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Duration of transients in outbreaks: when can infectiousness be estimated? 疫情的短暂持续时间：何时可以估计传染性？
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2024-12-20 DOI: 10.1007/s00285-024-02175-9
Adam Mielke, Lasse Engbo Christiansen
{"title":"Duration of transients in outbreaks: when can infectiousness be estimated?","authors":"Adam Mielke, Lasse Engbo Christiansen","doi":"10.1007/s00285-024-02175-9","DOIUrl":"10.1007/s00285-024-02175-9","url":null,"abstract":"<p><p>We investigate sub-leading orders of the classic SEIR-model using contact matrices from modeling of the Omicron and Delta variants of COVID-19 in Denmark. The goal of this is to illustrate when the growth rate, and by extension the infection transmission potential (basic or initial reproduction number), can be estimated in a new outbreak, e.g. after introduction of a new variant of a virus. In particular, we look at the time scale on which this happens in a realistic outbreak to guide future data collection. We find that as long as susceptible depletion is a minor effect, the transients are gone within around 3 weeks corresponding to about 4-5 times the incubation time. We also argue that this result generalizes to other airborne diseases in a fully mixed population.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 1","pages":"11"},"PeriodicalIF":2.2,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11659369/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142866043","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}
引用次数: 0
Optimal vaccination policy to prevent endemicity: a stochastic model. 预防地方病的最佳疫苗接种政策：一个随机模型。
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2024-12-19 DOI: 10.1007/s00285-024-02171-z
Félix Foutel-Rodier, Arthur Charpentier, Hélène Guérin
{"title":"Optimal vaccination policy to prevent endemicity: a stochastic model.","authors":"Félix Foutel-Rodier, Arthur Charpentier, Hélène Guérin","doi":"10.1007/s00285-024-02171-z","DOIUrl":"10.1007/s00285-024-02171-z","url":null,"abstract":"<p><p>We examine here the effects of recurrent vaccination and waning immunity on the establishment of an endemic equilibrium in a population. An individual-based model that incorporates memory effects for transmission rate during infection and subsequent immunity is introduced, considering stochasticity at the individual level. By letting the population size going to infinity, we derive a set of equations describing the large scale behavior of the epidemic. The analysis of the model's equilibria reveals a criterion for the existence of an endemic equilibrium, which depends on the rate of immunity loss and the distribution of time between booster doses. The outcome of a vaccination policy in this context is influenced by the efficiency of the vaccine in blocking transmissions and the distribution pattern of booster doses within the population. Strategies with evenly spaced booster shots at the individual level prove to be more effective in preventing disease spread compared to irregularly spaced boosters, as longer intervals without vaccination increase susceptibility and facilitate more efficient disease transmission. We provide an expression for the critical fraction of the population required to adhere to the vaccination policy in order to eradicate the disease, that resembles a well-known threshold for preventing an outbreak with an imperfect vaccine. We also investigate the consequences of unequal vaccine access in a population and prove that, under reasonable assumptions, fair vaccine allocation is the optimal strategy to prevent endemicity.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 1","pages":"10"},"PeriodicalIF":2.2,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11655619/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142856561","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}
引用次数: 0
Model-based conceptualization of thyroid hormone equilibrium via set point and stability behavior. 基于模型的甲状腺激素平衡的设定点和稳定性行为概念化。
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2024-12-18 DOI: 10.1007/s00285-024-02176-8
Corinna Modiz, Andreas Körner
{"title":"Model-based conceptualization of thyroid hormone equilibrium via set point and stability behavior.","authors":"Corinna Modiz, Andreas Körner","doi":"10.1007/s00285-024-02176-8","DOIUrl":"10.1007/s00285-024-02176-8","url":null,"abstract":"<p><p>The HPT complex, consisting of the hypothalamus, pituitary and thyroid, functions as a regulated system controlled by the respective hormones. This system maintains an intrinsic equilibrium, called the set point, which is unique to each individual. In order to optimize the treatment of thyroid patients and understand the dynamics of the system, a validated theoretical representation of this set point is required. Therefore, the research field of mathematical modeling of the HPT complex is significant as it provides insights into the interactions between hormones and the determination of this endogenous equilibrium. In literature, two mathematical approaches are presented for the theoretical determination of the set point in addition to a time-dependent model. The two approaches are based on the maximum curvature of the pituitary response function and the optimal gain factor in the representation of the HPT complex as a closed feedback system. This paper demonstrates that all hormone curves described by the model converge to the derived set point with increasing time. This result establishes a clear correlation between the physiological equilibrium described by the set point and the mathematical equilibrium with respect to autonomous systems of differential equations. It thus substantiates the validity of the theoretical set point approaches.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 1","pages":"9"},"PeriodicalIF":2.2,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11655583/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142856541","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}
引用次数: 0
An integral renewal equation approach to behavioural epidemic models with information index. 带信息指数的行为流行病模型的积分更新方程方法。
