Pub Date : 2025-12-04DOI: 10.1016/j.mbs.2025.109569
Guo Lin , Jiantao Lin , Shuxia Pan
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.
{"title":"Spreading dynamics of an SVIRS model","authors":"Guo Lin , Jiantao Lin , 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":"2025-12-04","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}
Pub Date : 2025-12-02DOI: 10.1016/j.mbs.2025.109588
Christian Parkinson , Weinan Wang
We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that noncompliance with protocols spreads as a social contagion. We begin by deriving the reproductive ratio for a deterministic version of the model, and use this to fully characterize the local stability of disease free equilibrium points. We then append the deterministic model with stochastic effects, specifically assuming that the transmission rate of the disease and the transmission rate of the social contagion are uncertain. We prove global existence and nonnegativity for our stochastic model. Then using suitably constructed stochastic Lyapunov functions, we analyze the behavior of the stochastic system with respect to certain disease free states. We demonstrate all of our results with numerical simulations.
{"title":"A compartmental model for epidemiology with human behavior and stochastic effects","authors":"Christian Parkinson , Weinan Wang","doi":"10.1016/j.mbs.2025.109588","DOIUrl":"10.1016/j.mbs.2025.109588","url":null,"abstract":"<div><div>We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that noncompliance with protocols spreads as a social contagion. We begin by deriving the reproductive ratio for a deterministic version of the model, and use this to fully characterize the local stability of disease free equilibrium points. We then append the deterministic model with stochastic effects, specifically assuming that the transmission rate of the disease and the transmission rate of the social contagion are uncertain. We prove global existence and nonnegativity for our stochastic model. Then using suitably constructed stochastic Lyapunov functions, we analyze the behavior of the stochastic system with respect to certain disease free states. We demonstrate all of our results with numerical simulations.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"392 ","pages":"Article 109588"},"PeriodicalIF":1.8,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145679935","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 : 2025-12-01DOI: 10.1016/j.mbs.2025.109587
Lingming Kong , Yanying Mo , Guanghu Zhu , Liang Chen , Zhen Wang
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 % (p < .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 R0 was estimated at 1.9 (95 % CI: 1.2–2.6). Bifurcation analysis confirmed global stability of the disease-free equilibrium when R0 < 1 and endemic persistence when R0 > 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.
{"title":"Environmental drivers of tuberculosis transmission in Guangdong, China: Integrating generalized additive models and dynamic simulations","authors":"Lingming Kong , Yanying Mo , Guanghu Zhu , Liang Chen , 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> < .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><sub>0</sub> 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><sub>0</sub> < 1 and endemic persistence when <em>R</em><sub>0</sub> > 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":"2025-12-01","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}
Pub Date : 2025-11-30DOI: 10.1016/j.mbs.2025.109586
Shangbing Ai , Jianhe Shen
