Mathematical Biosciences最新文献

{"title":"Dynamics and bifurcation of a hybrid competition model with applications to adaptive cancer therapy","authors":"Huansheng Sun ,&nbsp;Biao Tang ,&nbsp;Jonathan E. Forde ,&nbsp;Yanni Xiao","doi":"10.1016/j.mbs.2026.109636","DOIUrl":"10.1016/j.mbs.2026.109636","url":null,"abstract":"<div><div>Adaptive therapy is a novel cancer treatment strategy that proposes to tackle cancer drug resistance by leveraging resource competition between drug-sensitive and resistant cells. Because the underlying mathematical mechanisms of adaptive therapy remain unclear, determining the most effective rates of intervention is a significant challenge. In this paper, we propose a competition model incorporating fixed-time periodic tumor measurements with impulsive interventions performed if the number of tumor cells exceeds a threshold value. For the proposed model, we find a novel type of periodic solutions. Specifically, we demonstrate the existence of various (ℓ, <em>m</em>)<em>T</em> boundary periodic solutions and rigorously analyze their stability. Using bifurcation theory, we further prove the existence and stability of positive periodic solutions. Further, we perform numerical simulations to study these bifurcations with respect to key parameters such as the threshold value (<em>TV</em>) and the monitoring period (<em>T</em>). Numerical studies find that time to treatment failure exhibits a nonlinear dependence on the killing rate of drug-sensitive cells, i.e., it initially increases, reaches a plateau, and subsequently declines as the killing rate increases, revealing that maximizing the killing rate does not yield optimal therapeutic outcomes. The finding indicates that incorporating a threshold can extend patient’s survival time, implying the therapeutic benefit of threshold-based adaptive therapy for tumor control.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"394 ","pages":"Article 109636"},"PeriodicalIF":1.8,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146088587","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":"Propagation through a barrier: Numerical analysis of a reaction-diffusion model with free boundary","authors":"Narges Shabgard,&nbsp;Timothy M. Schaerf,&nbsp;Yihong Du","doi":"10.1016/j.mbs.2026.109624","DOIUrl":"10.1016/j.mbs.2026.109624","url":null,"abstract":"&lt;div&gt;&lt;div&gt;We try to better understand how a spatial barrier may affect the spreading of an invading species via numerical analysis of some variations of a free boundary model in [1, 2] (where only homogeneous environment was considered). Here we incorporate a spatial barrier by replacing a bistable growth term &lt;em&gt;f&lt;/em&gt;(&lt;em&gt;u&lt;/em&gt;) in the model with &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;em&gt;θ&lt;/em&gt; ∈ (0, 1/2) and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; except in the barrier region &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;l&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, in which &lt;em&gt;r&lt;/em&gt;(&lt;em&gt;x&lt;/em&gt;) becomes negative away from its boundary, representing the biological assumption that the environment becomes hostile to the species inside the barrier. A parameter &lt;em&gt;α&lt;/em&gt; &gt; 0 in the expression of &lt;em&gt;r&lt;/em&gt;(&lt;em&gt;x&lt;/em&gt;) is used to characterize the severity of the environmental hostility. We find that when all the other parameters are fixed there exists a critical value &lt;em&gt;l&lt;/em&gt;* of the barrier length &lt;em&gt;l&lt;/em&gt; such that successful spreading is continued past the barrier region when &lt;em&gt;l&lt;/em&gt; &lt; &lt;em&gt;l&lt;/em&gt;*, and the propagation is blocked when &lt;em&gt;l&lt;/em&gt; &gt; &lt;em&gt;l&lt;/em&gt;*. Similarly we show numerically that when all the other parameters are fixed, there is a critical value &lt;em&gt;α&lt;/em&gt;* of the barrier severity &lt;em&gt;α&lt;/em&gt; such that propagation can be continued when &lt;em&gt;α&lt;/em&gt; &lt; &lt;em&gt;α&lt;/em&gt;*, but it is blocked when &lt;em&gt;α&lt;/em&gt; &gt; &lt;em&gt;α&lt;/em&gt;*. The dependence of &lt;em&gt;l&lt;/em&gt;* (respectively &lt;em&gt;α&lt;/em&gt;*) on the other parameters are also analysed.&lt;/div&gt;&lt;div&gt;To include temporal fluctuations of the environment, we further replace &lt;em&gt;r&lt;/em&gt;(&lt;em&gt;x&lt;/em&gt;) by &lt;em&gt;a&lt;/em&gt;(&lt;em&gt;t&lt;/em&gt;)&lt;em&gt;r&lt;/em&gt;(&lt;em&gt;x&lt;/em&gt;) with &lt;em&gt;a&lt;/em&gt;(&lt;em&gt;t&lt;/em&gt;) a positive time-periodic function of average 1, to represent the periodic modulation of the environment. Our numerical simulations suggest that increasing the magnitude of temporal variation enhances the ability of species invasion, while increasing the frequency of such variation reduces this ability.