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2024-12-17 DOI: 10.1007/s00285-024-02172-y
Bruno Buonomo, Eleonora Messina, Claudia Panico, Antonia Vecchio
{"title":"An integral renewal equation approach to behavioural epidemic models with information index.","authors":"Bruno Buonomo, Eleonora Messina, Claudia Panico, Antonia Vecchio","doi":"10.1007/s00285-024-02172-y","DOIUrl":"10.1007/s00285-024-02172-y","url":null,"abstract":"<p><p>We propose an integral model describing an epidemic of an infectious disease. The model is behavioural in the sense that the force of infection includes the information index that describes the opinion-driven human behavioural changes. The information index contains a memory kernel to mimic how the individuals maintain memory of the past values of the infection. We obtain sufficient conditions for the endemic equilibrium to be locally stable. In particular, we show that when the infectivity function is represented by an exponential distribution, stability is guaranteed by the weak Erlang memory kernel. However, through numerical simulations, we show that oscillations, possibly self-sustained, may arise when the memory is more focused in the disease's past history, as exemplified by the strong Erlang kernel. We also show the model solutions in cases of different infectivity functions taken from studies where specific diseases like Influenza and SARS are considered.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 1","pages":"8"},"PeriodicalIF":2.2,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142840130","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
Exchangeable coalescents beyond the Cannings class. 坎宁类以外的可交换聚结物。
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2024-12-17 DOI: 10.1007/s00285-024-02173-x
Arno Siri-Jégousse, Alejandro H Wences
{"title":"Exchangeable coalescents beyond the Cannings class.","authors":"Arno Siri-Jégousse, Alejandro H Wences","doi":"10.1007/s00285-024-02173-x","DOIUrl":"10.1007/s00285-024-02173-x","url":null,"abstract":"<p><p>We propose a general framework for the study of the genealogy of neutral discrete-time populations. We remove the standard assumption of exchangeability of offspring distributions appearing in Cannings models, and replace it by a less restrictive condition of non-heritability of reproductive success. We provide a general criterion for the weak convergence of their genealogies to <math><mi>Ξ</mi></math> -coalescents, and apply it to a simple parametrization of our scenario (which, under mild conditions, we also prove to essentially include the general case). We provide examples for such populations, including models with highly-asymmetric offspring distributions and populations undergoing random but recurrent bottlenecks. Finally we study the limit genealogy of a new exponential model which, as previously shown for related models and in spite of its built-in (fitness) inheritance mechanism, can be brought into our setting.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 1","pages":"7"},"PeriodicalIF":2.2,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11652580/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142840132","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}
引用次数: 0
Replicator dynamics generalized for evolutionary matrix games under time constraints. 时间限制下进化矩阵博弈的复制器动力学。
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2024-12-15 DOI: 10.1007/s00285-024-02170-0
Tamás Varga
{"title":"Replicator dynamics generalized for evolutionary matrix games under time constraints.","authors":"Tamás Varga","doi":"10.1007/s00285-024-02170-0","DOIUrl":"10.1007/s00285-024-02170-0","url":null,"abstract":"<p><p>One of the central results of evolutionary matrix games is that a state corresponding to an evolutionarily stable strategy (ESS) is an asymptotically stable equilibrium point of the standard replicator dynamics. This relationship is crucial because it simplifies the analysis of dynamic phenomena through static inequalities. Recently, as an extension of classical evolutionary matrix games, matrix games under time constraints have been introduced (Garay et al. in J Theor Biol 415:1-12, 2017; Křivan and Cressman in J Theor Biol 416:199-207, 2017). In this model, after an interaction, players do not only receive a payoff but must also wait a certain time depending on their strategy before engaging in another interaction. This waiting period can significantly impact evolutionary outcomes. We found that while the aforementioned classical relationship holds for two-dimensional strategies in this model (Varga et al. in J Math Biol 80:743-774, 2020), it generally does not apply for three-dimensional strategies (Varga and Garay in Dyn Games Appl, 2024). To resolve this problem, we propose a generalization of the replicator dynamics that considers only individuals in active state, i.e., those not waiting, can interact and gain resources. We prove that using this generalized dynamics, the classical relationship holds true for matrix games under time constraints in any dimension: a state corresponding to an ESS is asymptotically stable. We believe this generalized replicator dynamics is more naturally aligned with the game theoretical model under time constraints than the classical form. It is important to note that this generalization reduces to the original replicator dynamics for classical matrix games.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 1","pages":"6"},"PeriodicalIF":2.2,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142824667","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
Analytic solutions for the circadian oscillator characterize cycle dynamics and its robustness. 昼夜节律振荡器的解析解描述了周期动态及其稳健性。
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2024-12-14 DOI: 10.1007/s00285-024-02164-y
Odile Burckard, Madalena Chaves
