Mathematical Biosciences最新文献_第2页

Employing nullclines to balance treatment efficacy and neurotoxicity for sustained tumor control 采用零线药物平衡治疗效果和神经毒性以持续控制肿瘤。

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-09-10 DOI: 10.1016/j.mbs.2025.109535

Lois C. Okereke , Ernesto A.B.F. Lima , Anna G. Sorace , Thomas E. Yankeelov

{"title":"Employing nullclines to balance treatment efficacy and neurotoxicity for sustained tumor control","authors":"Lois C. Okereke , Ernesto A.B.F. Lima , Anna G. Sorace , Thomas E. Yankeelov","doi":"10.1016/j.mbs.2025.109535","DOIUrl":"10.1016/j.mbs.2025.109535","url":null,"abstract":"<div><div>There is increasing interest in identifying therapeutic regimens capable of maintaining tumor burden within well-defined size boundaries with constraints on the amount and frequency of drugs on a patient-specific basis. We have developed coupled systems of ordinary differential equations (ODEs) capturing the temporal dynamics of tumor burden, treatment effects due to cytotoxic drugs, and neurotoxicity. The models account for tumor cell proliferation and phenotypic heterogeneity, drug availability due to continuous or impulsive drug delivery, drug-induced apoptosis and microglia activation. We utilize nullclines of the system to derive effective dose ranges that stabilize tumor burden and mitigate neurotoxicity. Our results generate bounded treatment regimens that can be validated in the experimental setting. We found that for tumors with a proliferation saturation index (i.e., pre-treatment volume to carrying capacity ratio) between 0.10 and 0.30, containing the tumor in the sense of RECIST can yield up to a 51.8% reduction in drug concentration when compared with regimens designed for tumor eradication. <em>In silico</em> experiments using data from a breast cancer study demonstrate that the nullcline-derived treatments maintained stable disease in the tumors with neurotoxicity maintained below the desired threshold. The methodology developed in this study provides a theoretical formalism to potentially explain several preclinical and clinical observations indicating that low dose therapy can stabilize tumor growth and result in an enhanced quality of life. Importantly, our model identified quantitative biologic indices that can offer practical guidance to the design of personalized regimens that balance treatment efficacy and toxicity.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109535"},"PeriodicalIF":1.8,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145056604","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}

引用次数: 0

Calibrating a parameterized stochastic Boolean network model of gene regulation using a single steady-state gene expression profile 校准一个参数化的随机布尔网络模型的基因调控使用一个单一的稳态基因表达谱。

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-09-09 DOI: 10.1016/j.mbs.2025.109523

Mohammad Taheri-Ledari , Sayed-Amir Marashi , Mohammad Hossein Ghahremani , Kaveh Kavousi

{"title":"Calibrating a parameterized stochastic Boolean network model of gene regulation using a single steady-state gene expression profile","authors":"Mohammad Taheri-Ledari , Sayed-Amir Marashi , Mohammad Hossein Ghahremani , Kaveh Kavousi","doi":"10.1016/j.mbs.2025.109523","DOIUrl":"10.1016/j.mbs.2025.109523","url":null,"abstract":"<div><div>Boolean networks (BNs), due to their capacity to replicate non-linear dynamics despite their simplicity, have garnered significant interest among researchers. BNs can be used to simulate the effect of perturbations in biological systems, including changes in environmental conditions, genetic mutations, or the introduction of a drug. A major application of dynamic gene regulatory network (GRN) models is to identify how a specific perturbation shifts a GRN’s behavioral mode towards another one. To this end, a gene expression profile, which snapshots the cell transcriptome at (quasi-)steady-state, can be exploited to adjust a stochastic Boolean GRN under a certain condition. Such tailored GRNs hold numerous implications for drug target discovery, novel therapeutic strategies, and personalized medicine. In this study, we introduce a methodology for estimating the parameters of a parameterized stochastic BN model of gene regulation using a single steady-state gene expression measurement. We employ certain simplifying assumptions to reformulate the problem as a system of linear equations, ensuring ergodicity and the existence of a unique solution. However, even under these simplifying conditions, the high time and space demand to solve the problem can be challenging. In the present study, we applied a simulation-based approach to estimating parameters, rather than explicitly deriving and solving the set of linear equations. Finally, we show the applicability and relevance of our approach on a set of randomly generated BNs as well as establishing “personalized” BNs for non-small cell lung cancer cell lines (NSCLC).</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109523"},"PeriodicalIF":1.8,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145042765","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}