<div><div>We study a Keller-Segel system with nonlinear chemical gradient and two parameters <em>c</em> > 0 and ε > 0. The system has a family of equilibria <span><math><mrow><mo>(</mo><msup><mi>u</mi><mo>*</mo></msup><mo>,</mo><msubsup><mi>v</mi><mrow><mo>±</mo></mrow><mo>*</mo></msubsup><mo>)</mo></mrow></math></span> with <span><math><mrow><msubsup><mi>u</mi><mn>1</mn><mo>*</mo></msubsup><mo><</mo><msup><mi>u</mi><mo>*</mo></msup><mo><</mo><msubsup><mi>u</mi><mn>2</mn><mo>*</mo></msubsup></mrow></math></span> where <span><math><msubsup><mi>u</mi><mn>1</mn><mo>*</mo></msubsup></math></span> and <span><math><msubsup><mi>u</mi><mn>2</mn><mo>*</mo></msubsup></math></span> are explicitly defined. We investigate the existence of traveling wave solutions <span><math><mrow><mo>(</mo><msubsup><mi>u</mi><mi>s</mi><mrow><mi>c</mi><mo>,</mo><mrow><mi>ε</mi></mrow></mrow></msubsup><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mi>s</mi><mi>t</mi><mo>)</mo></mrow><mo>,</mo><msubsup><mi>u</mi><mi>s</mi><mrow><mi>c</mi><mo>,</mo><mrow><mi>ε</mi></mrow></mrow></msubsup><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mi>s</mi><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></math></span> of this system that connect a pair of equilibria <span><math><mrow><mo>(</mo><msup><mi>u</mi><mo>*</mo></msup><mo>,</mo><msubsup><mi>v</mi><mrow><mo>±</mo></mrow><mo>*</mo></msubsup><mo>)</mo></mrow></math></span> and establish the following result: there exists <span><math><msubsup><mi>u</mi><mn>0</mn><mo>*</mo></msubsup></math></span> with <span><math><mrow><msubsup><mi>u</mi><mn>1</mn><mo>*</mo></msubsup><mo><</mo><msubsup><mi>u</mi><mn>0</mn><mo>*</mo></msubsup><mo><</mo><msubsup><mi>u</mi><mn>2</mn><mo>*</mo></msubsup></mrow></math></span> such that if <span><math><mrow><msubsup><mi>u</mi><mn>1</mn><mo>*</mo></msubsup><mo><</mo><msup><mi>u</mi><mo>*</mo></msup><mo>≤</mo><msubsup><mi>u</mi><mn>0</mn><mo>*</mo></msubsup></mrow></math></span>, then <span><math><mrow><mo>(</mo><msubsup><mi>u</mi><mi>s</mi><mrow><mi>c</mi><mo>,</mo><mrow><mi>ε</mi></mrow></mrow></msubsup><mo>,</mo><msubsup><mi>v</mi><mi>s</mi><mrow><mi>c</mi><mo>,</mo><mrow><mi>ε</mi></mrow></mrow></msubsup><mo>)</mo></mrow></math></span> exists for all <em>c</em> > 0 and <em>s</em> > 0 and sufficiently small ε > 0; if <span><math><mrow><msubsup><mi>u</mi><mn>0</mn><mo>*</mo></msubsup><mo><</mo><msup><mi>u</mi><mo>*</mo></msup><mo><</mo><msubsup><mi>u</mi><mn>2</mn><mo>*</mo></msubsup></mrow></math></span>, then there exists <em>c</em>* > 0 such that for <em>c</em> > <em>c</em>*, such a solution exists for all <em>s</em> > 0 and sufficiently small ε, while for 0 < <em>c</em> ≤ <em>c</em>*, such a solution exists only for <em>s</em> in a disconnected set of (0, ∞) which includes two connected components <span><math><mrow><mo>(</mo><mn>0</mn><mo>,</mo><msubsup><mi>s</mi><mi>c</mi><mo>*</mo></msubsup><mo>)</mo></mrow></math></span> and <span><math><mrow><mo>(</mo><msub><mover><mi>s</mi><mo>^
{"title":"New results on traveling wave solutions for a Keller-Segel system with nonlinear chemical gradient","authors":"Shangbing Ai , Jianhe Shen","doi":"10.1016/j.mbs.2025.109586","DOIUrl":"10.1016/j.mbs.2025.109586","url":null,"abstract":"<div><div>We study a Keller-Segel system with nonlinear chemical gradient and two parameters <em>c</em> > 0 and ε > 0. The system has a family of equilibria <span><math><mrow><mo>(</mo><msup><mi>u</mi><mo>*</mo></msup><mo>,</mo><msubsup><mi>v</mi><mrow><mo>±</mo></mrow><mo>*</mo></msubsup><mo>)</mo></mrow></math></span> with <span><math><mrow><msubsup><mi>u</mi><mn>1</mn><mo>*</mo></msubsup><mo><</mo><msup><mi>u</mi><mo>*</mo></msup><mo><</mo><msubsup><mi>u</mi><mn>2</mn><mo>*</mo></msubsup></mrow></math></span> where <span><math><msubsup><mi>u</mi><mn>1</mn><mo>*</mo></msubsup></math></span> and <span><math><msubsup><mi>u</mi><mn>2</mn><mo>*</mo></msubsup></math></span> are explicitly