Tyler Cassidy, Giulia Belluccini, Sarafa A Iyaniwura, Ruy M Ribeiro, Alan S Perelson
Multiscale mathematical models of hepatitis C infection have been instrumental in our understanding of direct acting antivirals. These models include the mechanisms driving intracellular viral production and explicitly model the intracellular concentration of viral RNA. However, incorporating proliferation of infected hepatocytes in these models can be subtle, as infected daughter cells inherit viral RNA from the proliferating mother cell. Here, we show how to incorporate this inheritance within a multiscale model of HCV infection. As in typical multiscale models of HCV infection, we show that this model is mathematically equivalent to a system of ordinary differential equations and perform bifurcation analysis of the resulting ODE that demonstrates that proliferation of infected hepatocytes can lead to infection persistence even if the basic reproductive number is less than one.
{"title":"INHERITANCE OF INTRACELLULAR VIRAL RNA IN A MULTISCALE MODEL OF HEPATITIS C INFECTION.","authors":"Tyler Cassidy, Giulia Belluccini, Sarafa A Iyaniwura, Ruy M Ribeiro, Alan S Perelson","doi":"10.1137/25m1765821","DOIUrl":"10.1137/25m1765821","url":null,"abstract":"<p><p>Multiscale mathematical models of hepatitis C infection have been instrumental in our understanding of direct acting antivirals. These models include the mechanisms driving intracellular viral production and explicitly model the intracellular concentration of viral RNA. However, incorporating proliferation of infected hepatocytes in these models can be subtle, as infected daughter cells inherit viral RNA from the proliferating mother cell. Here, we show how to incorporate this inheritance within a multiscale model of HCV infection. As in typical multiscale models of HCV infection, we show that this model is mathematically equivalent to a system of ordinary differential equations and perform bifurcation analysis of the resulting ODE that demonstrates that proliferation of infected hepatocytes can lead to infection persistence even if the basic reproductive number is less than one.</p>","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"86 3","pages":"791-813"},"PeriodicalIF":2.0,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13255569/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148254382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-01Epub Date: 2025-02-11DOI: 10.1137/24m1667555
Zixuan Cang, Yanxiang Zhao
Optimal transport has been an essential tool for reconstructing dynamics from complex data. With the increasingly available multifaceted data, a system can often be characterized across multiple spaces. Therefore, it is crucial to maintain coherence in the dynamics across these diverse spaces. To address this challenge, we introduce synchronized optimal transport (SyncOT), a novel approach to jointly model dynamics that represent the same system through multiple spaces. Given the correspondence between the spaces, SyncOT minimizes the aggregated cost of the dynamics induced across all considered spaces. The problem is discretized into a finite-dimensional convex problem using a staggered grid. Primal-dual algorithm-based approaches are then developed to solve the discretized problem. Various numerical experiments demonstrate the capabilities and properties of SyncOT and validate the effectiveness of the proposed algorithms.
{"title":"SYNCHRONIZED OPTIMAL TRANSPORT FOR JOINT MODELING OF DYNAMICS ACROSS MULTIPLE SPACES.","authors":"Zixuan Cang, Yanxiang Zhao","doi":"10.1137/24m1667555","DOIUrl":"10.1137/24m1667555","url":null,"abstract":"<p><p>Optimal transport has been an essential tool for reconstructing dynamics from complex data. With the increasingly available multifaceted data, a system can often be characterized across multiple spaces. Therefore, it is crucial to maintain coherence in the dynamics across these diverse spaces. To address this challenge, we introduce synchronized optimal transport (SyncOT), a novel approach to jointly model dynamics that represent the same system through multiple spaces. Given the correspondence between the spaces, SyncOT minimizes the aggregated cost of the dynamics induced across all considered spaces. The problem is discretized into a finite-dimensional convex problem using a staggered grid. Primal-dual algorithm-based approaches are then developed to solve the discretized problem. Various numerical experiments demonstrate the capabilities and properties of SyncOT and validate the effectiveness of the proposed algorithms.</p>","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"85 1","pages":"341-365"},"PeriodicalIF":2.1,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12395362/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144977687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Elena Beretta, Cecilia Cavaterra, Matteo Fornoni, Guillermo Lorenzo, Elisabetta Rocca
{"title":"Mathematical Analysis of a Model-Constrained Inverse Problem For the Reconstruction of Early States of Prostate Cancer Growth","authors":"Elena Beretta, Cecilia Cavaterra, Matteo Fornoni, Guillermo Lorenzo, Elisabetta Rocca","doi":"10.1137/24m1655469","DOIUrl":"https://doi.org/10.1137/24m1655469","url":null,"abstract":"","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"84 5","pages":"2000-2027"},"PeriodicalIF":0.0,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147905753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Applied Mathematics, Volume 84, Issue 5, Page 1937-1956, October 2024. Abstract. We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions [math]. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional conditions. A uniqueness result is derived as an immediate consequence of the stability result. Our approach relies on second-order linearization and multivariate finite differences, as well as the stability of the light-ray transform.
