Pub Date : 2025-07-07DOI: 10.1016/j.mbs.2025.109503
H. Djimramadji , Julien Arino , P.M. Tchepmo Djomegni , M.S. Daoussa Haggar
We consider a model for the spread of bovine tuberculosis in herds comprising three species (bovids, caprids and equids) in Chad. The epidemiological model is built on top of a classic Lotka–Volterra competition model, which is exploited in a regime where stable coexistence of the three species holds. The epidemiological model itself is an SLI model, because of the absence of treatment for herds in the area. After studying some mathematical properties of the model, we perform a short computational analysis, investigating sensitivity of the model and comparing solutions with and without competition. To gain more understanding on the timing of events, we also consider the continuous time Markov chain analogue of the model.
{"title":"Dynamics of bovine tuberculosis transmission in mixed herds in Chad","authors":"H. Djimramadji , Julien Arino , P.M. Tchepmo Djomegni , M.S. Daoussa Haggar","doi":"10.1016/j.mbs.2025.109503","DOIUrl":"10.1016/j.mbs.2025.109503","url":null,"abstract":"<div><div>We consider a model for the spread of bovine tuberculosis in herds comprising three species (bovids, caprids and equids) in Chad. The epidemiological model is built on top of a classic Lotka–Volterra competition model, which is exploited in a regime where stable coexistence of the three species holds. The epidemiological model itself is an SLI model, because of the absence of treatment for herds in the area. After studying some mathematical properties of the model, we perform a short computational analysis, investigating sensitivity of the model and comparing solutions with and without competition. To gain more understanding on the timing of events, we also consider the continuous time Markov chain analogue of the model.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"387 ","pages":"Article 109503"},"PeriodicalIF":1.9,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144579830","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 : 2025-07-05DOI: 10.1016/j.mbs.2025.109501
Zhitao Zhao , Jing Yang , Russell Milne , Yawen Yan
This paper explores two mixotroph-bacterium interaction dynamic models in different eutrophic aquatic environments. One is the spatially homogeneous ordinary differential equation model in a well-mixed aquatic environment. The other is the spatially heterogeneous reaction–diffusion-advection model in a poorly-mixed aquatic environment. Dynamical properties of the two models are investigated containing dissipativity, equilibria, steady states, and uniform persistence. The ecological reproductive indices are developed to characterize mixotrophs or bacteria invasion. We also explore the effects of light, autotrophic behavior of mixotrophs, turbulent diffusion, and advection on population dynamics. Numerical simulations reveal that two mixotroph-bacterium interaction dynamic models display bistability dynamics. Furthermore, our findings indicate that sufficient light and a high proportion of autotrophic behavior of mixotrophs contribute to the coexistence of mixotrophs and bacteria.
{"title":"Modeling mixotroph-bacterium dynamics: Spatial homogeneity vs heterogeneity","authors":"Zhitao Zhao , Jing Yang , Russell Milne , Yawen Yan","doi":"10.1016/j.mbs.2025.109501","DOIUrl":"10.1016/j.mbs.2025.109501","url":null,"abstract":"<div><div>This paper explores two mixotroph-bacterium interaction dynamic models in different eutrophic aquatic environments. One is the spatially homogeneous ordinary differential equation model in a well-mixed aquatic environment. The other is the spatially heterogeneous reaction–diffusion-advection model in a poorly-mixed aquatic environment. Dynamical properties of the two models are investigated containing dissipativity, equilibria, steady states, and uniform persistence. The ecological reproductive indices are developed to characterize mixotrophs or bacteria invasion. We also explore the effects of light, autotrophic behavior of mixotrophs, turbulent diffusion, and advection on population dynamics. Numerical simulations reveal that two mixotroph-bacterium interaction dynamic models display bistability dynamics. Furthermore, our findings indicate that sufficient light and a high proportion of autotrophic behavior of mixotrophs contribute to the coexistence of mixotrophs and bacteria.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"387 ","pages":"Article 109501"},"PeriodicalIF":1.9,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144577460","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 : 2025-07-01DOI: 10.1016/j.mbs.2025.109466
Zhuolin Qu , Lauren M. Childs
Malaria remains a significant infectious disease globally, causing hundreds of thousands of deaths each year. Traditional control methods, such as disease surveillance and mosquito control, along with the development of malaria vaccines, have made strides in reducing the disease’s impact, but new control methods are urgently needed. Wolbachia is a natural bacterium that can infect mosquitoes and reduce their ability to transmit diseases. While initially used to control dengue fever, recent research explored its potential for malaria control. In this study, we develop and analyze a novel mathematical model to assess the potential use of Wolbachia-based strategies for malaria control. The model describes the complex Wolbachia transmission dynamics among mosquitoes and incorporates key features of malaria transmission in humans with dynamical immunity feedback. We derive the basic reproduction number of the malaria disease transmission, which depends on the prevalence of Wolbachia in mosquitoes. Our findings reveal bifurcations in both Wolbachia transmission among mosquitoes and malaria transmission in humans, suggesting the potential for malaria elimination through Wolbachia-based interventions. The sensitivity analysis identifies the important parameters for the basic reproduction number and for malaria reduction and elimination. We numerically explore the integration of Wolbachia and other malaria controls. When control focuses on reducing the malaria burden in humans, there is a substantial rebound in malaria prevalence following the intervention in humans, and our results suggest post-Wolbachia malaria control leads to the greatest reduction in total days of infection. When Wolbachia release is integrated with pre-release mosquito control, there is a comparably large reduction in total days of infection if pre-release mosquito control occurs only a few days before Wolbachia release.