defined. We investigate the existence of traveling wave solutions <span><math><mrow><mo>(</mo><msubsup><mi>u</mi><mi>s</mi><mrow><mi>c</mi><mo>,</mo><mrow><mi>ε</mi></mrow></mrow></msubsup><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mi>s</mi><mi>t</mi><mo>)</mo></mrow><mo>,</mo><msubsup><mi>u</mi><mi>s</mi><mrow><mi>c</mi><mo>,</mo><mrow><mi>ε</mi></mrow></mrow></msubsup><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mi>s</mi><mi>t</mi><mo>)</mo></mrow><mo>)</mo></mrow></math></span> of this system that connect a pair of equilibria <span><math><mrow><mo>(</mo><msup><mi>u</mi><mo>*</mo></msup><mo>,</mo><msubsup><mi>v</mi><mrow><mo>±</mo></mrow><mo>*</mo></msubsup><mo>)</mo></mrow></math></span> and establish the following result: there exists <span><math><msubsup><mi>u</mi><mn>0</mn><mo>*</mo></msubsup></math></span> with <span><math><mrow><msubsup><mi>u</mi><mn>1</mn><mo>*</mo></msubsup><mo><</mo><msubsup><mi>u</mi><mn>0</mn><mo>*</mo></msubsup><mo><</mo><msubsup><mi>u</mi><mn>2</mn><mo>*</mo></msubsup></mrow></math></span> such that if <span><math><mrow><msubsup><mi>u</mi><mn>1</mn><mo>*</mo></msubsup><mo><</mo><msup><mi>u</mi><mo>*</mo></msup><mo>≤</mo><msubsup><mi>u</mi><mn>0</mn><mo>*</mo></msubsup></mrow></math></span>, then <span><math><mrow><mo>(</mo><msubsup><mi>u</mi><mi>s</mi><mrow><mi>c</mi><mo>,</mo><mrow><mi>ε</mi></mrow></mrow></msubsup><mo>,</mo><msubsup><mi>v</mi><mi>s</mi><mrow><mi>c</mi><mo>,</mo><mrow><mi>ε</mi></mrow></mrow></msubsup><mo>)</mo></mrow></math></span> exists for all <em>c</em> > 0 and <em>s</em> > 0 and sufficiently small ε > 0; if <span><math><mrow><msubsup><mi>u</mi><mn>0</mn><mo>*</mo></msubsup><mo><</mo><msup><mi>u</mi><mo>*</mo></msup><mo><</mo><msubsup><mi>u</mi><mn>2</mn><mo>*</mo></msubsup></mrow></math></span>, then there exists <em>c</em>* > 0 such that for <em>c</em> > <em>c</em>*, such a solution exists for all <em>s</em> > 0 and sufficiently small ε, while for 0 < <em>c</em> ≤ <em>c</em>*, such a solution exists only for <em>s</em> in a disconnected set of (0, ∞) which includes two connected components <span><math><mrow><mo>(</mo><mn>0</mn><mo>,</mo><msubsup><mi>s</mi><mi>c</mi><mo>*</mo></msubsup><mo>)</mo></mrow></math></span> and <span><math><mrow><mo>(</mo><msub><mover><mi>s</mi><mo>^","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"392 ","pages":"Article 109586"},"PeriodicalIF":1.8,"publicationDate":"2025-11-30","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}
In this paper, we study the dynamics of biological invasion through complementary modeling frameworks in the context of nonlocal resource-driven dispersal. During the very early stage of invasion, when only a few individuals are present, demographic variability is crucial: extinction may occur even under favorable average conditions. To capture this, we use a branching-process approximation that provides explicit formulas for extinction probabilities, survival conditions, and mean extinction times. At larger scales and higher densities, invasion is described by a deterministic system of nonlinear integro-differential equations. For this system, we establish well-posedness and derive lower and upper bounds on the asymptotic spreading speed. A unifying threshold parameter , defined as the spectral radius of a next-generation operator, characterizes invasion outcomes: if , extinction occurs; if , the invader persists and spreads. Importantly, the threshold derived from the early-stage approximation coincides with that of the deterministic model, thus providing a consistent criterion for invasion success. Finally, numerical simulations illustrate the transition between extinction and persistence and highlight how resource-driven dispersal shapes invasion speed.