{"title":"Analytic solutions for the circadian oscillator characterize cycle dynamics and its robustness.","authors":"Odile Burckard, Madalena Chaves","doi":"10.1007/s00285-024-02164-y","DOIUrl":"10.1007/s00285-024-02164-y","url":null,"abstract":"<p><p>Circadian clocks form a fundamental mechanism that promotes the correct behavior of many cellular and molecular processes by synchronizing them on a 24 h period. However, the circadian cycles remain difficult to describe mathematically. To overcome this problem, we first propose a segmentation of the circadian cycle into eight stages based on the levels of expression of the core clock components CLOCK:BMAL1, REV-ERB and PER:CRY. This cycle segmentation is next characterized through a piecewise affine model, whose analytical study allows us to propose an Algorithm to generate biologically-consistent circadian oscillators. Our study provides a characterization of the cycle dynamics in terms of four fundamental threshold parameters and one scaling parameter, shows robustness of the circadian system and its period, and identifies critical points for correct cycle progression.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 1","pages":"5"},"PeriodicalIF":2.2,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142824664","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
Optimizing control parameters for Huanglongbing disease in citrus orchards using SAIR-SI compartmental model, epidemic final size, and genetic algorithms. 利用 SAIR-SI 分区模型、流行病最终规模和遗传算法优化柑橘园黄龙病的控制参数。
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2024-12-13 DOI: 10.1007/s00285-024-02161-1
Andrés Anzo Hernández, Uvencio José Giménez Mujica, Carlos Arturo Hernández Gracidas, José Jacobo Oliveros Oliveros
{"title":"Optimizing control parameters for Huanglongbing disease in citrus orchards using SAIR-SI compartmental model, epidemic final size, and genetic algorithms.","authors":"Andrés Anzo Hernández, Uvencio José Giménez Mujica, Carlos Arturo Hernández Gracidas, José Jacobo Oliveros Oliveros","doi":"10.1007/s00285-024-02161-1","DOIUrl":"10.1007/s00285-024-02161-1","url":null,"abstract":"<p><p>Huanglongbing (HLB) is a bacterial disease that affects citrus trees worldwide. We present an innovative approach for identifying optimal control and risk measures for HLB in citrus orchards. Our method is based on a mathematical model that incorporates the number of roguing trees and a logistic growth model for the dynamic of the Asian Citrus Psyllid (ACP), the primary vector for HLB transmission. We derive an expression for: (1) the basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> ; (2) the final size for the number of roguing trees; and (3) the transmission risk. The above let us propose a difference map equation that assesses this final size with a low computational cost. We use this difference map in an evolutionary algorithm to identify the most effective combination of control parameter values for reducing HLB transmission, including the timing and frequency of roguing and the use of insecticides. In this sense, we propose two control strategies, which we called tree-centered and vector-centered.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 1","pages":"4"},"PeriodicalIF":2.2,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11645321/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142819878","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}
引用次数: 0
On a model of evolution of subspecies. 在亚种进化的模型上。
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2024-12-06 DOI: 10.1007/s00285-024-02165-x
Rahul Roy, Hideki Tanemura
{"title":"On a model of evolution of subspecies.","authors":"Rahul Roy, Hideki Tanemura","doi":"10.1007/s00285-024-02165-x","DOIUrl":"10.1007/s00285-024-02165-x","url":null,"abstract":"<p><p>Ben-Ari and Schinazi (J Stat Phys 162:415-425, 2016) introduced a stochastic model to study 'virus-like evolving population with high mutation rate'. This model is a birth and death model with an individual at birth being either a mutant with a random fitness parameter in [0, 1] or having one of the existing fitness parameters with uniform probability; whereas a death event removes the entire population of the least fitness. We change this to incorporate the notion of 'survival of the fittest', by requiring that a non-mutant individual, at birth, has a fitness according to a preferential attachment mechanism, i.e., it has a fitness f with a probability proportional to the size of the population of fitness f. Also death just removes one individual with the least fitness. This preferential attachment rule leads to a power law behaviour in the asymptotics, unlike the exponential behaviour obtained by Ben-Ari and Schinazi (J Stat Phys 162:415-425, 2016).</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 1","pages":"3"},"PeriodicalIF":2.2,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142787499","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 properties of pump-leak-cotransport models. 泵-泄漏-共输模型的数学性质。
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2024-12-03 DOI: 10.1007/s00285-024-02163-z
Vincent Ouellet, Nicolas Doyon, Antoine G Godin, Pierre Marquet
{"title":"Mathematical properties of pump-leak-cotransport models.","authors":"Vincent Ouellet, Nicolas Doyon, Antoine G Godin, Pierre Marquet","doi":"10.1007/s00285-024-02163-z","DOIUrl":"10.1007/s00285-024-02163-z","url":null,"abstract":"<p><p>Models of ordinary differential equations are often used to describe the electrical, ionic and volumetric responses of cells to external stimuli. Although these cellular models are often solved numerically, rigorous evidence regarding their steady state solutions is scarce. In this work, we provide a formalism defining the conditions ensuring the existence and uniqueness of a steady-state solution in a large class of models including leak channels, a pump and cotransporters. Our work generalizes previous results and provides explicit conditions that a model must satisfy to guarantee the existence and uniqueness of a steady state.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 1","pages":"2"},"PeriodicalIF":2.2,"publicationDate":"2024-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142774375","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
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