Mathematical Biosciences最新文献

{"title":"Spreading dynamics of an SVIRS model","authors":"Guo Lin ,&nbsp;Jiantao Lin ,&nbsp;Shuxia Pan","doi":"10.1016/j.mbs.2025.109569","DOIUrl":"10.1016/j.mbs.2025.109569","url":null,"abstract":"<div><div>The geographic spread of a disease epidemic has long been a key focus of public attention. This article investigates the spreading properties of a reaction-diffusion system, which models the Susceptible-Vaccinated-Infected-Recovered-Susceptible (SVIRS for short) process. Assume that the habitat of the entire population expands or contracts in a wave front pattern. Then we study the corresponding initial value problems and traveling wave solutions, which model the spatial expanding ability of the disease. A constant associated with the disease’s transmission capacity is given, enabling the exploration of practical factors that influence disease spreading. For example, both the vaccination rate and vaccines’ effective protection rate can reduce the spatial transmission capacity of diseases. Moreover, we numerically find that the proportion of recovered individuals who lose their immunity does not affect the spreading ability but changes the prevalence scale.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"392 ","pages":"Article 109569"},"PeriodicalIF":1.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145688842","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}

{"title":"Bifurcation analysis of an SIS epidemic reaction-diffusion model with maturation delay and nonlinear birth","authors":"Qianqian Sun ,&nbsp;Chunjin Wei ,&nbsp;Junjie Wei","doi":"10.1016/j.mbs.2025.109599","DOIUrl":"10.1016/j.mbs.2025.109599","url":null,"abstract":"<div><div>In this paper, we investigate the dynamics of SIS epidemic reaction-diffusion model with maturation delay and nonlinear birth. The stability of disease free equilibrium (DFE) and endemic equilibrium (EE) is determined by analyzing the distribution of the eigenvalues. Based on this investigation, a bifurcation set in the parameter plane is constructed, revealing how the system’s behavior evolves with varying parameters. Furthermore, we obtain some local Hopf bifurcation results and derive formulas for determining the bifurcation direction and the stability of the bifurcated periodic solution. Finally, numerical simulations are conducted to validate the theoretical results and further illustrate the dynamic behavior of the model.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"392 ","pages":"Article 109599"},"PeriodicalIF":1.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145829393","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}

{"title":"Environmental drivers of tuberculosis transmission in Guangdong, China: Integrating generalized additive models and dynamic simulations","authors":"Lingming Kong ,&nbsp;Yanying Mo ,&nbsp;Guanghu Zhu ,&nbsp;Liang Chen ,&nbsp;Zhen Wang","doi":"10.1016/j.mbs.2025.109587","DOIUrl":"10.1016/j.mbs.2025.109587","url":null,"abstract":"<div><div>Tuberculosis (TB) remains a critical global public health challenge, particularly in high-burden regions like Guangdong Province, China. This study develops an integrated framework combining generalized additive models (GAM) and non-autonomous dynamical modeling to elucidate the synergistic effects of environmental and socioeconomic factors on TB transmission dynamics. Utilizing weekly TB case data, air quality index (AQI), absolute humidity (AH), and holiday indicators from Guangdong (2014–2019), GAM quantified nonlinear lagged effects of environmental exposures (AQI, AH) and aperiodic drivers (holidays) on incidence. Results revealed that a 10-unit increase in AQI elevated TB risk by 3.8 % (95 % CI: 1.2–6.5 %), while AH exhibited a negative regulatory effect on transmission. Holiday-related population aggregation amplified case fluctuations by 37 % (<em>p</em> &lt; .01), with post-holiday rebounds up to 68 %. These time-varying parameters were incorporated into a non-autonomous SEIR model with recurrence mechanisms. The basic reproduction number <em>R</em>₀ was estimated at 1.9 (95 % CI: 1.2–2.6). Bifurcation analysis confirmed global stability of the disease-free equilibrium when <em>R</em>₀ &lt; 1 and endemic persistence when <em>R</em>₀ &gt; 1. Sensitivity analysis identified infection rate and relapse probability as dominant drivers of transmission intensity. The model predicted a declining long-term trend (-2.6 % annually) but persistent winter-spring seasonality. This hybrid approach providing a quantitative tool for optimizing intervention strategies. Key recommendations include reducing airborne pollutants, enhancing surveillance, and targeting relapse prevention to mitigate endemic persistence.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"392 ","pages":"Article 109587"},"PeriodicalIF":1.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145673324","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}