{"title":"Early-stage invasion and spreading speed in a resource-dependent dispersal model","authors":"Jean-Baptiste Burie , Arnaud Ducrot , Ousmane Seydi","doi":"10.1016/j.mbs.2025.109585","DOIUrl":"10.1016/j.mbs.2025.109585","url":null,"abstract":"<div><div>In this paper, we study the dynamics of biological invasion through complementary modeling frameworks in the context of nonlocal resource-driven dispersal. During the very early stage of invasion, when only a few individuals are present, demographic variability is crucial: extinction may occur even under favorable average conditions. To capture this, we use a branching-process approximation that provides explicit formulas for extinction probabilities, survival conditions, and mean extinction times. At larger scales and higher densities, invasion is described by a deterministic system of nonlinear integro-differential equations. For this system, we establish well-posedness and derive lower and upper bounds on the asymptotic spreading speed. A unifying threshold parameter <span><math><msub><mi>T</mi><mn>0</mn></msub></math></span>, defined as the spectral radius of a next-generation operator, characterizes invasion outcomes: if <span><math><mrow><msub><mi>T</mi><mn>0</mn></msub><mo>≤</mo><mn>1</mn></mrow></math></span>, extinction occurs; if <span><math><mrow><msub><mi>T</mi><mn>0</mn></msub><mo>></mo><mn>1</mn></mrow></math></span>, the invader persists and spreads. Importantly, the threshold derived from the early-stage approximation coincides with that of the deterministic model, thus providing a consistent criterion for invasion success. Finally, numerical simulations illustrate the transition between extinction and persistence and highlight how resource-driven dispersal shapes invasion speed.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"392 ","pages":"Article 109585"},"PeriodicalIF":1.8,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145650660","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 : 2025-11-27DOI: 10.1016/j.mbs.2025.109571
Jie Qi , Ruth E. Baker
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.
{"title":"Optimal experimental design for parameter estimation in the presence of observation noise","authors":"Jie Qi , 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":"2025-11-27","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}
Pub Date : 2025-11-25DOI: 10.1016/j.mbs.2025.109583
Rebecca A. Bekker , Renee Brady-Nicholls , Lisette de Pillis , Jana L. Gevertz , Harsh Vardhan Jain
In silico clinical trials offer a powerful tool for overcoming several limitations of traditional clinical trials. Conventional trials are time- and resource-intensive, typically designed to assess average effects across a population while being restricted to studying the impact of a fixed treatment protocol. In contrast, in silico trials are cost-effective, flexible in their design, and able to explore heterogeneity in treatment response. These trials generally rely on expert-developed and data-calibrated mechanistic mathematical models and the identification of model parameterizations that satisfy biological or clinical constraints. With the growing availability of multi-scale and high-resolution clinical data, it is the opportune time to thoughtfully consider how machine learning (ML) methods can enhance the feasibility, interpretability, and reliability of these in silico trials. In this perspective piece, we explore both the opportunities and the challenges of introducing ML tools at various stages of this process, from biomarker identification to interpreting the results of the trial. We argue that in the hands of an expert modeler, the thoughtful application of ML tools can result in more accurate and informative in silico clinical trials that may potentially accelerate drug development and find the right drug/protocol for the right patient.