&lt;/div&gt;&lt;div&gt;To see how Allee effect may influence the invasion with a barrier, our results based on a bistable &lt;em&gt;f&lt;/em&gt; discussed above are compared with that for a model obtained from a standard monostable function (no Allee effect), namely &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;f&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; with the same &lt;em&gt;r&lt;/em&gt;(&lt;em&gt;x&lt;/em&gt;). A parallel numerical analysis shows that qualitatively everything is the same in the monostable case, including the numerical results incorporating seasonal changes (w","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"394 ","pages":"Article 109624"},"PeriodicalIF":1.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146044540","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":"Adaptive foraging under stoichiometric constraints can reshape competitive outcomes","authors":"Oluwagbemisola Oladepo ,&nbsp;Angela Peace","doi":"10.1016/j.mbs.2026.109625","DOIUrl":"10.1016/j.mbs.2026.109625","url":null,"abstract":"<div><div>Competition for resources is a central concept in ecology that is traditionally constrained by the Competitive Exclusion Principle, which states that n consumers cannot stably coexist on fewer than n resources. However, studies have shown that incorporating ecological stoichiometry (linking organisms’ growth and survival to nutrient ratios of elements like carbon, nitrogen, and phosphorus) into competition models with two consumers feeding on a single resource reveals that nutrient composition, not just quantity, can determine competitive outcomes, potentially allowing stable coexistence regions. Building on these foundations, this study extends stoichiometric competition models to include <em>adaptive foraging</em>, where consumer feeding effort dynamically responds to resource quality. Two frameworks were analyzed: a base model with fixed feeding effort for both consumers and an adaptive model where the initially disadvantaged competitor’s feeding effort evolves over time. Analytical and numerical results demonstrate that adaptive foraging can expand conditions for persistence, enable coexistence, and even reverse dominance hierarchies by allowing inferior consumers to compensate for nutrient or efficiency disadvantages. However, these benefits decline under extreme enrichment, where prey nutrient quality deteriorates beyond compensation limits. Additionally, the speed of adaptation influences competitive outcome, as the initially disadvantaged consumer must adapt fast enough to see the benefit of adaptation. Overall, the study shows that adaptive foraging under stoichiometric constraints fundamentally reshapes ecological competition, highlighting the interplay between nutrient dynamics, behavioral plasticity, and adaptation in maintaining biodiversity.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"394 ","pages":"Article 109625"},"PeriodicalIF":1.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146044539","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":"Impulsive stem cell transplantation to modulate psoriasis: Insights of complex cytokine network","authors":"Subhankar Kushary ,&nbsp;Tushar Ghosh ,&nbsp;Priti Kumar Roy","doi":"10.1016/j.mbs.2026.109623","DOIUrl":"10.1016/j.mbs.2026.109623","url":null,"abstract":"<div><div>Psoriasis is caused by abnormal interactions between immune cells, cytokines, and keratinocytes. In this study, we develop a dynamical model that includes epidermal stem-cell differentiation, activated T cells, activated dendritic cells, keratinocytes, and a selected cytokine network (TNF, TGF-<em>β</em>, IL-23, IL-17, IL-10). The model considers two-way interactions between cytokines and cells, and the quasi-steady-state approximation is applied to reduce complexity. We determine the invariant region that ensures bounded solutions and analyze the local stability of the interior equilibrium. Sensitivity analysis shows key parameters that strongly influence keratinocyte growth. Hopf bifurcation analysis with respect to TNF-driven keratinocyte up-regulation (<em>ζ</em>₃) and IL-10 production by stem cells (<em>p</em>₇) reveals that higher <em>ζ</em>₃ or lower <em>p</em>₇ induce oscillatory, flare-like dynamics, while stronger IL-10 feedback stabilizes the system. Numerical simulations test therapeutic strategies, including TNF inhibition and stem cell infusion, modeled with impulsive control. The mathematical results show conditions under which impulsive periodic orbits become stable. Simulations indicate that TNF inhibition gives only temporary benefit, whereas stem cell infusion provides sustained control of immune activation and keratinocyte overgrowth. Overall, the study highlights the importance of cytokine balance and supports stem cell therapy as a promising approach for restoring immune-epidermal homeostasis in psoriasis.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"394 ","pages":"Article 109623"},"PeriodicalIF":1.8,"publicationDate":"2026-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146014060","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":"A discrete nonlinear model for HPV immune suppression and evasion","authors":"Francisco J. Solis ,&nbsp;Luz M. Gonzalez","doi":"10.1016/j.mbs.2026.109622","DOIUrl":"10.1016/j.mbs.2026.109622","url":null,"abstract":"<div><div>In this paper we present a nonlinear discrete model in order to describe defective interactions of immune system cells with Human Papillomavirus (HPV) infected cells. Statistics show than only a percentage of the HPV infected population will develop malignancy diseases. Our goal is to develop a prototypical mathematical model that is analitically tratable with a statistical complexity to reproduce qualitative and quantitative information of the consequences of HPV-evasion of host defenses and suppression of an efficient immune response. Numerical results obtained from the model confirm the intrinsic relationships of its nonlinear terms representing the earlier evolution of mature infected cells with a successful virus invasion.