{"title":"Stable Determination of Time-Dependent Collision Kernel in the Nonlinear Boltzmann Equation","authors":"Ru-Yu Lai, Lili Yan","doi":"10.1137/23m1604060","DOIUrl":"https://doi.org/10.1137/23m1604060","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 5, Page 1937-1956, October 2024. <br/> Abstract. We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions [math]. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional conditions. A uniqueness result is derived as an immediate consequence of the stability result. Our approach relies on second-order linearization and multivariate finite differences, as well as the stability of the light-ray transform.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"39 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249470","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 5, Page 1910-1936, October 2024. Abstract. This paper studies the phenomenon of conduction block in model neurons using high-frequency biphasic stimulation (HFBS). The focus is investigating the triggering of undesired onset action potentials when the HFBS is turned on. The approach analyzes the transient behavior of an averaged system corresponding to the FitzHugh–Nagumo neuron model using Lyapunov and quasi-static methods. The first result provides a more comprehensive understanding of the onset activation through a mathematical proof of how to avoid it using a ramp in the amplitude of the oscillatory source. The second result tests the response of the blocked system to a piecewise linear stimulus, providing a quantitative description of how the HFBS strength translates into conduction block robustness. The results of this work can provide insights for the design of electrical neurostimulation therapies.
{"title":"The Impact of High-Frequency-Based Stability on the Onset of Action Potentials in Neuron Models","authors":"Eduardo Cerpa, Nathaly Corrales, Matías Courdurier, Leonel E. Medina, Esteban Paduro","doi":"10.1137/24m1645632","DOIUrl":"https://doi.org/10.1137/24m1645632","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 5, Page 1910-1936, October 2024. <br/> Abstract. This paper studies the phenomenon of conduction block in model neurons using high-frequency biphasic stimulation (HFBS). The focus is investigating the triggering of undesired onset action potentials when the HFBS is turned on. The approach analyzes the transient behavior of an averaged system corresponding to the FitzHugh–Nagumo neuron model using Lyapunov and quasi-static methods. The first result provides a more comprehensive understanding of the onset activation through a mathematical proof of how to avoid it using a ramp in the amplitude of the oscillatory source. The second result tests the response of the blocked system to a piecewise linear stimulus, providing a quantitative description of how the HFBS strength translates into conduction block robustness. The results of this work can provide insights for the design of electrical neurostimulation therapies.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"16 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249471","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 5, Page 1891-1909, October 2024. Abstract. Organisms inhabit streams, rivers, and estuaries where they are constantly subject to drift and overfishing. Consequently, these organisms often confront the risk of extinction. Can a reasonable fishing ban satisfy the human need for sufficient aquatic proteins without depleting fishery resources? We propose a reaction-diffusion-advection model to answer this question. The model consists of two subequations, which are constantly switched to describe closed seasons and open seasons with Michaelis–Menten type harvesting. We define a threshold value [math] for the duration of the fishing ban ([math]) and establish the relationships between [math] and each of the downstream end [math], the advection rate [math], and the diffusion rate [math]. Under certain conditions, the trivial equilibrium point 0 is globally asymptotically stable if [math]. When [math], we obtain sufficient conditions on the existence of a globally asymptotically stable periodic solution based on the thresholds in all parameter settings. Finally, some discussions on our findings are provided.
