Pub Date : 2025-06-07DOI: 10.1016/j.mbs.2025.109481
Saoussen Latrach , Eric Ogier-Denis , Nicolas Vauchelet , Hatem Zaag
Ulcerative colitis (UC) is a chronic inflammatory bowel disease (IBD) with mechanisms that are still partially unclear. Unlike other types of IBD, inflammation in UC is limited to the inner lining of the large intestine and rectum, spreading continuously without breaks between affected areas, creating a uniform pattern of inflammation along the colon. In this paper, we develop a mathematical model based on a reaction–diffusion system to describe the inflammation caused by the interaction between a pathogen and immune cells in the context of UC. Our contributions are both theoretical and numerical. We demonstrate the existence of traveling wave solutions, showing how the disease progresses in a homogeneous environment. We then identify the conditions under which the spread of inflammatory waves can be stopped in a heterogeneous environment. Numerical simulations are used to highlight and validate these theoretical results.
{"title":"Mathematical study of the spread and blocking in inflammatory bowel disease","authors":"Saoussen Latrach , Eric Ogier-Denis , Nicolas Vauchelet , Hatem Zaag","doi":"10.1016/j.mbs.2025.109481","DOIUrl":"10.1016/j.mbs.2025.109481","url":null,"abstract":"<div><div>Ulcerative colitis (UC) is a chronic inflammatory bowel disease (IBD) with mechanisms that are still partially unclear. Unlike other types of IBD, inflammation in UC is limited to the inner lining of the large intestine and rectum, spreading continuously without breaks between affected areas, creating a uniform pattern of inflammation along the colon. In this paper, we develop a mathematical model based on a reaction–diffusion system to describe the inflammation caused by the interaction between a pathogen and immune cells in the context of UC. Our contributions are both theoretical and numerical. We demonstrate the existence of traveling wave solutions, showing how the disease progresses in a homogeneous environment. We then identify the conditions under which the spread of inflammatory waves can be stopped in a heterogeneous environment. Numerical simulations are used to highlight and validate these theoretical results.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"387 ","pages":"Article 109481"},"PeriodicalIF":1.9,"publicationDate":"2025-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144259770","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}
Gene silencing via small interfering RNA (siRNA) represents a transformative tool in cancer therapy, offering specificity and reduced off-target effects compared to conventional treatments. A crucial step in siRNA-based therapies is endosomal escape, the release of siRNA from endosomes into the cytoplasm. Quantifying endosomal escape is challenging due to the dynamic nature of the process and limitations in imaging and analytical techniques. Traditional methods often rely on fluorescence intensity measurements or manual image processing, which are time-intensive and fail to capture continuous dynamics. This paper presents a novel computational framework that integrates automated image processing to analyze time-lapse fluorescent microscopy data of endosomal escape, hierarchical Bayesian inference, and stochastic simulations. Our method employs image segmentation techniques such as binary masks, Gaussian filters, and multichannel color quantification to extract precise spatial and temporal data from microscopy images. Using a hierarchical Bayesian approach, we estimate the parameters of a compartmental model that describes endosomal escape dynamics, accounting for variability over time. These parameters inform a Gillespie stochastic simulation algorithm, ensuring realistic simulations of siRNA release events over time. By combining these techniques, our framework provides a scalable and reproducible method for quantifying endosomal escape. The model captures uncertainty and variability in parameter estimation, and endosomal escape dynamics. Additionally, synthetic data generation allows researchers to validate experimental findings and explore alternative conditions without extensive laboratory work. This integrated approach not only improves the accuracy of endosomal escape quantification but also provides predictive insights for optimizing siRNA delivery systems and advancing gene therapy research.