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"393 ","pages":"Article 109622"},"PeriodicalIF":1.8,"publicationDate":"2026-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145968287","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":"Identification of significant SNPs and the quantification of correlation using genomic informational field theory (GIFT)","authors":"Scott Gadsby ,&nbsp;Cyril Rauch ,&nbsp;Jonathan A D Wattis","doi":"10.1016/j.mbs.2025.109606","DOIUrl":"10.1016/j.mbs.2025.109606","url":null,"abstract":"<div><div>Given data on genotypes and phenotypes from a sample population, we show how ordering the data by phenotype and analysing the information contained in the corresponding list of genotypes can identify those SNPs which have a significant correlation with phenotype. We derive formulae for <em>p</em>-values to quantify the significance of each SNP, and show how to analyse the correlations <em>between</em> different SNPs. As well as using classical covariance and correlations, we introduce an information-theoretic measure of correlation which is based on Shannon’s informational entropy. This variational formulation also gives rise to other ways of determining the strength of a SNP’s influence on phenotype in a biallelic population using ‘field’ functions which account for the relationship between phenotype and genotype. By computing this field for each SNP, we are able to quantify the correlations between SNPs. The results are shown to depend on the number of each genostate (aa, Aa and AA) in the population in a predictable manner. The methods are illustrated using data on horse height.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"393 ","pages":"Article 109606"},"PeriodicalIF":1.8,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145961005","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 vaccine failures and behavioral change: Effects on disease transmission dynamics and thresholds","authors":"Irasema Pedroza-Meza ,&nbsp;M. Adrian Acuña-Zegarra ,&nbsp;Jorge X. Velasco-Hernández","doi":"10.1016/j.mbs.2026.109619","DOIUrl":"10.1016/j.mbs.2026.109619","url":null,"abstract":"<div><div>Vaccination is a cornerstone of infectious disease control, yet vaccines are not fully protective, leaving a fraction of the vaccinated population susceptible to infection. This partial protection can alter behavior, as individuals who perceive themselves as immune may reduce adherence to preventive measures. Motivated by this, we investigate how behavioral changes among non-immune vaccinated individuals influence the dynamics of a directly transmitted disease and the basic reproduction number. We propose a model that incorporates vaccine failure through three facets (take, degree, and duration) alongside a behavioral parameter that modifies contact rates according to compliance with mitigation measures.</div><div>Our analysis highlights the critical role of the behavioral index in key phenomena, including backward bifurcation and overall disease dynamics. We identify two thresholds. The first specifies the values of the behavioral index for which backward bifurcation does not arise, thereby indicating the conditions under which the disease may persist. The second establishes a relationship between the behavioral index and vaccine efficacy, which allows us to compare the transmission dynamics of our model with those of the classical vaccination model.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"393 ","pages":"Article 109619"},"PeriodicalIF":1.8,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145947158","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":"Dynamics of a tick-borne disease transmission model with acquired tick resistance","authors":"Junfang Cheng,&nbsp;Xue Zhang","doi":"10.1016/j.mbs.2026.109618","DOIUrl":"10.1016/j.mbs.2026.109618","url":null,"abstract":"<div><div>Tick-borne diseases pose a potential threat to public health, and mathematical models have been developed and used to analyze the spread mechanisms of tick-borne diseases. An important host behavior, acquired tick resistance (ATR), to defend against tick infestation, has not yet been modeled and qualitatively analyzed. This paper proposes a model of tick-borne disease transmission incorporating ATR, where hosts are categorized into subgroups based on their infection status and tick bite counts. For the tick-host population model, we derive four distribution patterns of the host subpopulations and analyze the global asymptotic stability of the positive equilibrium. For the disease transmission model, we calculate the basic reproduction number and prove the global asymptotic stability of both the disease-free equilibrium and the endemic equilibrium. Numerical simulations illustrate that the emergence of ATR effectively reduces the number of infected hosts, while an increase in the co-feeding transmission probability leads to a rise in the number of infected ticks.