{"title":"Assessing the impact of the Wolbachia-based control of malaria","authors":"Zhuolin Qu , Lauren M. Childs","doi":"10.1016/j.mbs.2025.109466","DOIUrl":"10.1016/j.mbs.2025.109466","url":null,"abstract":"<div><div>Malaria remains a significant infectious disease globally, causing hundreds of thousands of deaths each year. Traditional control methods, such as disease surveillance and mosquito control, along with the development of malaria vaccines, have made strides in reducing the disease’s impact, but new control methods are urgently needed. <em>Wolbachia</em> is a natural bacterium that can infect mosquitoes and reduce their ability to transmit diseases. While initially used to control dengue fever, recent research explored its potential for malaria control. In this study, we develop and analyze a novel mathematical model to assess the potential use of <em>Wolbachia</em>-based strategies for malaria control. The model describes the complex <em>Wolbachia</em> transmission dynamics among mosquitoes and incorporates key features of malaria transmission in humans with dynamical immunity feedback. We derive the basic reproduction number of the malaria disease transmission, which depends on the prevalence of <em>Wolbachia</em> in mosquitoes. Our findings reveal bifurcations in both <em>Wolbachia</em> transmission among mosquitoes and malaria transmission in humans, suggesting the potential for malaria elimination through <em>Wolbachia</em>-based interventions. The sensitivity analysis identifies the important parameters for the basic reproduction number and for malaria reduction and elimination. We numerically explore the integration of <em>Wolbachia</em> and other malaria controls. When control focuses on reducing the malaria burden in humans, there is a substantial rebound in malaria prevalence following the intervention in humans, and our results suggest post-<em>Wolbachia</em> malaria control leads to the greatest reduction in total days of infection. When <em>Wolbachia</em> release is integrated with pre-release mosquito control, there is a comparably large reduction in total days of infection if pre-release mosquito control occurs only a few days before <em>Wolbachia</em> release.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"387 ","pages":"Article 109466"},"PeriodicalIF":1.9,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144562489","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 : 2025-06-29DOI: 10.1016/j.mbs.2025.109495
Xiaoke Ma, Ying Su
The release of Wolbachia-infected mosquitoes is a promising and biologically safe measure for controlling wild mosquitoes. Numerous studies have been devoted to finding optimal control strategies using mathematical tools. However, the effects of dispersal of uninfected and infected mosquitoes remain poorly understood. To characterize the spatial discretization of release sites, we investigate a two-patch mosquito suppression model with time delay and impulsive release. Specifically, we assume that the waiting period between two consecutive releases is equal to the sexual lifespan of infected males. We confirm the well-posedness and monotonicity of the solution and explore the existence and stability of equilibria. By some technical skills, sufficient conditions for the bistable dynamics are provided. Then, the existence of the unstable separatrix is established by some sharp estimates when choosing constant functions as initial values. More interestingly, the monotonicity of this separatrix in the release number is proved, implying the existence of an optimal release strategy. We further find that uniform release on two patches is more effective than single-patch release. Additionally, the higher the cytoplasmic incompatibility intensity, the more likely wild mosquitoes are to be suppressed.