引用次数: 0

Impacts of competition and phenotypic plasticity on the viability of adaptive therapy 竞争和表型可塑性对适应性治疗生存能力的影响。

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-09-09 DOI: 10.1016/j.mbs.2025.109522

B. Vibishan , Paras Jain , Vedant Sharma , Kishore Hari , Claus Kadelka , Jason T. George , Mohit Kumar Jolly

{"title":"Impacts of competition and phenotypic plasticity on the viability of adaptive therapy","authors":"B. Vibishan , Paras Jain , Vedant Sharma , Kishore Hari , Claus Kadelka , Jason T. George , Mohit Kumar Jolly","doi":"10.1016/j.mbs.2025.109522","DOIUrl":"10.1016/j.mbs.2025.109522","url":null,"abstract":"<div><div>Cancer is heterogeneous and variability in drug sensitivity is widely documented across cancer types. Adaptive therapy is an emerging treatment strategy that leverages this heterogeneity to improve therapeutic outcomes. Current standard treatments eliminate a majority of drug-sensitive cells, leading to relapse by competitive release. Adaptive therapy retains some drug-sensitive cells, limiting resistant cell growth by ecological competition. This strategy has shown some early promise, but current methods largely assume cell phenotypes to remain constant, even though cell-state transitions could permit drug-sensitive and -resistant phenotypes to interchange and thus escape therapy. We address this gap using a deterministic model of population growth, in which sensitive and resistant cells grow under competition and undergo cell-state transitions. The model’s steady-state behaviour and temporal dynamics identify optimal balances of competition and transitions suitable for effective adaptive versus constant dose therapy. Furthermore, under adaptive therapy, models with cell-state transitions show slower oscillations than those without, suggesting that the competition-transitions balance could impinge on population-level dynamical properties. Our analyses also identify key limitations of phenomenological models in therapy design and implementation, particularly with cell-state transitions. These findings elucidate the relevance of phenotypic plasticity for emerging cancer treatment strategies using population dynamics as an investigation framework.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109522"},"PeriodicalIF":1.8,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145042781","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}

引用次数: 0

Dynamics of a pine wilt disease control model with nonlocal competition and memory diffusion 具有非局部竞争和记忆扩散的松材萎蔫病防治模型动力学研究

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-09-08 DOI: 10.1016/j.mbs.2025.109524

Yuting Ding , Pei Yu

{"title":"Dynamics of a pine wilt disease control model with nonlocal competition and memory diffusion","authors":"Yuting Ding , Pei Yu","doi":"10.1016/j.mbs.2025.109524","DOIUrl":"10.1016/j.mbs.2025.109524","url":null,"abstract":"<div><div>Pine wilt disease (PWD) is mainly spread by Monochamus alternatus (in short, M. alternatus). Woodpecker, as the natural predator of M. alternatus, is considered for biological prevention and controlling the PWD. In this paper, we propose a new M. alternatus-woodpecker model with nonlocal competition and memory-based diffusion, which makes the model more realistic for the PWD control. We focus on the dynamics and bifurcations of the model with various combinations of the memory diffusion and nonlocal competition. It is shown that the nonlocal competition can only cause the stable constant steady state to lose stability, while the memory-based diffusion can induce unstable spatially inhomogeneous periodic solutions due to Hopf bifurcation. Consequently, we can explain the spatiotemporal heterogeneity problem in ecology by innovatively using mathematical modelling. Normal form theory with the multiple time scales method is applied to particularly consider Hopf bifurcation, showing complex dynamical behaviours involving various oscillating motions. Finally, numerical simulations are presented with the parameter values chosen from the real forest data of Yuan’an County, Hubei Province, China, confirming the theoretical results of the spatiotemporal heterogeneity of forest diseases and pests, as well as the PWD control.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109524"},"PeriodicalIF":1.8,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027736","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}