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"393 ","pages":"Article 109618"},"PeriodicalIF":1.8,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145947179","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":"Predator-prey dynamics with personality-dependent foraging and maturation delay: stability switches, Hopf and Bogdanov-Takens bifurcations","authors":"Heping Jiang ,&nbsp;Shan Gao ,&nbsp;Hao Wang","doi":"10.1016/j.mbs.2025.109609","DOIUrl":"10.1016/j.mbs.2025.109609","url":null,"abstract":"<div><div>Individual differences in predator boldness can alter encounter and attack rates, while maturation introduces biologically realistic time lags. We couple these two mechanisms in a Rosenzweig-MacArthur framework by modeling a nonlinear, personality-dependent attack rate and deriving a stage-structured maturation delay for predators, yielding a delay differential equation system. For the delay-free model, we establish positivity and boundedness, characterize boundary and interior equilibria, and provide a complete local bifurcation picture: transcritical and saddle-node bifurcations together with Hopf bifurcations that generate stable cycles; at codimension two, we prove the occurrence of cusp/Bogdanov-Takens points with accompanying homoclinic loops. Introducing maturation delay produces delay-induced complexity: multiple stability switches, sequences of Hopf bifurcations on distinct frequency branches, and global Hopf continua that connect critical delays. Analytical predictions are corroborated numerically via continuation (DDE-BIFTOOL), revealing periodic and quasi-periodic oscillations as well as bistability between coexistence and boundary states. Our results identify personality heterogeneity and developmental timing as interacting drivers of oscillatory and multistable dynamics, and provide parameter thresholds, expressed in biologically interpretable combinations, for when coexistence equilibria lose or regain stability. These findings refine theory for delayed predator-prey interactions and suggest targets (e.g., handling/harvest and juvenile survival) for stabilizing management in systems with behavioral variation.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"393 ","pages":"Article 109609"},"PeriodicalIF":1.8,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145927974","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":"Stability analysis of a time-delayed SIQR epidemic model with nonlinear transmission and control parameters","authors":"Kaijiao Huang ,&nbsp;Lifei Wang ,&nbsp;Faisal Mehmood","doi":"10.1016/j.mbs.2025.109608","DOIUrl":"10.1016/j.mbs.2025.109608","url":null,"abstract":"<div><div>We introduce an SIQR epidemic model that integrates nonlinear transmission and two discrete time delays corresponding to incubation and treatment durations. The model seeks to encapsulate essential dynamical characteristics of epidemic advancement while being suitable for thorough stability examination. The local asymptotic stability of the disease-free and endemic equilibria is examined by Lyapunov-Krasovskii functionals and delay-dependent linear matrix inequalities (LMIs), which mitigate conservatism in the established stability constraints compared to time-invariant criteria. In the absence of delays, we obtain the classical Routh-Hurwitz criteria for local stability, and for positive delays, we formulate characteristic equations whose roots are examined to identify Hopf bifurcations. Transversality requirements are checked to ensure the presence of Hopf bifurcations and to determine key delay thresholds beyond which persistent oscillations form. We propose a delay-dependent feedback control rule that adaptively modifies transmission and quarantine rates; necessary conditions for stability under this control are provided in LMI form and converted into explicit, interpretable constraints on permissible delays and minimum control intensity. The model is augmented to incorporate basic demographic turnover and multi-stage infection delays to provide subgroup-specific treatment representations. Numerical simulations and bifurcation diagrams demonstrate and validate the theoretical findings, indicating how augmented delays or intensified nonlinear transmission can alter stability thresholds and provoke recurring outbreaks. Our findings quantify (i) essential delay durations that undermine stability and (ii) the control effort necessary to reestablish equilibrium, results that can be articulated as definitive decision thresholds for conversion into policy-relevant outputs.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"393 ","pages":"Article 109608"},"PeriodicalIF":1.8,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145902060","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}