{"title":"Stochastic model of siRNA endosomal escape mediated by fusogenic peptides","authors":"Nisha Yadav , Jessica Boulos , Angela Alexander-Bryant , Keisha Cook","doi":"10.1016/j.mbs.2025.109476","DOIUrl":"10.1016/j.mbs.2025.109476","url":null,"abstract":"<div><div>Gene silencing via small interfering RNA (siRNA) represents a transformative tool in cancer therapy, offering specificity and reduced off-target effects compared to conventional treatments. A crucial step in siRNA-based therapies is endosomal escape, the release of siRNA from endosomes into the cytoplasm. Quantifying endosomal escape is challenging due to the dynamic nature of the process and limitations in imaging and analytical techniques. Traditional methods often rely on fluorescence intensity measurements or manual image processing, which are time-intensive and fail to capture continuous dynamics. This paper presents a novel computational framework that integrates automated image processing to analyze time-lapse fluorescent microscopy data of endosomal escape, hierarchical Bayesian inference, and stochastic simulations. Our method employs image segmentation techniques such as binary masks, Gaussian filters, and multichannel color quantification to extract precise spatial and temporal data from microscopy images. Using a hierarchical Bayesian approach, we estimate the parameters of a compartmental model that describes endosomal escape dynamics, accounting for variability over time. These parameters inform a Gillespie stochastic simulation algorithm, ensuring realistic simulations of siRNA release events over time. By combining these techniques, our framework provides a scalable and reproducible method for quantifying endosomal escape. The model captures uncertainty and variability in parameter estimation, and endosomal escape dynamics. Additionally, synthetic data generation allows researchers to validate experimental findings and explore alternative conditions without extensive laboratory work. This integrated approach not only improves the accuracy of endosomal escape quantification but also provides predictive insights for optimizing siRNA delivery systems and advancing gene therapy research.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"387 ","pages":"Article 109476"},"PeriodicalIF":1.9,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144251660","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}
Pub Date : 2025-06-03DOI: 10.1016/j.mbs.2025.109468
D. Cerrone , D. Riccobelli , S. Gazzoni , P. Vitullo , F. Ballarin , J. Falco , F. Acerbi , A. Manzoni , P. Zunino , P. Ciarletta
Glioblastoma is among the most aggressive brain tumors in adults, characterized by patient-specific invasion patterns driven by the underlying brain microstructure. In this work, we present a proof-of-concept for a mathematical model of GBL growth, enabling real-time prediction and patient-specific parameter identification from longitudinal neuroimaging data.
The framework exploits a diffuse-interface mathematical model to describe the tumor evolution and a reduced-order modeling strategy, relying on proper orthogonal decomposition, trained on synthetic data derived from patient-specific brain anatomies reconstructed from magnetic resonance imaging and diffusion tensor imaging. A neural network surrogate learns the inverse mapping from tumor evolution to model parameters, achieving significant computational speed-up while preserving high accuracy.
To ensure robustness and interpretability, we perform both global and local sensitivity analyses, identifying the key biophysical parameters governing tumor dynamics and assessing the stability of the inverse problem solution. These results establish a methodological foundation for future clinical deployment of patient-specific digital twins in neuro-oncology.
