Mathematical Biosciences最新文献

{"title":"Modeling cholera transmission dynamics with antibiotic resistance and mutation: A case study in Zimbabwe","authors":"Wei Wang ,&nbsp;Yuan Lou ,&nbsp;Xiunan Wang","doi":"10.1016/j.mbs.2025.109545","DOIUrl":"10.1016/j.mbs.2025.109545","url":null,"abstract":"<div><div>Cholera remains a significant cause of morbidity and mortality worldwide. Although antibiotic use can reduce transmission, misuse, overuse, or incomplete treatment can foster the emergence of antibiotic resistance. Selective pressure plays a crucial role in shaping the dynamics of resistance in <span><math><mrow><mi>V</mi><mi>i</mi><mi>b</mi><mi>r</mi><mi>i</mi><mi>o</mi><mspace></mspace><mi>c</mi><mi>h</mi><mi>o</mi><mi>l</mi><mi>e</mi><mi>r</mi><mi>a</mi><mi>e</mi></mrow></math></span>, particularly by increasing the mutation rate that transforms antibiotic-sensitive strains into resistant ones. In this study, we develop a novel mathematical model to investigate the impact of antibiotic resistance on cholera transmission dynamics. We establish the existence and stability of equilibria and fit the model to cholera outbreak data from Zimbabwe. Our results reveal a critical interplay between mutation rates and strain fitness: when resistant strains have low reproductive fitness, increased mutation rates alone fail to establish their dominance; however, when resistance carries a fitness advantage, higher mutation rates trigger a regime shift to resistant strain dominance—a newly identified phenomenon with implications for resistance management. We further demonstrate that incomplete treatment (lower recovery rates) exacerbates resistance by prolonging antibiotic exposure. Crucially, our findings underscore that judicious antibiotic use can simultaneously curb resistance emergence and outbreak spread in Zimbabwe, offering actionable insights for public health strategies.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"390 ","pages":"Article 109545"},"PeriodicalIF":1.8,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223626","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":"Model formulation and oscillatory patterns in immune-pathogen dynamics during Brucellosis infection","authors":"Zehui Li ,&nbsp;Junpeng Liu ,&nbsp;Linhua Zhou ,&nbsp;Chunhua Shan ,&nbsp;Meng Fan","doi":"10.1016/j.mbs.2025.109543","DOIUrl":"10.1016/j.mbs.2025.109543","url":null,"abstract":"<div><div>Brucellosis, a global zoonosis imposing major health and economic burdens, is clinically marked by recurrent undulant fever linked to Brucella’s persistence within macrophages. To decipher the immune-pathogen dynamics underlying this fever periodicity, this study develops a novel mathematical model that integrates macrophage self-renewal, logistic growth constrained by cellular carrying capacity, and intracellular Brucella replication. Stability and bifurcation analyses reveal two crucial thresholds: one for infection persistence, requiring <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span>, and another for the emergence of undulant fever, triggered by a supercritical Hopf bifurcation. This bifurcation occurs when the macrophage self-renewal rate (<span><math><mi>r</mi></math></span>) surpasses its mortality rate (<span><math><mi>d</mi></math></span>) and the infection rate (<span><math><mi>θ</mi></math></span>) lies in a critical range, marking a transition from stable equilibrium to stable limit cycles. These periodic oscillations, stemming from a dynamic imbalance between immune regeneration and bacterial proliferation, provide a direct mechanistic explanation for recurrent febrile episodes. Counterintuitively, excessive macrophage renewal or carrying capacity can destabilize the system, exacerbating febrile cycles. Our findings posit that interventions simultaneously preventing immune resource exhaustion and curbing intracellular bacterial survival could suppress these pathological oscillations, thereby proposing novel perspectives for managing chronic brucellosis.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"390 ","pages":"Article 109543"},"PeriodicalIF":1.8,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145214835","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":"Spatio-temporal modeling and analysis of two HIV strain infections via demographic–geographic data","authors":"Peng Wu ,&nbsp;Tong Chen ,&nbsp;Shigui Ruan","doi":"10.1016/j.mbs.2025.109539","DOIUrl":"10.1016/j.mbs.2025.109539","url":null,"abstract":"<div><div>The emergence of drug resistance poses a significant challenge to the clinical treatment of HIV/AIDS, making the spread of drug-resistant strains among the infected population a key focus in the monitoring and control of HIV/AIDS. In this paper, we construct a reaction–diffusion model with two HIV strains (drug-sensitive and drug-resistant) to study the spatio-temporal dynamics of HIV/AIDS transmission. With spatial heterogeneity, we derive the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and