode positions in head imaging by electrical impedance tomography. The study is motivated by maximizing the sensitivity of electrode measurements to conductivity changes when monitoring the condition of a stroke patient, which justifies adopting a linearized version of the complete electrode model as the forward model. The algorithm is based on finding a (locally) A-optimal measurement configuration via gradient descent with respect to the electrode positions. The efficient computation of the needed derivatives of the complete electrode model is one of the focal points. Two algorithms are introduced and numerically tested on a three-layer head model. The first one assumes a region of interest and a Gaussian prior for the conductivity in the brain, and it can be run offline, i.e., prior to taking any measurements. The second algorithm first computes a reconstruction of the conductivity anomaly caused by the stroke with an initial electrode configuration by combining lagged diffusivity iteration with sequential linearizations, which can be interpreted to produce an approximate Gaussian probability density for the conductivity perturbation. It then resorts to the first algorithm to find new, more informative positions for the available electrodes with the constructed density as the prior.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"135 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942528","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}
Habib Ammari, Silvio Barandun, Bryn Davies, Erik Orvehed Hiltunen, Ping Liu
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1697-1717, August 2024. Abstract. This paper shows both analytically and numerically that the skin effect in systems of non-Hermitian subwavelength resonators is robust with respect to random imperfections in the system. The subwavelength resonators are highly contrasting material inclusions that resonate in a low-frequency regime. The non-Hermiticity is due to the introduction of a directional damping term (motivated by an imaginary gauge potential), which leads to a skin effect that is manifested by the system’s eigenmodes accumulating at one edge of the structure. We elucidate the topological protection of the associated (real) eigenfrequencies and illustrate numerically the competition between the two different localization effects present when the system is randomly perturbed: the non-Hermitian skin effect and the disorder-induced Anderson localization. We show numerically that, as the strength of the disorder increases, more and more eigenmodes become localized in the bulk. Our results are based on an asymptotic matrix model for subwavelength physics and can be generalized also to tight-binding models in condensed matter theory.
{"title":"Stability of the Non-Hermitian Skin Effect in One Dimension","authors":"Habib Ammari, Silvio Barandun, Bryn Davies, Erik Orvehed Hiltunen, Ping Liu","doi":"10.1137/23m1610537","DOIUrl":"https://doi.org/10.1137/23m1610537","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1697-1717, August 2024. <br/> Abstract. This paper shows both analytically and numerically that the skin effect in systems of non-Hermitian subwavelength resonators is robust with respect to random imperfections in the system. The subwavelength resonators are highly contrasting material inclusions that resonate in a low-frequency regime. The non-Hermiticity is due to the introduction of a directional damping term (motivated by an imaginary gauge potential), which leads to a skin effect that is manifested by the system’s eigenmodes accumulating at one edge of the structure. We elucidate the topological protection of the associated (real) eigenfrequencies and illustrate numerically the competition between the two different localization effects present when the system is randomly perturbed: the non-Hermitian skin effect and the disorder-induced Anderson localization. We show numerically that, as the strength of the disorder increases, more and more eigenmodes become localized in the bulk. Our results are based on an asymptotic matrix model for subwavelength physics and can be generalized also to tight-binding models in condensed matter theory.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"45 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942440","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1668-1696, August 2024. Abstract. Exploring the mechanism of phosphate ([math]) uptake by algae is essential to accurate prediction and a comprehensive understanding of harmful algal blooms (HABs). Previous experimental studies have revealed the existence of two distinct [math] pools, namely the surface-adsorbed [math] pool and the intracellular [math] pool, in certain species of algae. Motivated by these observations, a novel stoichiometric model, which incorporates a two-stage [math] uptake process, is proposed and analyzed to investigate the impact of these [math] pools on algal growth. Model validation results show that with proper parameterizations, this model can accurately capture algal growth dynamics in the laboratory and in the field. The asymptotic dynamics are explored through a complete mathematical analysis and the transient dynamics are explored through multiscale analysis, revealing the driving mechanism of different growth phases of algae. Furthermore, we derive an approximate formula for estimating the switching time from high to low growth rate in algae, which can serve as a valuable tool for predicting the duration of HABs. These findings contribute to the strengthening of prediction and improving understanding of HABs.
