Journal of Mathematical Biology最新文献

A spatial multiscale mathematical model of Plasmodium vivax transmission.

IF 2.2 4区数学

Journal of Mathematical Biology Pub Date : 2024-12-24 DOI: 10.1007/s00285-024-02166-w

Shoshana Elgart, Mark B Flegg, Somya Mehra, Jennifer A Flegg

{"title":"A spatial multiscale mathematical model of Plasmodium vivax transmission.","authors":"Shoshana Elgart, Mark B Flegg, Somya Mehra, Jennifer A Flegg","doi":"10.1007/s00285-024-02166-w","DOIUrl":"https://doi.org/10.1007/s00285-024-02166-w","url":null,"abstract":"The epidemiological behavior of Plasmodium vivax malaria occurs across spatial scales including within-host, population, and metapopulation levels. On the within-host scale, P. vivax sporozoites inoculated in a host may form latent hypnozoites, the activation of which drives secondary infections and accounts for a large proportion of P. vivax illness; on the metapopulation level, the coupled human-vector dynamics characteristic of the population level are further complicated by the migration of human populations across patches with different malaria forces of (re-)infection. To explore the interplay of all three scales in a single two-patch model of Plasmodium vivax dynamics, we construct and study a system of eight integro-differential equations with periodic forcing (arising from the single-frequency sinusoidal movement of a human sub-population). Under the numerically-informed ansatz that the limiting solutions to the system are closely bounded by sinusoidal ones for certain regions of parameter space, we derive a single nonlinear equation from which all approximate limiting solutions may be drawn, and devise necessary and sufficient conditions for the equation to have only a disease-free solution. Our results illustrate the impact of movement on P. vivax transmission and suggest a need to focus vector control efforts on forest mosquito populations. The three-scale model introduced here provides a more comprehensive framework for studying the clinical, behavioral, and geographical factors underlying P. vivax malaria endemicity.","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 1","pages":"13"},"PeriodicalIF":2.2,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142883513","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

Age-structured modeling of COVID-19 dynamics: the role of treatment and vaccination in controlling the pandemic.

IF 2.2 4区数学

Journal of Mathematical Biology Pub Date : 2024-12-24 DOI: 10.1007/s00285-024-02168-8

Shuanglin Jing, Ling Xue, Xuezhi Li, Fanqin Zeng, Junyuan Yang

{"title":"Age-structured modeling of COVID-19 dynamics: the role of treatment and vaccination in controlling the pandemic.","authors":"Shuanglin Jing, Ling Xue, Xuezhi Li, Fanqin Zeng, Junyuan Yang","doi":"10.1007/s00285-024-02168-8","DOIUrl":"https://doi.org/10.1007/s00285-024-02168-8","url":null,"abstract":"In addition to non-pharmaceutical interventions, antiviral drugs and vaccination are considered as the optimal solutions to control and eliminate the COVID-19 pandemic. It is necessary to couple within-host and between-host models to investigate the impact of treatment and vaccination. Hence, we propose an age-structured model, where the infection age is used to link the within-host viral dynamics and the disease dynamics at the population level. We conduct a detailed analysis of the local and global dynamics of the model, and the threshold dynamics are completely determined by the basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> . Thus, the disease-free equilibrium is globally asymptotically stable and the disease eventually dies out when <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo><</mo> <mn>1</mn></mrow> </math> ; the disease-free equilibrium is globally attractive when <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo>=</mo> <mn>1</mn></mrow> </math> ; the disease is uniformly persistent, and the unique endemic equilibrium is globally asymptotically stable when <math> <mrow><msub><mi>R</mi> <mn>0</mn></msub> <mo>></mo> <mn>1</mn></mrow> </math> . The numerical simulation quantitatively studies the impact of the within-host viral dynamics on between-host transmission dynamics. The results show that the combination of antiviral drugs and vaccines can play a key role in mitigating the spread of COVID-19, but it is challenging to eliminate COVID-19 alone. To achieve the complete elimination of COVID-19, we need highly effective antiviral drugs and near-universal vaccine coverage.","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"90 1","pages":"12"},"PeriodicalIF":2.2,"publicationDate":"2024-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142883515","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

Duration of transients in outbreaks: when can infectiousness be estimated?

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

引用次数: 0

Optimal vaccination policy to prevent endemicity: a stochastic model.

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":"https://doi.org/10.1007/s00285-024-02171-z","url":null,"abstract":"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.","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":"","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":"","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.

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":"https://doi.org/10.1007/s00285-024-02176-8","url":null,"abstract":"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.","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":"","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":"","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.

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

引用次数: 0

Exchangeable coalescents beyond the Cannings class.

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

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":"https://doi.org/10.1007/s00285-024-02170-0","url":null,"abstract":"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.","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

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":"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.","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