show that it is a threshold for the outbreak of the disease; that is, when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&lt;</mo><mn>1</mn></mrow></math></span> the disease will eventually die out, while when <span><math><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>1</mn></mrow></math></span> the disease is uniformly persistent. In particular, when the model parameters are independent of the space variable, global stability of the infection equilibrium is proven by constructing an appropriate Lyapunov functional. In the numerical simulation part, we discuss the traveling wave phenomenon of HIV/AIDS infection in the population under different diffusion forms and different initial value distributions. We combine the population statistical data, geographical data, and data of different strain infection cases in Zhejiang Province, China, and simulate the spatial spread of HIV/AIDS in Zhejiang Province through the finite element method with the aid of COMSOL Multiphysics software. This provides a new perspective to analyze the impact of dispersal on the spatio-temporal transmission of HIV/AIDS. Numerical simulations show that: (i) High adherence to treatment can effectively reduce the proportion of acquired drug-resistant cases among the total number of cases; (ii) The form of population diffusion has a huge impact on the spatio-temporal transmission of HIV/AIDS, which means that population movement will be one of the important contents of HIV/AIDS prevention and monitoring; (iii) Ignoring the differences in population movement will misjudge the overall trend of HIV/AIDS in the region, so the differences in spatial diffusion in HIV/AIDS prevention and control cannot be ignored.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109539"},"PeriodicalIF":1.8,"publicationDate":"2025-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145208794","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 mathematical model for cancer dynamics with treatment and saboteur bacteria","authors":"Anna Geretovszky ,&nbsp;Gergely Röst","doi":"10.1016/j.mbs.2025.109541","DOIUrl":"10.1016/j.mbs.2025.109541","url":null,"abstract":"<div><div>We construct a mathematical model of cancer dynamics with chemotherapeutic treatment, in the presence of bacteria that are capable of metabolizing the chemotherapeutic drug, hence sabotaging the treatment. We investigate the possibility of complementing the cancer treatment with antibiotic drugs, thus eradicating the bacteria or at least mitigating their negative impact on the prospects of therapy. Our model is a nonlinear system of four differential equations, for which we perform a complete analysis, explicitly characterizing the four possible outcomes, depending on whether the cancer cells or the bacteria become extinct or persist. Global stability results are proven by the iterative application of a comparison principle, and a bifurcation diagram is created to show the transitions between scenarios with respect to the controllable parameters. We apply our model to an experiment on mice with colon cancer and the drug Gemcitabine.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109541"},"PeriodicalIF":1.8,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159542","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 mathematical study of anti-VEGF and cytotoxic therapies of cancer with optimal control","authors":"Shikun Li ,&nbsp;Xiaoming Zheng ,&nbsp;Ling Xue ,&nbsp;Kun Zhao","doi":"10.1016/j.mbs.2025.109542","DOIUrl":"10.1016/j.mbs.2025.109542","url":null,"abstract":"<div><div>This work studies two cancer treatments, anti-angiogenic therapy and chemotherapy, with a novel mathematical model and the associated optimal control problem. The model includes tumor cells, endothelial cells, immune cells, and Vascular Endothelial Growth Factor (VEGF), where the anti-angiogenic therapy only targets VEGF and the chemotherapy kills all cells indiscriminately. The optimal control problem minimizes the tumor burden and drug toxicity over a set of time-variant drug doses. The mathematical analysis shows the existence of the positive invariant set of the model over all the therapeutic strategies, the stability of multiple steady state solutions, as well as the existence and uniqueness of the optimal control solutions. The analysis and simulations lead to several significant findings. First, all the steady states with the vanished tumor are unstable under the anti-VEGF therapy, which confirms its limited efficacy as observed in clinics. Second, the Hopf bifurcation appears in each treatment approach with a common feature: the system exhibits periodic oscillations at low drug doses and transitions to a stable coexistence state at higher drug doses. Third, the optimal treatment strategy involves a delicate combination of both treatment types. This strategy is particularly effective when the anti-VEGF drug has a high binding affinity to VEGF molecules, and the chemotherapy drug has a small killing rate of immune cells and large killing rates of endothelial cells and tumor cells.