{"title":"Integrating machine learning into the in silico clinical trial pipeline","authors":"Rebecca A. Bekker , Renee Brady-Nicholls , Lisette de Pillis , Jana L. Gevertz , Harsh Vardhan Jain","doi":"10.1016/j.mbs.2025.109583","DOIUrl":"10.1016/j.mbs.2025.109583","url":null,"abstract":"<div><div><em>In silico</em> clinical trials offer a powerful tool for overcoming several limitations of traditional clinical trials. Conventional trials are time- and resource-intensive, typically designed to assess average effects across a population while being restricted to studying the impact of a fixed treatment protocol. In contrast, <em>in silico</em> trials are cost-effective, flexible in their design, and able to explore heterogeneity in treatment response. These trials generally rely on expert-developed and data-calibrated mechanistic mathematical models and the identification of model parameterizations that satisfy biological or clinical constraints. With the growing availability of multi-scale and high-resolution clinical data, it is the opportune time to thoughtfully consider how machine learning (ML) methods can enhance the feasibility, interpretability, and reliability of these <em>in silico</em> trials. In this perspective piece, we explore both the opportunities and the challenges of introducing ML tools at various stages of this process, from biomarker identification to interpreting the results of the trial. We argue that in the hands of an expert modeler, the thoughtful application of ML tools can result in more accurate and informative <em>in silico</em> clinical trials that may potentially accelerate drug development and find the right drug/protocol for the right patient.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"391 ","pages":"Article 109583"},"PeriodicalIF":1.8,"publicationDate":"2025-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145644167","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 : 2025-11-24DOI: 10.1016/j.mbs.2025.109582
Taylor Kearney , Mark B. Flegg
Particle-based simulations are an essential tool for the study of biochemical systems for scales between molecular/Brownian dynamics and the reaction-diffusion master equation. These simulations utilise proximity-based reaction conditions and are typically limited to elementary (mass-action) kinetics. We present a novel framework for directly simulating non-elementary bimolecular kinetics in a particle-based framework. By mimicking the behaviour of a third implicit reactant, we adapt non-elementary reaction conditions, previously restricted to trimolecular chemical interactions, to biomolecular reactions for the first time. We implement our approach in an event-driven simulation, which we validate by reproducing Michaelis-Menten kinetics. We then demonstrate its utility by simulating the classical Goldbeter model of circadian oscillations completely at the level of individual molecules. This model features multiple non-elementary reactions and requires the incorporation of several existing simulation techniques. Our method accurately reproduces the target non-elementary kinetics, without simulating the implied underlying fast elementary reactions, thereby significantly reducing the computational cost. This work expands the class of reaction networks accessible to particle-based simulations and provides a practical alternative to explicitly simulating all elementary steps in systems where quasi-steady-state approximations are applicable.
{"title":"Particle-based simulation of non-elementary bimolecular kinetics","authors":"Taylor Kearney , Mark B. Flegg","doi":"10.1016/j.mbs.2025.109582","DOIUrl":"10.1016/j.mbs.2025.109582","url":null,"abstract":"<div><div>Particle-based simulations are an essential tool for the study of biochemical systems for scales between molecular/Brownian dynamics and the reaction-diffusion master equation. These simulations utilise proximity-based reaction conditions and are typically limited to elementary (mass-action) kinetics. We present a novel framework for directly simulating non-elementary bimolecular kinetics in a particle-based framework. By mimicking the behaviour of a third implicit reactant, we adapt non-elementary reaction conditions, previously restricted to trimolecular chemical interactions, to biomolecular reactions for the first time. We implement our approach in an event-driven simulation, which we validate by reproducing Michaelis-Menten kinetics. We then demonstrate its utility by simulating the classical Goldbeter model of circadian oscillations completely at the level of individual molecules. This model features multiple non-elementary reactions and requires the incorporation of several existing simulation techniques. Our method accurately reproduces the target non-elementary kinetics, without simulating the implied underlying fast elementary reactions, thereby significantly reducing the computational cost. This work expands the class of reaction networks accessible to particle-based simulations and provides a practical alternative to explicitly simulating all elementary steps in systems where quasi-steady-state approximations are applicable.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"391 ","pages":"Article 109582"},"PeriodicalIF":1.8,"publicationDate":"2025-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145625144","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 : 2025-11-24DOI: 10.1016/j.mbs.2025.109572
Shizhao Ma , Xiulan Lai
Acute myeloid leukemia (AML) is characterized by the uncontrolled proliferation of abnormal myeloid cells in the bone marrow and peripheral blood. In this study, we develop a stochastic differential equation model to capture the dynamic interactions among hematopoietic, osteoblastic, and leukemic cell populations within the bone marrow microenvironment. We calibrate model parameters using clinical data via an optimal control framework. Our study provides a mathematical framework to investigate how leukemic cells may remodel the heterogeneous bone marrow niche through dynamic interactions with osteoblastic lineages. This remodeling process disrupts both the quantity and functional capacity of hematopoietic populations, thereby offering insights into how leukemic-niche interactions may contribute to AML treatment failure. Furthermore, we evaluate the efficacy of combination therapies (traditional chemotherapy with targeted therapy) and compare their therapeutic outcomes. These findings offer a theoretical foundation for optimizing clinical strategies and advancing personalized treatment approaches for AML.