引用次数: 0

Nonhomogeneous mixing reduces disease prevalence 非均匀混合降低了疾病患病率

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-09-01 DOI: 10.1016/j.mbs.2025.109521

Daozhou Gao , Xin Li

{"title":"Nonhomogeneous mixing reduces disease prevalence","authors":"Daozhou Gao , Xin Li","doi":"10.1016/j.mbs.2025.109521","DOIUrl":"10.1016/j.mbs.2025.109521","url":null,"abstract":"<div><div>Human movement and spatial heterogeneity shape the spatial distribution of infections. Factors such as physical condition, availability of medical resources, socioeconomic status, and exit-entry screening can lead to variations in movement rate and pattern (or called habitat connectivity in discrete diffusion and dispersal kernel in continuous diffusion) among people with different health states. While the effects of movement rate on disease spread have been extensively studied, the role of movement pattern remains less understood. In this paper, for a susceptible–infected–susceptible (SIS) patch model incorporating either Eulerian, Lagrangian, or hybrid Lagrangian–Eulerian movement, as well as an SIS nonlocal dispersal model, we derive an upper bound on the global disease prevalence that is independent of movement. In a homogeneous environment, the nonhomogeneous mixing of susceptible and infected individuals always reduces disease prevalence. The prevalence attains its maximum when the susceptible and infected populations adopt the same distribution strategy. Numerical simulations further illustrate some new phenomena arising from different movement patterns. These results deepen our understanding on the impact of human movement on disease spread and pathogen evolution, thereby improving control measures to reduce disease burden.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"388 ","pages":"Article 109521"},"PeriodicalIF":1.8,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932070","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}

引用次数: 0

Go-or-grow-or-die as a framework for the mathematical modeling of glioblastoma dynamics 作为胶质母细胞瘤动力学数学建模的框架

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-08-22 DOI: 10.1016/j.mbs.2025.109520

Aisha Tursynkozha , Duane C. Harris , Yang Kuang , Ardak Kashkynbayev

{"title":"Go-or-grow-or-die as a framework for the mathematical modeling of glioblastoma dynamics","authors":"Aisha Tursynkozha , Duane C. Harris , Yang Kuang , Ardak Kashkynbayev","doi":"10.1016/j.mbs.2025.109520","DOIUrl":"10.1016/j.mbs.2025.109520","url":null,"abstract":"<div><div>We investigate a three-dimensional reaction–diffusion model of avascular glioblastoma growth, introducing a new <em>go-or-grow-or-die</em> framework that incorporates reversible phenotypic switching between migratory and proliferative states, while accounting for the contribution of necrotic cells. To model necrotic cell accumulation, a quasi-steady-state approximation is employed, allowing the necrotic population to be expressed as a function of proliferating cell density. Analytical and numerical analyses of the model reveal that the traveling wave speed is consistently lower than that predicted by the classical Fisher–Kolmogorov–Petrovsky–Piskunov equation, highlighting the significance of phenotypic heterogeneity. In particular, we confirm the role of the switching parameter in modulating invasion speed. Approximate wave profiles derived using Canosa’s method show strong agreement with numerical simulations. Furthermore, model predictions are validated against experimental data for the <span><math><mrow><mi>U</mi><mn>87</mn><mi>W</mi><mi>T</mi></mrow></math></span> glioblastoma cell line, demonstrating improved accuracy in capturing tumor invasion when both phenotypic switching and necrosis are included. These findings underscore the importance of the <em>go-or-grow-or-die</em> framework in understanding tumor progression and establish a novel, generalizable framework for modeling cancer dynamics.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"388 ","pages":"Article 109520"},"PeriodicalIF":1.8,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896291","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}

引用次数: 0

A new optimized regularized Stokeslet model reveals the effects of multicellular protozoan colony configuration on hydrodynamic performance 一个新的优化正则化Stokeslet模型揭示了多细胞原生动物群落结构对水动力性能的影响。