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109542"},"PeriodicalIF":1.8,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145182294","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":"Nucleation feedback can drive establishment and maintenance of biased microtubule polarity in neurites","authors":"Hannah G. Scanlon ,&nbsp;Gibarni Mahata ,&nbsp;Anna C. Nelson ,&nbsp;Scott A. McKinley ,&nbsp;Melissa M. Rolls ,&nbsp;Maria-Veronica Ciocanel","doi":"10.1016/j.mbs.2025.109538","DOIUrl":"10.1016/j.mbs.2025.109538","url":null,"abstract":"<div><div>The microtubule cytoskeleton is comprised of dynamic, polarized filaments that facilitate transport within the cell. Polarized microtubule arrays are key to facilitating cargo transport in long cells such as neurons. Microtubules also undergo dynamic instability, where the plus and minus ends of the filaments switch between growth and shrinking phases, leading to frequent microtubule turnover. Although microtubules often completely disassemble and new filaments nucleate, microtubule arrays have been observed to both maintain their biased orientation throughout the cell lifetime and to rearrange their polarity as an adaptive response to injury. Motivated by cytoskeleton organization in neurites, we propose a spatially-explicit stochastic model of microtubule arrays and investigate how nucleation of new filaments could generate biased polarity in a simple linear domain. Using a continuous-time Markov chain model of microtubule growth dynamics, we model and parameterize two experimentally-validated nucleation mechanisms: nucleation feedback, where the direction of filament growth depends on existing microtubule content, and a checkpoint mechanism, where microtubules that nucleate in a direction opposite to the majority experience frequent catastrophe. When incorporating these validated mechanisms into the spatial model, we find that nucleation feedback is sufficient to establish biased polarity in neurites of different lengths, and that the emergence and maintenance of biased polarity is relatively stable in spite of stochastic fluctuations. This work provides a framework to study the relationship between microtubule nucleation and polarity, and could extend to give insights into mechanisms that drive the formation of polarized filament arrays in other biological settings.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109538"},"PeriodicalIF":1.8,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145139810","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 dynamic model for Waddington’s landscape accounting for cell-to-cell communication","authors":"Simon Merkt ,&nbsp;Lara Fuhrmann ,&nbsp;Erika Dudkin ,&nbsp;Andreas Schlitzer ,&nbsp;Barbara Niethammer ,&nbsp;Jan Hasenauer","doi":"10.1016/j.mbs.2025.109537","DOIUrl":"10.1016/j.mbs.2025.109537","url":null,"abstract":"<div><div>Waddington’s landscape provides a conceptual model for developmental processes. It is the basis of various mathematical models describing cell maturation and development at cell and population levels. Yet, these mathematical models mostly disregard cell-to-cell communication, an essential process that modulates cellular decision-making and population dynamics.</div><div>In this study, we provide a dynamical model for cell maturation and development which can be seen as an extension of Waddington’s landscape. The coupled system of partial and ordinary differential equations describes cell density along the cell state together with ligand concentrations. Cell-state-dependent ligand production determines ligand availability, which controls population-level processes. We provide proof of the existence and uniqueness of solutions for our coupled differential equation system and demonstrate the model’s validity by analyzing single-cell transcriptomics data. Our results show that cell-to-cell communication is essential for accurately depicting biological recovery processes, such as the regeneration of stem cells in the intestine’s crypt and the response of immune cells upon LSP stimulation.</div><div>Our findings underscore the importance of incorporating cell-to-cell communication into mathematical models of biological development. By doing so, we unlock the potential for deeper insights into complex processes such as tissue regeneration and immune responses, offering new avenues for understanding and predicting the dynamics of biological recovery and cell activation.