{"title":"Patient-specific prediction of glioblastoma growth via reduced order modeling and neural networks","authors":"D. Cerrone , D. Riccobelli , S. Gazzoni , P. Vitullo , F. Ballarin , J. Falco , F. Acerbi , A. Manzoni , P. Zunino , P. Ciarletta","doi":"10.1016/j.mbs.2025.109468","DOIUrl":"10.1016/j.mbs.2025.109468","url":null,"abstract":"<div><div>Glioblastoma is among the most aggressive brain tumors in adults, characterized by patient-specific invasion patterns driven by the underlying brain microstructure. In this work, we present a proof-of-concept for a mathematical model of GBL growth, enabling real-time prediction and patient-specific parameter identification from longitudinal neuroimaging data.</div><div>The framework exploits a diffuse-interface mathematical model to describe the tumor evolution and a reduced-order modeling strategy, relying on proper orthogonal decomposition, trained on synthetic data derived from patient-specific brain anatomies reconstructed from magnetic resonance imaging and diffusion tensor imaging. A neural network surrogate learns the inverse mapping from tumor evolution to model parameters, achieving significant computational speed-up while preserving high accuracy.</div><div>To ensure robustness and interpretability, we perform both global and local sensitivity analyses, identifying the key biophysical parameters governing tumor dynamics and assessing the stability of the inverse problem solution. These results establish a methodological foundation for future clinical deployment of patient-specific digital twins in neuro-oncology.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"387 ","pages":"Article 109468"},"PeriodicalIF":1.9,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144223529","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}
Pub Date : 2025-05-31DOI: 10.1016/j.mbs.2025.109467
Nazia Afrin , Stanca M. Ciupe , Jessica M. Conway , Hayriye Gulbudak
Understanding the mechanisms responsible for different clinical outcomes following hepatitis B infection requires a systems investigation of dynamical interactions between the virus and the immune system. To help elucidate mechanisms of protection and those responsible from transition from acute to chronic disease, we developed a deterministic mathematical model of hepatitis B infection that accounts for cytotoxic immune responses resulting in infected cell death, non-cytotoxic immune responses resulting in infected cell cure and protective immunity from reinfection, and cell proliferation. We analyzed the model and presented outcomes based on three important disease markers: the basic reproduction number , the infected cells death rate (describing the effect of cytotoxic immune responses), and the liver carrying capacity (describing the liver susceptibility to infection). Using asymptotic and bifurcation analysis techniques, we determined regions where virus is cleared, virus persists, and where clearance-persistence is determined by the size of viral inoculum. These results can guide the development of personalized intervention.
{"title":"Bistability between acute and chronic states in a Model of Hepatitis B Virus Dynamics","authors":"Nazia Afrin , Stanca M. Ciupe , Jessica M. Conway , Hayriye Gulbudak","doi":"10.1016/j.mbs.2025.109467","DOIUrl":"10.1016/j.mbs.2025.109467","url":null,"abstract":"<div><div>Understanding the mechanisms responsible for different clinical outcomes following hepatitis B infection requires a systems investigation of dynamical interactions between the virus and the immune system. To help elucidate mechanisms of protection and those responsible from transition from acute to chronic disease, we developed a deterministic mathematical model of hepatitis B infection that accounts for cytotoxic immune responses resulting in infected cell death, non-cytotoxic immune responses resulting in infected cell cure and protective immunity from reinfection, and cell proliferation. We analyzed the model and presented outcomes based on three important disease markers: the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, the infected cells death rate <span><math><mi>δ</mi></math></span> (describing the effect of cytotoxic immune responses), and the liver carrying capacity <span><math><mi>K</mi></math></span> (describing the liver susceptibility to infection). Using asymptotic and bifurcation analysis techniques, we determined regions where virus is cleared, virus persists, and where clearance-persistence is determined by the size of viral inoculum. These results can guide the development of personalized intervention.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"387 ","pages":"Article 109467"},"PeriodicalIF":1.9,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144210592","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}
Pub Date : 2025-05-28DOI: 10.1016/j.mbs.2025.109465
Dan Li, Ying Liu, Longxing Qi
Meteorological factors such as temperature and humidity significantly affect the transmission efficiency of influenza viruses in temperate regions. School-age children aged 5 to 14 years are more susceptible to influenza A virus infection than other age groups. To reveal the impact of seasonal fluctuations in meteorological factors on the spread of influenza and the role of school-age children in disease transmission, we first develop a metapopulation ordinary differential equation model with the seasonal variation of infection probability upon contacting an infectious individual. The basic reproduction number is obtained. To incorporate demographic variability, a time-nonhomogeneous Markov chain model is reformulated on the basis of the deterministic model. An analytic estimate for the probability of a disease outbreak, as well as an explicit expression for the mean(variance) of the disease extinction time in the absence of an outbreak, is derived. Finally, in the case where the population is divided into two subgroups based on age: school-age children aged 5 to 14 years and individuals of other age groups, our model is applied to study seasonal outbreaks of influenza A viruses in temperate regions. Numerical simulations suggest that: (i) the probability of a disease outbreak depends on the number of reported and unreported infections introduced for the first time, the timing of introduction, and their age group; (ii) the impact of demographic stochasticity on the final size and time until extinction after a disease outbreak depends mainly on the timing of influenza virus introduction; (iii) regardless of the season in which an unreported infected individual is introduced, timely treatment of infected school-age children can help reduce the likelihood of disease outbreaks and lower the mean final size after an outbreak.