{"title":"Asymptotic and Transient Dynamics of a Stoichiometric Algal Growth Model with Two-Stage Phosphate Uptake","authors":"Shufei Gao, Sanling Yuan, Anglu Shen, Hao Wang","doi":"10.1137/23m1611750","DOIUrl":"https://doi.org/10.1137/23m1611750","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1668-1696, August 2024. <br/> Abstract. Exploring the mechanism of phosphate ([math]) uptake by algae is essential to accurate prediction and a comprehensive understanding of harmful algal blooms (HABs). Previous experimental studies have revealed the existence of two distinct [math] pools, namely the surface-adsorbed [math] pool and the intracellular [math] pool, in certain species of algae. Motivated by these observations, a novel stoichiometric model, which incorporates a two-stage [math] uptake process, is proposed and analyzed to investigate the impact of these [math] pools on algal growth. Model validation results show that with proper parameterizations, this model can accurately capture algal growth dynamics in the laboratory and in the field. The asymptotic dynamics are explored through a complete mathematical analysis and the transient dynamics are explored through multiscale analysis, revealing the driving mechanism of different growth phases of algae. Furthermore, we derive an approximate formula for estimating the switching time from high to low growth rate in algae, which can serve as a valuable tool for predicting the duration of HABs. These findings contribute to the strengthening of prediction and improving understanding of HABs.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"52 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141885388","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1658-1667, August 2024. Abstract. In this paper, the classical problem of two-dimensional flow in a cylindrical domain, driven by a nonuniform tangential velocity imposed at the boundary, is reconsidered in straightforward manner. When the boundary velocity is a pure rotation [math] plus a small perturbation [math] and when the Reynolds number based on [math] is large (Re [math]), this flow is of “Prandtl–Batchelor” type, namely, a flow of uniform vorticity [math] in a core region inside a viscous boundary layer of thickness O(Re)[math]. The O[math] contribution to [math] is determined here by asymptotic analysis up to O[math]. The result is in good agreement with numerical computation for Re [math].
{"title":"Prandtl–Batchelor Flow in a Cylindrical Domain","authors":"Emmanuel Dormy, H. Keith Moffatt","doi":"10.1137/24m1637313","DOIUrl":"https://doi.org/10.1137/24m1637313","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1658-1667, August 2024. <br/> Abstract. In this paper, the classical problem of two-dimensional flow in a cylindrical domain, driven by a nonuniform tangential velocity imposed at the boundary, is reconsidered in straightforward manner. When the boundary velocity is a pure rotation [math] plus a small perturbation [math] and when the Reynolds number based on [math] is large (Re [math]), this flow is of “Prandtl–Batchelor” type, namely, a flow of uniform vorticity [math] in a core region inside a viscous boundary layer of thickness O(Re)[math]. The O[math] contribution to [math] is determined here by asymptotic analysis up to O[math]. The result is in good agreement with numerical computation for Re [math].","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"75 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141885389","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1631-1657, August 2024. Abstract. This paper addresses the inverse scattering problem for Maxwell’s equations in three-dimensional anisotropic periodic media. We study a new imaging functional for the fast and robust reconstruction of the shape of anisotropic periodic scatterers from boundary measurements of the scattered field. The implementation of this imaging functional is simple and avoids the need to solve an ill-posed problem. The resolution and stability analysis of the imaging functional is investigated. Results from our numerical study indicate that this imaging functional is more stable than that of the factorization method and more accurate than that of the orthogonality sampling method in reconstructing periodic scatterers.
{"title":"A Stable Imaging Functional for Anisotropic Periodic Media in Electromagnetic Inverse Scattering","authors":"Dinh-Liem Nguyen, Trung Truong","doi":"10.1137/23m1577080","DOIUrl":"https://doi.org/10.1137/23m1577080","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1631-1657, August 2024. <br/> Abstract. This paper addresses the inverse scattering problem for Maxwell’s equations in three-dimensional anisotropic periodic media. We study a new imaging functional for the fast and robust reconstruction of the shape of anisotropic periodic scatterers from boundary measurements of the scattered field. The implementation of this imaging functional is simple and avoids the need to solve an ill-posed problem. The resolution and stability analysis of the imaging functional is investigated. Results from our numerical study indicate that this imaging functional is more stable than that of the factorization method and more accurate than that of the orthogonality sampling method in reconstructing periodic scatterers.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"30 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141872131","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}
Sebastian Acosta, Jesse Chan, Raven Johnson, Benjamin Palacios
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1609-1630, August 2024. Abstract. To strike a balance between modeling accuracy and computational efficiency for simulations of ultrasound waves in soft tissues, we derive a pseudodifferential factorization of the wave operator with fractional attenuation. This factorization allows us to approximately solve the Helmholtz equation via one-way (transmission) or two-way (transmission and reflection) sweeping schemes tailored to high-frequency wave fields. We provide explicitly the three highest order terms of the pseudodifferential expansion to incorporate the well-known square-root first order symbol for wave propagation, the zeroth order symbol for amplitude modulation due to changes in wave speed and damping, and the next symbol to model fractional attenuation. We also propose wide-angle Padé approximations for the pseudodifferential operators corresponding to these three highest order symbols. Our analysis provides insights regarding the role played by the frequency and the Padé approximations in the estimation of error bounds. We also provide a proof-of-concept numerical implementation of the proposed method and test the error estimates numerically.