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"390 ","pages":"Article 109537"},"PeriodicalIF":1.8,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145115771","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":"Turing patterns in a morphogenetic model with single regulatory function","authors":"Mohamed Amine Ouchdiri ,&nbsp;Saad Benjelloun ,&nbsp;Adnane Saoud ,&nbsp;Irene Otero-Muras","doi":"10.1016/j.mbs.2025.109536","DOIUrl":"10.1016/j.mbs.2025.109536","url":null,"abstract":"<div><div>Confirming Turing’s theory of morphogens in developmental processes is challenging, and synthetic biology has opened new avenues for testing Turing’s predictions. Synthetic mammalian pattern formation has been recently achieved through a reaction–diffusion system based on the short-range activator (Nodal) and the long-range inhibitor (Lefty) topology, where a single function regulates both morphogens. In this paper, we investigate the emergence of Turing patterns in the synthetic Nodal-Lefty system. First, we prove the existence of a global solution and derive conditions for Turing instability through linear stability analysis. Subsequently, we examine the behavior of the system near the bifurcation threshold, employing weakly nonlinear analysis, and using multiple time scales, we derive the amplitude equations for supercritical and subcritical cases. The results demonstrate the ability of the system to support various patterns, with the subcritical Turing instability playing a crucial role in the formation of dissipative structures observed experimentally.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109536"},"PeriodicalIF":1.8,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093328","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 bistable dynamics arising from macrophage–tumor interactions in the tumor microenvironment","authors":"Hwayeon Ryu ,&nbsp;Susanna Röblitz ,&nbsp;Kamila Larripa ,&nbsp;Anna-Simone Frank","doi":"10.1016/j.mbs.2025.109534","DOIUrl":"10.1016/j.mbs.2025.109534","url":null,"abstract":"<div><div>Macrophages in the tumor microenvironment (TME), known as tumor-associated macrophages (TAMs), originate primarily from circulating monocytes that differentiate under the influence of tumor-derived signals. Within the TME, naïve macrophages can adopt either a pro-inflammatory, anti-tumor (M1-like) or anti-inflammatory, pro-tumor (M2-like) phenotype. These phenotypic shifts significantly affect tumor progression, making TAMs attractive targets for therapeutic intervention aimed at blocking recruitment, promoting anti-tumor polarization, or disrupting tumor–macrophage interactions. In this study, we develop a mathematical model capturing the temporal dynamics of tumor volume alongside populations of naïve, M1-like, M2-like, and mixed (M1/M2) phenotype TAMs. The model incorporates the bidirectional influence between tumor development and macrophage polarization. Through numerical simulations with different parameter sets, our tumor–macrophage population model exhibits the emergence of bistability, demonstrating the system becomes more controllable, responsive to perturbations, and sensitive to immunotherapy. We conduct the bifurcation as well as global sensitivity analyses to identify regions of bistability for tumor dynamics in the parameter space and the impact of sensitive parameters on TME. These results are then linked to treatment strategies that may effectively induce transitions from high to low tumor burden.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109534"},"PeriodicalIF":1.8,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145088768","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":"CAR T-cell and oncolytic virus dynamics and determinants of combination therapy success for glioblastoma","authors":"Martina Conte ,&nbsp;Agata Xella ,&nbsp;Ryan T. Woodall ,&nbsp;Kevin A. Cassady ,&nbsp;Sergio Branciamore ,&nbsp;Christine E. Brown ,&nbsp;Russell C. Rockne","doi":"10.1016/j.mbs.2025.109531","DOIUrl":"10.1016/j.mbs.2025.109531","url":null,"abstract":"<div><div>Glioblastoma is a highly aggressive and treatment-resistant primary brain cancer. While chimeric antigen receptor (CAR) T-cell therapy has demonstrated promising results in targeting these tumors, it has not yet been curative. An innovative approach to improve CAR T-cell efficacy is to combine them with other immune modulating therapies. In this study, we investigate <em>in vitro</em> combination of IL-13R<span><math><mi>α</mi></math></span>2 targeted CAR T-cells with an oncolytic virus (OV) and study the complex interplay between tumor cells, CAR T-cells, and OV dynamics with a novel mathematical model. We fit the model to data collected from experiments with each therapy individually and in combination to reveal determinants of therapy synergy and improved efficacy. Our analysis reveals that the virus bursting size is a critical parameter in determining the net tumor infection rate and overall combination treatment efficacy. Moreover, the model predicts that administering the oncolytic virus simultaneously with, or prior to, CAR T-cells could maximize therapeutic efficacy.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"389 ","pages":"Article 109531"},"PeriodicalIF":1.8,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145082921","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}