{"title":"Effect of demographic and seasonal variability on an influenza epidemic in a metapopulation model","authors":"Dan Li, Ying Liu, Longxing Qi","doi":"10.1016/j.mbs.2025.109465","DOIUrl":"10.1016/j.mbs.2025.109465","url":null,"abstract":"<div><div>Meteorological factors such as temperature and humidity significantly affect the transmission efficiency of influenza viruses in temperate regions. School-age children aged 5 to 14 years are more susceptible to influenza A virus infection than other age groups. To reveal the impact of seasonal fluctuations in meteorological factors on the spread of influenza and the role of school-age children in disease transmission, we first develop a metapopulation ordinary differential equation model with the seasonal variation of infection probability upon contacting an infectious individual. The basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is obtained. To incorporate demographic variability, a time-nonhomogeneous Markov chain model is reformulated on the basis of the deterministic model. An analytic estimate for the probability of a disease outbreak, as well as an explicit expression for the mean(variance) of the disease extinction time in the absence of an outbreak, is derived. Finally, in the case where the population is divided into two subgroups based on age: school-age children aged 5 to 14 years and individuals of other age groups, our model is applied to study seasonal outbreaks of influenza A viruses in temperate regions. Numerical simulations suggest that: (i) the probability of a disease outbreak depends on the number of reported and unreported infections introduced for the first time, the timing of introduction, and their age group; (ii) the impact of demographic stochasticity on the final size and time until extinction after a disease outbreak depends mainly on the timing of influenza virus introduction; (iii) regardless of the season in which an unreported infected individual is introduced, timely treatment of infected school-age children can help reduce the likelihood of disease outbreaks and lower the mean final size after an outbreak.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"386 ","pages":"Article 109465"},"PeriodicalIF":1.9,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144188737","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}
Pub Date : 2025-05-21DOI: 10.1016/j.mbs.2025.109455
Bandar Muidh Alharbi , Hannah E. Williams , Tim Parr , John M Brameld , Christopher Fallaize , Jonathan A.D. Wattis
We propose a mathematical model based on coupled ordinary differential equations (ODEs) for metabolite concentrations with the aim of investigating how modifications to the rates affects outputs from a regulatory network. Our aim is to model the relationships between energy metabolism and the biosynthesis of non-essential amino acids, such as serine. We consider a network of cytosolic glycolysis, the mitochondrial TCA cycle, and the associated serine synthesis pathway, with the aim of modelling the role of metabolic reprogramming as a mechanism to enhance protein synthesis and growth, particularly in skeletal muscle. Our objective is to explore the consequences of overexpressing two key enzymes, phosphoenolpyruvate carboxykinase 2 (PCK2), and phosphoglycerate dehydrogenase (PHGDH), on the TCA cycle and on serine production. We investigate how the rate of serine synthesis is affected by upregulating both enzymes simultaneously, or each one individually. We find a range of steady-states which depend upon input fluxes into the network. As input fluxes are altered, steady states cease to exist due to a bifurcation to one of two states in which some metabolites grow linearly in time whilst others decay to zero. Asymptotic analysis provides approximations for steady-state solutions near these bifurcation points, and conditions on parameter values which determine where in parameter space the system’s behaviour changes. We also perform a parameter sensitivity analysis to determine the effect of perturbations to rate constants and input rates. Our numerical simulations show that the up-regulation of PHGDH, the initial rate limiting enzyme in the serine-synthesis pathway, causes an increase in serine production but that, contrary to our hypothesis, increased expression of PCK2 has no effect. This model aids our understanding of both the effects of drugs and changes in enzyme expression or activities which upregulate one or more reactions in a pathway.