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-08-18 DOI: 10.1016/j.mbs.2025.109519

Hongfei Chen , Tom Hata , Ricardo Cortez , Hoa Nguyen , M.A.R. Koehl , Lisa Fauci

{"title":"A new optimized regularized Stokeslet model reveals the effects of multicellular protozoan colony configuration on hydrodynamic performance","authors":"Hongfei Chen , Tom Hata , Ricardo Cortez , Hoa Nguyen , M.A.R. Koehl , Lisa Fauci","doi":"10.1016/j.mbs.2025.109519","DOIUrl":"10.1016/j.mbs.2025.109519","url":null,"abstract":"<div><div>Many microbial eukaryotes have unicellular life stages, but can also form multicellular colonies. We explored hydrodynamic consequences of colony morphology, which affects swimming and flux of prey-carrying water to cells in a colony, using the choanoflagellate, <em>Choanoeca flexa</em>, which forms cup-like colonies that can turn inside-out so flagella line the cup’s interior or cover its outside surface. Detailed hydrodynamic models incorporating cell morphologies are not feasible for colonies with many cells. Therefore, we designed a reduced model of each cell using regularized-force-dipoles with parameters optimized (by selecting the regularized delta function from a given class) to match the flow-field of a detailed model of a cell. Calculated swimming speeds and water flux to flagella-in colonies match those measured for living <em>C. flexa</em>. For a given shape (flat bowls, hemispheres, spherical cups) of flagella-in colony, models showed that swimming speed and water flux towards the colony increases with cell density, although flux per cell is independent of density. Denser packing of cells at the front of flagella-in colonies increases swimming speed and flux to cells at all positions in the colonies. Flagella-in colonies swim more slowly, but produce higher water flux per cell than do flagella-out colonies of the same configuration, suggesting that flagella-out colonies are better swimmers, whereas flagella-in colonies are better feeders. A model flagella-out colony with morphology matched to a real <em>C. flexa</em> requires a flagellar force 5–10 times greater than that for flagella-in colonies to achieve the measured swimming speed, suggesting flagella beat differently on flagella-out colonies.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109519"},"PeriodicalIF":1.8,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144984281","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}

引用次数: 0

Mathematical model of replication–mutation dynamics in coronaviruses 冠状病毒复制-突变动力学的数学模型

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-08-18 DOI: 10.1016/j.mbs.2025.109518

K.B. Blyuss, Y.N. Kyrychko

{"title":"Mathematical model of replication–mutation dynamics in coronaviruses","authors":"K.B. Blyuss, Y.N. Kyrychko","doi":"10.1016/j.mbs.2025.109518","DOIUrl":"10.1016/j.mbs.2025.109518","url":null,"abstract":"<div><div>RNA viruses are known for their fascinating evolutionary dynamics, characterised by high mutation rates, fast replication, and ability to form quasispecies — clouds of genetically related mutants. Fast replication in RNA viruses is achieved by a very fast but error-prone RNA-dependent RNA polymerase (RdRP). High mutation rates are a double-edged sword: they provide RNA viruses with a mechanism of fast adaptation to a changing environment or host immune system, but at the same time they pose risk to virus survivability in terms of either virus population being dominated by mutants (error catastrophe), or extinction of all viral sequences due to accumulation of mutations (lethal mutagenesis). Coronaviruses, being a subset of RNA viruses, are unique in having a special enzyme, exoribonuclease (ExoN), responsible for proofreading and correcting errors induced by the RdRP. In this paper we consider replication dynamics of coronaviruses with account for mutations that can be neutral, deleterious or lethal. Compared to earlier models of replication of RNA viruses, our model also explicitly includes ExoN and its effects on mediating viral replication. Special attention is paid to different virus replication modes that are known to be crucial for controlling the dynamics of virus populations. We analyse extinction, mutant-only and quasispecies steady states, and study their stability in terms of different parameters, identifying regimes of error catastrophe and lethal mutagenesis. With coronaviruses being responsible for some of the largest pandemics in the last twenty years, we also model the effects of antiviral treatment with various replication inhibitors and mutagenic drugs.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"388 ","pages":"Article 109518"},"PeriodicalIF":1.8,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144879013","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}