{"title":"Exploring the role of osteoblast-lineage cells in the evolutionary dynamics of acute myeloid leukemia through a stochastic differential equation model","authors":"Shizhao Ma , Xiulan Lai","doi":"10.1016/j.mbs.2025.109572","DOIUrl":"10.1016/j.mbs.2025.109572","url":null,"abstract":"<div><div>Acute myeloid leukemia (AML) is characterized by the uncontrolled proliferation of abnormal myeloid cells in the bone marrow and peripheral blood. In this study, we develop a stochastic differential equation model to capture the dynamic interactions among hematopoietic, osteoblastic, and leukemic cell populations within the bone marrow microenvironment. We calibrate model parameters using clinical data via an optimal control framework. Our study provides a mathematical framework to investigate how leukemic cells may remodel the heterogeneous bone marrow niche through dynamic interactions with osteoblastic lineages. This remodeling process disrupts both the quantity and functional capacity of hematopoietic populations, thereby offering insights into how leukemic-niche interactions may contribute to AML treatment failure. Furthermore, we evaluate the efficacy of combination therapies (traditional chemotherapy with targeted therapy) and compare their therapeutic outcomes. These findings offer a theoretical foundation for optimizing clinical strategies and advancing personalized treatment approaches for AML.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"391 ","pages":"Article 109572"},"PeriodicalIF":1.8,"publicationDate":"2025-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145625143","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}
The effectiveness of oncolytic virotherapy is significantly affected by several elements of the tumour microenvironment, which reduce the ability of the virus to infect cancer cells. In this work, we focus on the influence of hypoxia on this therapy and develop a novel continuous mathematical model that considers both the spatial and epigenetic heterogeneity of the tumour. We investigate how oxygen gradients within tumours affect the spatial distribution and replication of both the tumour and oncolytic viruses, focusing on regions of severe hypoxia versus normoxic areas. Additionally, we analyse the evolutionary dynamics of tumour cells under hypoxic conditions and their influence on susceptibility to viral infection. Our findings show that the reduced metabolic activity of hypoxic cells may significantly impact the virotherapy effectiveness; the knowledge of the tumour’s oxygenation could, therefore, suggest the most suitable type of virus to optimise the outcome. The combination of numerical simulations and theoretical results for the model equilibrium values allows us to elucidate the complex interplay between viruses, tumour evolution and oxygen dynamics, ultimately contributing to developing more effective and personalised cancer treatments.
{"title":"A phenotype-structured mathematical model for the influence of hypoxia on oncolytic virotherapy","authors":"David Morselli , Giulia Chiari , Federico Frascoli , Marcello Edoardo Delitala","doi":"10.1016/j.mbs.2025.109570","DOIUrl":"10.1016/j.mbs.2025.109570","url":null,"abstract":"<div><div>The effectiveness of oncolytic virotherapy is significantly affected by several elements of the tumour microenvironment, which reduce the ability of the virus to infect cancer cells. In this work, we focus on the influence of hypoxia on this therapy and develop a novel continuous mathematical model that considers both the spatial and epigenetic heterogeneity of the tumour. We investigate how oxygen gradients within tumours affect the spatial distribution and replication of both the tumour and oncolytic viruses, focusing on regions of severe hypoxia versus normoxic areas. Additionally, we analyse the evolutionary dynamics of tumour cells under hypoxic conditions and their influence on susceptibility to viral infection. Our findings show that the reduced metabolic activity of hypoxic cells may significantly impact the virotherapy effectiveness; the knowledge of the tumour’s oxygenation could, therefore, suggest the most suitable type of virus to optimise the outcome. The combination of numerical simulations and theoretical results for the model equilibrium values allows us to elucidate the complex interplay between viruses, tumour evolution and oxygen dynamics, ultimately contributing to developing more effective and personalised cancer treatments.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"391 ","pages":"Article 109570"},"PeriodicalIF":1.8,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145575201","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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