{"title":"Mathematical modelling of carbohydrate and protein metabolism in muscle","authors":"Bandar Muidh Alharbi , Hannah E. Williams , Tim Parr , John M Brameld , Christopher Fallaize , Jonathan A.D. Wattis","doi":"10.1016/j.mbs.2025.109455","DOIUrl":"10.1016/j.mbs.2025.109455","url":null,"abstract":"<div><div>We propose a mathematical model based on coupled ordinary differential equations (ODEs) for metabolite concentrations with the aim of investigating how modifications to the rates affects outputs from a regulatory network. Our aim is to model the relationships between energy metabolism and the biosynthesis of non-essential amino acids, such as serine. We consider a network of cytosolic glycolysis, the mitochondrial TCA cycle, and the associated serine synthesis pathway, with the aim of modelling the role of metabolic reprogramming as a mechanism to enhance protein synthesis and growth, particularly in skeletal muscle. Our objective is to explore the consequences of overexpressing two key enzymes, phosphoenolpyruvate carboxykinase 2 (PCK2), and phosphoglycerate dehydrogenase (PHGDH), on the TCA cycle and on serine production. We investigate how the rate of serine synthesis is affected by upregulating both enzymes simultaneously, or each one individually. We find a range of steady-states which depend upon input fluxes into the network. As input fluxes are altered, steady states cease to exist due to a bifurcation to one of two states in which some metabolites grow linearly in time whilst others decay to zero. Asymptotic analysis provides approximations for steady-state solutions near these bifurcation points, and conditions on parameter values which determine where in parameter space the system’s behaviour changes. We also perform a parameter sensitivity analysis to determine the effect of perturbations to rate constants and input rates. Our numerical simulations show that the up-regulation of PHGDH, the initial rate limiting enzyme in the serine-synthesis pathway, causes an increase in serine production but that, contrary to our hypothesis, increased expression of PCK2 has no effect. This model aids our understanding of both the effects of drugs and changes in enzyme expression or activities which upregulate one or more reactions in a pathway.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"386 ","pages":"Article 109455"},"PeriodicalIF":1.9,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144125160","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}
Pub Date : 2025-05-15DOI: 10.1016/j.mbs.2025.109463
Robert Jencks
Zebrafish have been used as a model organism in many areas of biology, including the study of pattern formation. The mean-field survival model is a coupled ODE system describing the expected evolution of chromatophores coordinating to form stripes in zebrafish. This paper presents analysis of the model focusing on parameters for the number of cells, length of distant-neighbor interactions, and rates related to birth and death of chromatophores. We derive the conditions on these parameters for a Turing bifurcation to occur and show that the model predicts patterns qualitatively similar to those in nature.
In addition to answering questions about this particular model, this paper also serves as a case study for Turing analysis on coupled ODE systems. The qualitative behavior of such coupled ODE models may deviate significantly from continuum limit models. The ability to analyze such systems directly avoids this concern and allows for a more accurate description of the behavior at physically relevant scales.
{"title":"The mean-field survival model for stripe formation in zebrafish exhibits Turing instability","authors":"Robert Jencks","doi":"10.1016/j.mbs.2025.109463","DOIUrl":"10.1016/j.mbs.2025.109463","url":null,"abstract":"<div><div>Zebrafish have been used as a model organism in many areas of biology, including the study of pattern formation. The mean-field survival model is a coupled ODE system describing the expected evolution of chromatophores coordinating to form stripes in zebrafish. This paper presents analysis of the model focusing on parameters for the number of cells, length of distant-neighbor interactions, and rates related to birth and death of chromatophores. We derive the conditions on these parameters for a Turing bifurcation to occur and show that the model predicts patterns qualitatively similar to those in nature.</div><div>In addition to answering questions about this particular model, this paper also serves as a case study for Turing analysis on coupled ODE systems. The qualitative behavior of such coupled ODE models may deviate significantly from continuum limit models. The ability to analyze such systems directly avoids this concern and allows for a more accurate description of the behavior at physically relevant scales.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"385 ","pages":"Article 109463"},"PeriodicalIF":1.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144071016","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}
Pub Date : 2025-05-14DOI: 10.1016/j.mbs.2025.109456
Elliott Hughes , Miguel Moyers-Gonzalez , Rua Murray , Phillip L. Wilson
Invasive pine trees pose a threat to biodiversity in a variety of Southern Hemisphere countries, but understanding of the dynamics of invasions and the factors that retard or accelerate spread is limited. We review past mathematical models of wilding pine spread, including spatially explicit individual-based models, recursive partitioning methods, and integrodifference matrix models (IDMs). In contrast to these approaches, we use partial differential equations to model an invasion. We show that invasions are almost static for a significant period of time before rapidly accelerating to spread at a constant rate, matching observed behaviour in at least some field sites. Our work suggests that prior methods for estimating invasion speeds may not accurately predict spread and are sensitive to assumptions about the distribution of parameters. However, we present alternative estimation methods and suggest directions for further research.