{"title":"Periodic Dynamics of a Reaction-Diffusion-Advection Model with Michaelis–Menten Type Harvesting in Heterogeneous Environments","authors":"Yunfeng Liu, Jianshe Yu, Yuming Chen, Zhiming Guo","doi":"10.1137/23m1600852","DOIUrl":"https://doi.org/10.1137/23m1600852","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 5, Page 1891-1909, October 2024. <br/> Abstract. Organisms inhabit streams, rivers, and estuaries where they are constantly subject to drift and overfishing. Consequently, these organisms often confront the risk of extinction. Can a reasonable fishing ban satisfy the human need for sufficient aquatic proteins without depleting fishery resources? We propose a reaction-diffusion-advection model to answer this question. The model consists of two subequations, which are constantly switched to describe closed seasons and open seasons with Michaelis–Menten type harvesting. We define a threshold value [math] for the duration of the fishing ban ([math]) and establish the relationships between [math] and each of the downstream end [math], the advection rate [math], and the diffusion rate [math]. Under certain conditions, the trivial equilibrium point 0 is globally asymptotically stable if [math]. When [math], we obtain sufficient conditions on the existence of a globally asymptotically stable periodic solution based on the thresholds in all parameter settings. Finally, some discussions on our findings are provided.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"59 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219280","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 1845-1867, August 2024. Abstract. In recent years, algebraic tools have been proven useful in phylogenetic reconstruction and model selection through the study of phylogenetic invariants. However, up to now, the models studied from an algebraic viewpoint are either too general or too restrictive (as group-based models with a uniform stationary distribution) to be used in practice. In this paper we provide a new framework to study time-reversible models, which are the most widely used by biologists. In our approach we consider algebraic time-reversible models on phylogenetic trees (as defined by Allman and Rhodes) and introduce a new inner product to make all transition matrices of the process diagonalizable through the same orthogonal eigenbasis. This framework generalizes the Fourier transform widely used to work with group-based models and recovers some of the well-known results. As illustration, we combine our technique with algebraic geometry tools to provide relevant phylogenetic invariants for trees evolving under the Tamura–Nei model of nucleotide substitution.
{"title":"A Novel Algebraic Approach to Time-Reversible Evolutionary Models","authors":"Marta Casanellas, Roser Homs, Angélica Torres","doi":"10.1137/23m1605302","DOIUrl":"https://doi.org/10.1137/23m1605302","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1845-1867, August 2024. <br/> Abstract. In recent years, algebraic tools have been proven useful in phylogenetic reconstruction and model selection through the study of phylogenetic invariants. However, up to now, the models studied from an algebraic viewpoint are either too general or too restrictive (as group-based models with a uniform stationary distribution) to be used in practice. In this paper we provide a new framework to study time-reversible models, which are the most widely used by biologists. In our approach we consider algebraic time-reversible models on phylogenetic trees (as defined by Allman and Rhodes) and introduce a new inner product to make all transition matrices of the process diagonalizable through the same orthogonal eigenbasis. This framework generalizes the Fourier transform widely used to work with group-based models and recovers some of the well-known results. As illustration, we combine our technique with algebraic geometry tools to provide relevant phylogenetic invariants for trees evolving under the Tamura–Nei model of nucleotide substitution.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"13 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219278","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 1868-1889, August 2024. Abstract. We investigate the increasing stability of the inverse Schrödinger potential problem with integer power type nonlinearities at a large wavenumber. By considering the first order linearized problem with respect to the unknown potential function, a combination formula of the first order linearization is proposed, which provides a Lipschitz type stability for the recovery of the Fourier coefficients of the unknown potential function in low frequency mode. These stability results highlight the advantage of nonlinearity in solving this inverse potential problem by explicitly quantifying the dependence on the wavenumber and the nonlinearity index. A reconstruction algorithm for integer power type nonlinearities is also provided. Several numerical examples illuminate the efficiency of our proposed algorithm.