{"title":"New results on traveling wave solutions for a Keller-Segel system with nonlinear chemical gradient","authors":"Shangbing Ai ,&nbsp;Jianhe Shen","doi":"10.1016/j.mbs.2025.109586","DOIUrl":"10.1016/j.mbs.2025.109586","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We study a Keller-Segel system with nonlinear chemical gradient and two parameters &lt;em&gt;c&lt;/em&gt; &gt; 0 and ε &gt; 0. The system has a family of equilibria &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msubsup&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;±&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msubsup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msubsup&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msup&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; where &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; are explicitly defined. We investigate the existence of traveling wave solutions &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; of this system that connect a pair of equilibria &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msubsup&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;±&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msubsup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and establish the following result: there exists &lt;span&gt;&lt;math&gt;&lt;msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msubsup&gt;&lt;/math&gt;&lt;/span&gt; with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msubsup&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msubsup&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; such that if &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msubsup&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msup&gt;&lt;mo&gt;≤&lt;/mo&gt;&lt;msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, then &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msubsup&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;ε&lt;/mi&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; exists for all &lt;em&gt;c&lt;/em&gt; &gt; 0 and &lt;em&gt;s&lt;/em&gt; &gt; 0 and sufficiently small ε &gt; 0; if &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msubsup&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msup&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;msubsup&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, then there exists &lt;em&gt;c&lt;/em&gt;* &gt; 0 such that for &lt;em&gt;c&lt;/em&gt; &gt; &lt;em&gt;c&lt;/em&gt;*, such a solution exists for all &lt;em&gt;s&lt;/em&gt; &gt; 0 and sufficiently small ε, while for 0 &lt; &lt;em&gt;c&lt;/em&gt; ≤ &lt;em&gt;c&lt;/em&gt;*, such a solution exists only for &lt;em&gt;s&lt;/em&gt; in a disconnected set of (0, ∞) which includes two connected components &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msubsup&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msubsup&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mover&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;^","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"392 ","pages":"Article 109586"},"PeriodicalIF":1.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145663105","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}

{"title":"Optimal experimental design for parameter estimation in the presence of observation noise","authors":"Jie Qi ,&nbsp;Ruth E. Baker","doi":"10.1016/j.mbs.2025.109571","DOIUrl":"10.1016/j.mbs.2025.109571","url":null,"abstract":"<div><div>Mathematical models play an increasingly important role in interpreting experiments, particularly in biology and ecology. Accurate parameter estimation is vital for quantifying observed behaviours, inferring unmeasurable ones, and making predictions. However, the reliability of parameter estimates depends on the quality, quantity, and timing of collected data—a concept known as parameter identifiability. For many dynamical models, parameter uncertainty can shift dramatically as observation times vary. In this study, we explore local sensitivity measures from the Fisher information matrix and global measures from Sobol’ indices to examine how parameter uncertainty varies as a result of changes in the number and timing of observations. We then embed these measures within an optimisation algorithm to identify observation schedules that minimise uncertainty. Applying this framework to models with both correlated and uncorrelated observation noise reveals that noise correlations can substantially affect optimal observation times. This underscores the importance of correctly accounting for the observation noise structure when designing experiments.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"392 ","pages":"Article 109571"},"PeriodicalIF":1.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145644122","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}

{"title":"How human behavior drives the balance of symptomatic and asymptomatic cases in emerging infections","authors":"Asma Azizi ,&nbsp;Zhuolin Qu ,&nbsp;Caner Kazanci","doi":"10.1016/j.mbs.2025.109601","DOIUrl":"10.1016/j.mbs.2025.109601","url":null,"abstract":"<div><div>Human behavioral changes in response to observing disease in others play a crucial role in the spread of epidemics. These behaviors create selective pressures that influence a virus’s ability to survive. This study explores how human behavioral adaptations influence the co-evolution of symptomatic and asymptomatic pathogen strains during an epidemic. Using a deterministic Susceptible-Infectious-Removed (SIR) model, it examines the role of spontaneous social distancing (SD) in shaping the selection pressures on these strains. The analysis highlights how behavioral changes can drive shifts in the prevalence of symptomatic versus asymptomatic cases, offering insights into the evolutionary dynamics of pathogen variants. Individuals initiate SD after contact with symptomatic cases, either by reducing interactions with everyone or by specifically avoiding symptomatic individuals. The analysis shows that homogeneous contact reduction tends to favor symptomatic strain, while targeted avoidance of symptomatic cases promotes the selection of asymptomatic one. The study underscores the complex, non-linear dynamics of selections under different levels of social distancing. A global sensitivity analysis highlights the significance of behavioral parameters in controlling the overall size of the infection. The findings emphasize the need for public health strategies that account for human behavior to effectively limit the spread and evolution of viral strains.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"392 ","pages":"Article 109601"},"PeriodicalIF":1.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145844636","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}

{"title":"Asymmetric diffusion of prey in predation systems with multiple patches","authors":"Weiting Song ,&nbsp;Shikun Wang ,&nbsp;Yuanshi Wang","doi":"10.1016/j.mbs.2025.109600","DOIUrl":"10.1016/j.mbs.2025.109600","url":null,"abstract":"<div><div>This paper considers predator-prey systems with multiple patches, where individuals of the prey move among patches. Rigorous analysis on the model shows nonnegativeness and boundedness of the solutions. Further study shows conditions by which the system admits an equilibrium that is globally asymptotically stable. For two-patch systems, it is shown that varying the diffusion of prey could make the predator transition between persisting in two patches, survival only in one of the patches, and extinction in both patches in a smooth fashion. For multi-patch systems, it is shown that the diffusion of prey could lead to a win-win situation, where total population abundances of both prey and predator are larger than those without dispersal, which extends previous theory. A novel prediction of this work is that the preference in diffusion could lead to the increase of population abundance, even lead to the maximal abundance. These results are important in ecological conservation and management.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"392 ","pages":"Article 109600"},"PeriodicalIF":1.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145806615","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}