{"title":"A mathematically robust model of exotic pine invasions","authors":"Elliott Hughes , Miguel Moyers-Gonzalez , Rua Murray , Phillip L. Wilson","doi":"10.1016/j.mbs.2025.109456","DOIUrl":"10.1016/j.mbs.2025.109456","url":null,"abstract":"<div><div>Invasive pine trees pose a threat to biodiversity in a variety of Southern Hemisphere countries, but understanding of the dynamics of invasions and the factors that retard or accelerate spread is limited. We review past mathematical models of wilding pine spread, including spatially explicit individual-based models, recursive partitioning methods, and integrodifference matrix models (IDMs). In contrast to these approaches, we use partial differential equations to model an invasion. We show that invasions are almost static for a significant period of time before rapidly accelerating to spread at a constant rate, matching observed behaviour in at least some field sites. Our work suggests that prior methods for estimating invasion speeds may not accurately predict spread and are sensitive to assumptions about the distribution of parameters. However, we present alternative estimation methods and suggest directions for further research.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"386 ","pages":"Article 109456"},"PeriodicalIF":1.9,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144087133","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}
Pub Date : 2025-05-14DOI: 10.1016/j.mbs.2025.109464
Zainab O. Dere , N.G. Cogan , Bhargav R. Karamched
Given the global increase in antibiotic resistance, new effective strategies must be developed to treat bacteria that do not respond to first or second line antibiotics. One novel method uses bacterial phage therapy to control bacterial populations. Phage viruses replicate and infect bacterial cells and are regarded as the most prevalent biological agent on earth. This paper presents a comprehensive model capturing the dynamics of wild-type bacteria , antibiotic-resistant bacteria , and virus-infected () bacteria population, incorporating virus inclusion. Our model integrates biologically relevant parameters governing bacterial birth rates, death rates, mutation probabilities and incorporates infection dynamics via contact with a virus. We employ an optimal control approach to study the influence of virus inclusion on bacterial population dynamics. Through numerical simulations, we establish insights into the stability of various system equilibria and bacterial population responses to varying infection rates. By examining the equilibria, we reveal the impact of virus inclusion on population trajectories, describe a medical intervention for antibiotic-resistant bacterial infections through the lense of optimal control theory, and discuss how to implement it in a clinical setting. Our findings underscore the necessity of considering virus inclusion in antibiotic resistance studies, shedding light on subtle yet influential dynamics in bacterial ecosystems.