{"title":"Increasing Stability of the First Order Linearized Inverse Schrödinger Potential Problem with Integer Power Type Nonlinearities","authors":"Sen Zou, Shuai Lu, Boxi Xu","doi":"10.1137/22m1542817","DOIUrl":"https://doi.org/10.1137/22m1542817","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1868-1889, August 2024. <br/> Abstract. We investigate the increasing stability of the inverse Schrödinger potential problem with integer power type nonlinearities at a large wavenumber. By considering the first order linearized problem with respect to the unknown potential function, a combination formula of the first order linearization is proposed, which provides a Lipschitz type stability for the recovery of the Fourier coefficients of the unknown potential function in low frequency mode. These stability results highlight the advantage of nonlinearity in solving this inverse potential problem by explicitly quantifying the dependence on the wavenumber and the nonlinearity index. A reconstruction algorithm for integer power type nonlinearities is also provided. Several numerical examples illuminate the efficiency of our proposed algorithm.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"28 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219277","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 1818-1844, August 2024. Abstract. For problems in the Calculus of Variations that exhibit the Lavrentiev phenomenon, it is known that a repulsion property may hold, that is, if one approximates the global minimizer in these problems by smooth functions, then the approximate energies will blow up. Thus, standard numerical schemes, like the finite element method, may fail when applied directly to these types of problems. In this paper we prove that a repulsion property holds for variational problems in three-dimensional elasticity that exhibit cavitation. In addition, we propose a numerical scheme that circumvents the repulsion property, which is an adaptation of the Modica and Mortola functional for phase transitions in liquids, in which the phase function is coupled, via the determinant of the deformation gradient, to the stored energy functional. We show that the corresponding approximations by this method satisfy the lower bound [math]–convergence property in the multidimensional, nonradial, case. The convergence to the actual cavitating minimizer is established for a spherical body, in the case of radial deformations.
{"title":"The Repulsion Property in Nonlinear Elasticity and a Numerical Scheme to Circumvent It","authors":"Pablo V. Negrón-Marrero, Jeyabal Sivaloganathan","doi":"10.1137/23m1583144","DOIUrl":"https://doi.org/10.1137/23m1583144","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1818-1844, August 2024. <br/> Abstract. For problems in the Calculus of Variations that exhibit the Lavrentiev phenomenon, it is known that a repulsion property may hold, that is, if one approximates the global minimizer in these problems by smooth functions, then the approximate energies will blow up. Thus, standard numerical schemes, like the finite element method, may fail when applied directly to these types of problems. In this paper we prove that a repulsion property holds for variational problems in three-dimensional elasticity that exhibit cavitation. In addition, we propose a numerical scheme that circumvents the repulsion property, which is an adaptation of the Modica and Mortola functional for phase transitions in liquids, in which the phase function is coupled, via the determinant of the deformation gradient, to the stored energy functional. We show that the corresponding approximations by this method satisfy the lower bound [math]–convergence property in the multidimensional, nonradial, case. The convergence to the actual cavitating minimizer is established for a spherical body, in the case of radial deformations.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"4 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219279","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 1792-1817, August 2024. Abstract. We revisit the problem of nonlinear water wave propagation in the presence of an abrupt depth transition. To this end, we use an asymptotic approach conducted to order 3 with respect to the shallowness parameter, in order to capture the first nonlinear and dispersive contributions. However, the discontinuity of bathymetry, as opposed to slowly varying bathymetry, requires the use of a consistent three-scale analysis framework and the consideration of different regions, far from the step and free surface, near the free surface, and near the step. This framework enables consistent navigation, ultimately providing Boussinesq equations supplemented by jump conditions at the depth discontinuity that encompass the effect of step on wave propagation.
{"title":"Jump Conditions for Boussinesq Equations Due to an Abrupt Depth Transition","authors":"Eduardo Monsalve, Kim Pham, Agnès Maurel","doi":"10.1137/23m1602437","DOIUrl":"https://doi.org/10.1137/23m1602437","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1792-1817, August 2024. <br/> Abstract. We revisit the problem of nonlinear water wave propagation in the presence of an abrupt depth transition. To this end, we use an asymptotic approach conducted to order 3 with respect to the shallowness parameter, in order to capture the first nonlinear and dispersive contributions. However, the discontinuity of bathymetry, as opposed to slowly varying bathymetry, requires the use of a consistent three-scale analysis framework and the consideration of different regions, far from the step and free surface, near the free surface, and near the step. This framework enables consistent navigation, ultimately providing Boussinesq equations supplemented by jump conditions at the depth discontinuity that encompass the effect of step on wave propagation.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"4 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219284","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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