{"title":"Stochastic environments and migrating population dynamics","authors":"Yogesh Trivedi,&nbsp;Anushaya Mohapatra","doi":"10.1016/j.mbs.2025.109589","DOIUrl":"10.1016/j.mbs.2025.109589","url":null,"abstract":"<div><div>Environmental stochasticity is pivotal in shaping population dynamics by introducing random fluctuations in habitat conditions, resource availability, and survival probabilities. These fluctuations often drive critical ecological processes, influencing persistence, extinction, and adaptive strategies. Especially in the context of population migration, environmental stochasticity plays a critical role in shaping movement patterns, survival rates, and population structure. There are various forms of population migration, and among them, partial migration is a widespread phenomenon, where only a portion of the population undertakes seasonal or periodic movements while the rest remain resident in the same area year-round. In this study, we develop discrete time stochastic population models to investigate how environmental fluctuations and disturbances affects partially migrating populations. In one class of models, random fluctuations are incorporated through density-dependent fertility functions, while in another class of models, episodic disturbance events are addressed that reduce migratory populations. By deriving the stochastic growth rate through the dominant Lyapunov exponent, we establish thresholds for population persistence and extinction. Furthermore, we explore the conditions under which partial migration emerges as an evolutionarily stable strategy (ESS) in fluctuating environments and with disturbance events. As an application, we develop our framework to incorporate temperature-dependent fertility functions, analyzing the impact of climate-driven temperature fluctuations on population dynamics. Our findings reveal that environmental stochasticity can either enhance or undermine the persistence of partially migratory populations, depending on the nature of the disturbances and the distribution of environmental variability. Numerical simulations validate these theoretical insights, demonstrating how extreme events, such as climatic shocks, shape migration patterns and population structure. This study advances the understanding of partial migration dynamics, offering a robust framework for predicting population responses to environmental changes in the context of ongoing climate variability.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"392 ","pages":"Article 109589"},"PeriodicalIF":1.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145688892","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}

{"title":"Quantifying the risk of long-term chikungunya persistence in Miami-Dade county","authors":"Antonio Gondim,&nbsp;Leonardo Schultz,&nbsp;Xi Huo,&nbsp;Shigui Ruan","doi":"10.1016/j.mbs.2025.109597","DOIUrl":"10.1016/j.mbs.2025.109597","url":null,"abstract":"<div><div>Chikungunya virus (CHIKV) is a mosquito-borne arbovirus with the potential to establish sustained transmission in subtropical regions like Florida, where climatic and ecological conditions support vector proliferation. In this study, we develop a Continuous-Time Markov Chain (CTMC) model to assess the probability of long-term CHIKV establishment in Miami-Dade County following repeated introductions of external infectious individuals over a finite period of time. This work aims to identify seasonal windows of heightened endemic risk and evaluate the impact of vector control strategies on mitigating the likelihood of persistent transmission. These results generate insights into the dynamics of CHIKV and inform targeted interventions to prevent its transition from minor sporadic outbreaks to endemic circulation.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"392 ","pages":"Article 109597"},"PeriodicalIF":1.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145746381","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}

{"title":"Modeling and analysis of the transmission dynamics in metapopulation networks incorporating individual contact heterogeneity","authors":"Pengle Sun ,&nbsp;Shanshan Feng ,&nbsp;Zhen Jin","doi":"10.1016/j.mbs.2025.109598","DOIUrl":"10.1016/j.mbs.2025.109598","url":null,"abstract":"<div><div>In studies of traditional metapopulation networks, researchers typically assumed that individuals within subpopulations were well-mixed, ignoring individual contact heterogeneity. However, in real life, individual contact exhibits high levels of heterogeneity. To address this, we build an SIS model that couples individual contact heterogeneity on a metapopulation network, which is characterized by constructing dynamic subnetworks within subpopulations. Theoretically, the basic reproduction number is obtained, the existence and uniqueness of equilibria, as well as their global stability, are proved. Through numerical simulations, theoretical results are validated. Additionally, the findings reveal a positive correlation between individual contact heterogeneity and the basic reproduction number, while its effect on the scale of the epidemic exhibits a dual nature, contingent upon infection rate and the degree of subpopulations. Furthermore, when the order of magnitude of the migration rate is below <span><math><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math></span>, the scale of the epidemic expands while showing no dependence on the basic reproduction number; and when the order of magnitude of the migration rate exceeds <span><math><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math></span>, the scale decreases and displays a negative correlation with the basic reproduction number. Based on the research findings, we propose a systematic disease control framework, which can serve as a strategic reference and practical guide for future infectious disease prevention efforts.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"392 ","pages":"Article 109598"},"PeriodicalIF":1.8,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145758946","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}