{"title":"Optimal control strategies for mitigating antibiotic resistance: Integrating virus dynamics for enhanced intervention design","authors":"Zainab O. Dere , N.G. Cogan , Bhargav R. Karamched","doi":"10.1016/j.mbs.2025.109464","DOIUrl":"10.1016/j.mbs.2025.109464","url":null,"abstract":"<div><div>Given the global increase in antibiotic resistance, new effective strategies must be developed to treat bacteria that do not respond to first or second line antibiotics. One novel method uses bacterial phage therapy to control bacterial populations. Phage viruses replicate and infect bacterial cells and are regarded as the most prevalent biological agent on earth. This paper presents a comprehensive model capturing the dynamics of wild-type bacteria <span><math><mrow><mo>(</mo><mi>S</mi><mo>)</mo></mrow></math></span>, antibiotic-resistant bacteria <span><math><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></math></span>, and virus-infected (<span><math><mi>I</mi></math></span>) bacteria population, incorporating virus inclusion. Our model integrates biologically relevant parameters governing bacterial birth rates, death rates, mutation probabilities and incorporates infection dynamics via contact with a virus. We employ an optimal control approach to study the influence of virus inclusion on bacterial population dynamics. Through numerical simulations, we establish insights into the stability of various system equilibria and bacterial population responses to varying infection rates. By examining the equilibria, we reveal the impact of virus inclusion on population trajectories, describe a medical intervention for antibiotic-resistant bacterial infections through the lense of optimal control theory, and discuss how to implement it in a clinical setting. Our findings underscore the necessity of considering virus inclusion in antibiotic resistance studies, shedding light on subtle yet influential dynamics in bacterial ecosystems.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"386 ","pages":"Article 109464"},"PeriodicalIF":1.9,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144087138","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}
Mutation in the SARS-CoV-2 virus may lead to the evolution of new variants. The dynamics of these variants varied among countries. Identification of the governing factors responsible for distinctions in their dynamics is important for preparedness against future severe variants. This study investigates the impact of cross immunity and control measures on the competition dynamics of the Alpha, Gamma, Delta, and Omicron variants. The following questions are addressed using an n-strain deterministic model: (i) Why do a few variants fail to cause a wave even after winning the competition? (ii) In what scenarios a new variant cannot replace the previous one? The model is fitted and cross-validated with the data of COVID-19 and its variants for the USA, UK, and Brazil. The model analysis highlights implementations of the following measures against any deadlier future variant: (i) an effective population-wide cross-immunity from less lethal strains and (ii) strain-specific vaccines targeting the novel variant. The system exhibits a fascinating dynamical behavior known as an endemic bubble due to Hopf bifurcation. It is observed that the actual situation in which Omicron won the competition from Delta followed by no wave due to Delta may turn into a competitive periodic coexistence of two strains due to substantial disparity in fading rates of cross-immunity. Global sensitivity analysis is conducted to quantify uncertainties of model parameters. It is found that examining the impact of cross-immunity is as crucial as vaccination.
{"title":"Modeling the effects of cross immunity and control measures on competitive dynamics of SARS-CoV-2 variants in the USA, UK, and Brazil","authors":"Komal Basaiti , Anil Kumar Vashishth , Tonghua Zhang","doi":"10.1016/j.mbs.2025.109450","DOIUrl":"10.1016/j.mbs.2025.109450","url":null,"abstract":"<div><div>Mutation in the SARS-CoV-2 virus may lead to the evolution of new variants. The dynamics of these variants varied among countries. Identification of the governing factors responsible for distinctions in their dynamics is important for preparedness against future severe variants. This study investigates the impact of cross immunity and control measures on the competition dynamics of the Alpha, Gamma, Delta, and Omicron variants. The following questions are addressed using an n-strain deterministic model: (i) Why do a few variants fail to cause a wave even after winning the competition? (ii) In what scenarios a new variant cannot replace the previous one? The model is fitted and cross-validated with the data of COVID-19 and its variants for the USA, UK, and Brazil. The model analysis highlights implementations of the following measures against any deadlier future variant: (i) an effective population-wide cross-immunity from less lethal strains and (ii) strain-specific vaccines targeting the novel variant. The system exhibits a fascinating dynamical behavior known as an endemic bubble due to Hopf bifurcation. It is observed that the actual situation in which Omicron won the competition from Delta followed by no wave due to Delta may turn into a competitive periodic coexistence of two strains due to substantial disparity in fading rates of cross-immunity. Global sensitivity analysis is conducted to quantify uncertainties of model parameters. It is found that examining the impact of cross-immunity is as crucial as vaccination.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"385 ","pages":"Article 109450"},"PeriodicalIF":1.9,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936853","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}
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