{"title":"Pseudodifferential Models for Ultrasound Waves with Fractional Attenuation","authors":"Sebastian Acosta, Jesse Chan, Raven Johnson, Benjamin Palacios","doi":"10.1137/24m1634011","DOIUrl":"https://doi.org/10.1137/24m1634011","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1609-1630, August 2024. <br/> Abstract. To strike a balance between modeling accuracy and computational efficiency for simulations of ultrasound waves in soft tissues, we derive a pseudodifferential factorization of the wave operator with fractional attenuation. This factorization allows us to approximately solve the Helmholtz equation via one-way (transmission) or two-way (transmission and reflection) sweeping schemes tailored to high-frequency wave fields. We provide explicitly the three highest order terms of the pseudodifferential expansion to incorporate the well-known square-root first order symbol for wave propagation, the zeroth order symbol for amplitude modulation due to changes in wave speed and damping, and the next symbol to model fractional attenuation. We also propose wide-angle Padé approximations for the pseudodifferential operators corresponding to these three highest order symbols. Our analysis provides insights regarding the role played by the frequency and the Padé approximations in the estimation of error bounds. We also provide a proof-of-concept numerical implementation of the proposed method and test the error estimates numerically.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"58 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141778882","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1557-1579, August 2024. Abstract. In this paper, taking into account the maturation period of prey, we propose a predator-prey model with time delay and fear effect. We confirm the well-posedness of the model system, explore the stability of the equilibria and uniform persistence of the model, and investigate Hopf bifurcations. Moreover, we also numerically explore the global continuation of the Hopf bifurcation. Interestingly, our results show that as the delay increases, the stable and unstable periodic solutions may both disappear and the unstable positive equilibrium may regain its stability. These results reveal how the maturation delay and the fear effect jointly impact the population dynamics of the predator-prey system.
{"title":"Joint Impact of Maturation Delay and Fear Effect on the Population Dynamics of a Predator-Prey System","authors":"Xiaoke Ma, Ying Su, Xingfu Zou","doi":"10.1137/23m1596569","DOIUrl":"https://doi.org/10.1137/23m1596569","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1557-1579, August 2024. <br/> Abstract. In this paper, taking into account the maturation period of prey, we propose a predator-prey model with time delay and fear effect. We confirm the well-posedness of the model system, explore the stability of the equilibria and uniform persistence of the model, and investigate Hopf bifurcations. Moreover, we also numerically explore the global continuation of the Hopf bifurcation. Interestingly, our results show that as the delay increases, the stable and unstable periodic solutions may both disappear and the unstable positive equilibrium may regain its stability. These results reveal how the maturation delay and the fear effect jointly impact the population dynamics of the predator-prey system.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"63 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141742491","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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1580-1608, August 2024. Abstract. We derive accurate, closed-form analytical approximations for the phase-plane trajectories of the standard susceptible-infectious-removed (SIR) epidemic model, including host births and deaths, giving a complete description of the transient dynamics. Our approximations for the SIR ordinary differential equations also allow us to provide convenient, accurate analytical approximations for the associated Poincaré map, and the minimum and maximum susceptible and infectious host densities in each epidemic wave. Our analysis involves matching asymptotic expansions across branch cuts of the Lambert [math] function.
{"title":"Uniform Asymptotic Approximations for the Phase Plane Trajectories of the SIR Model with Vital Dynamics","authors":"Todd L. Parsons, David J. D. Earn","doi":"10.1137/23m1576050","DOIUrl":"https://doi.org/10.1137/23m1576050","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1580-1608, August 2024. <br/> Abstract. We derive accurate, closed-form analytical approximations for the phase-plane trajectories of the standard susceptible-infectious-removed (SIR) epidemic model, including host births and deaths, giving a complete description of the transient dynamics. Our approximations for the SIR ordinary differential equations also allow us to provide convenient, accurate analytical approximations for the associated Poincaré map, and the minimum and maximum susceptible and infectious host densities in each epidemic wave. Our analysis involves matching asymptotic expansions across branch cuts of the Lambert [math] function.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"94 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141778881","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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