引用次数: 0

Modeling and dynamics of Brucella infection-induced macrophage apoptosis inhibition 布鲁氏菌感染诱导巨噬细胞凋亡抑制的模型和动力学

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-08-11 DOI: 10.1016/j.mbs.2025.109515

Huidi Chu , Meng Fan , Huaiping Zhu

{"title":"Modeling and dynamics of Brucella infection-induced macrophage apoptosis inhibition","authors":"Huidi Chu , Meng Fan , Huaiping Zhu","doi":"10.1016/j.mbs.2025.109515","DOIUrl":"10.1016/j.mbs.2025.109515","url":null,"abstract":"<div><div>Brucella is an intracellular bacterium that causes the widespread zoonotic disease brucellosis. Within their hosts, Brucella has evolved various immune evasion strategies, including the ability to survive and replicate within host cells, especially within macrophages. This leads brucellosis from an acute phase to a chronic phase that is difficult to cure. In order to explore the key factors for the survival of Brucella and the mechanisms of persistent chronic infection, a mathematical model is developed to characterize the interactions between Brucella and macrophages, which incorporates a saturable apoptosis-inhibiting function within an infected host. The dynamics are well investigated in mathematics such as the invariance and boundedness, the existence and stability of equilibria, the bifurcation dynamics, and the threshold criteria for the clearance of Brucella infection. In particular, it is elaborated that the model can undergo forward and backward bifurcation, Hopf bifurcation, and Bogdanov–Takens bifurcation of codimension 2 by applying the central manifold theorem and normal form theory. Numerical analyses indicate that the presence of bistability complicates the clearance processes of Brucella. In addition, the infection rate of Brucella and the baseline apoptosis rate of infected macrophages are identified as key factors in determining Brucella clearance, the persistence of chronic infection, and the occurrence of undulating fever. The main findings highlight that increasing immune clearance capacity and reducing the virulence of Brucella are critical for controlling Brucella infections.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"388 ","pages":"Article 109515"},"PeriodicalIF":1.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144840862","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}

引用次数: 0

Distributions of prevalence and daily new cases in a stochastic linear SEIR model 随机线性SEIR模型中流行率和每日新病例的分布

IF 1.8 4区数学

Mathematical Biosciences Pub Date : 2025-08-11 DOI: 10.1016/j.mbs.2025.109508

Manting Wang, P. van den Driessche, Laura L.E. Cowen, Junling Ma

{"title":"Distributions of prevalence and daily new cases in a stochastic linear SEIR model","authors":"Manting Wang, P. van den Driessche, Laura L.E. Cowen, Junling Ma","doi":"10.1016/j.mbs.2025.109508","DOIUrl":"10.1016/j.mbs.2025.109508","url":null,"abstract":"<div><div>Model parameters are typically estimated by calibrating the model to new case counts. This is important for understanding disease dynamics and guiding control measures. For parameter estimation, it is essential to identify the distribution of new cases and establish an appropriate likelihood function. This study employs a stochastic linear SEIR model to approximate the distributions of the number of infectious individuals and the number of daily new cases. We show that the probability-generating function (PGF) of the number of infectious individuals can be approximated as the product of PGFs of two birth-and-death processes. We theoretically derive formulas for the mean and variance of both the number of infectious individuals and daily new cases. Furthermore, we demonstrate that the distribution of the infectious population size can be approximated by a binomial or negative binomial distribution, depending on the relationship between its mean and variance. The distribution of daily new cases can also be well approximated by a binomial or negative binomial distribution, depending on the distribution of the infectious population. Specifically, if the number of infectious individuals follows a binomial distribution, the number of daily new cases is also binomial; if it follows a negative binomial distribution, the number of daily new cases is negative binomial as well. These findings provide a robust theoretical basis for parameter estimation and epidemic forecasting.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"388 ","pages":"Article 109508"},"PeriodicalIF":1.8,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144829841","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}

引用次数: 0