{"title":"Threshold dynamics of a Wolbachia-driven mosquito suppression model on two patches","authors":"Xiaoke Ma, Ying Su","doi":"10.1016/j.mbs.2025.109495","DOIUrl":"10.1016/j.mbs.2025.109495","url":null,"abstract":"<div><div>The release of <em>Wolbachia</em>-infected mosquitoes is a promising and biologically safe measure for controlling wild mosquitoes. Numerous studies have been devoted to finding optimal control strategies using mathematical tools. However, the effects of dispersal of uninfected and infected mosquitoes remain poorly understood. To characterize the spatial discretization of release sites, we investigate a two-patch mosquito suppression model with time delay and impulsive release. Specifically, we assume that the waiting period between two consecutive releases is equal to the sexual lifespan of infected males. We confirm the well-posedness and monotonicity of the solution and explore the existence and stability of equilibria. By some technical skills, sufficient conditions for the bistable dynamics are provided. Then, the existence of the unstable separatrix is established by some sharp estimates when choosing constant functions as initial values. More interestingly, the monotonicity of this separatrix in the release number is proved, implying the existence of an optimal release strategy. We further find that uniform release on two patches is more effective than single-patch release. Additionally, the higher the cytoplasmic incompatibility intensity, the more likely wild mosquitoes are to be suppressed.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"387 ","pages":"Article 109495"},"PeriodicalIF":1.9,"publicationDate":"2025-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144532102","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 : 2025-06-29DOI: 10.1016/j.mbs.2025.109499
Arsène Jaurès Ouemba Tassé , Yibetal Terefe , Jean Lubuma
Mpox, originating primarily in African rodents, has led to human outbreaks over recent years. This study presents a mathematical model for Mpox, distinguishing between individuals with and without HIV who are susceptible. We explore scenarios involving both rodent-to-human transmission and those without it. In the absence of this transmission route, the model undergoes a backward bifurcation, suggesting that reducing the basic reproduction number below one would not eliminate the disease unless further control strategies are used. With the account of rodent-to-human transmission, if Mpox is endemic in the rodent population, a unique interior equilibrium, globally asymptotically stable, exists, requiring targeted interventions like quarantine or vaccination for people with HIV (PWH) for disease control. Model validation using USA case data (May 2022–July 2024) shows that both human-to-human and rodent-to-human transmissions prevail in the population, but the disease is not endemic. Projections indicate that the outbreak will be overcome by May 2027, with a total of 35,811 cases. We design a nonstandard finite difference (NSFD) scheme which is dynamically consistent with respect to the qualitative properties of the continuous model. Numerical simulations demonstrate that reducing the recruitment rate of PWH is essential, and rodent-to-human transmission is identified as highly influential in increasing the number of Mpox cases.
{"title":"Assessing the influence of HIV on the spread of Mpox disease","authors":"Arsène Jaurès Ouemba Tassé , Yibetal Terefe , Jean Lubuma","doi":"10.1016/j.mbs.2025.109499","DOIUrl":"10.1016/j.mbs.2025.109499","url":null,"abstract":"<div><div>Mpox, originating primarily in African rodents, has led to human outbreaks over recent years. This study presents a mathematical model for Mpox, distinguishing between individuals with and without HIV who are susceptible. We explore scenarios involving both rodent-to-human transmission and those without it. In the absence of this transmission route, the model undergoes a backward bifurcation, suggesting that reducing the basic reproduction number below one would not eliminate the disease unless further control strategies are used. With the account of rodent-to-human transmission, if Mpox is endemic in the rodent population, a unique interior equilibrium, globally asymptotically stable, exists, requiring targeted interventions like quarantine or vaccination for people with HIV (PWH) for disease control. Model validation using USA case data (May 2022–July 2024) shows that both human-to-human and rodent-to-human transmissions prevail in the population, but the disease is not endemic. Projections indicate that the outbreak will be overcome by May 2027, with a total of 35,811 cases. We design a nonstandard finite difference (NSFD) scheme which is dynamically consistent with respect to the qualitative properties of the continuous model. Numerical simulations demonstrate that reducing the recruitment rate of PWH is essential, and rodent-to-human transmission is identified as highly influential in increasing the number of Mpox cases.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"387 ","pages":"Article 109499"},"PeriodicalIF":1.9,"publicationDate":"2025-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144517846","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 : 2025-06-27DOI: 10.1016/j.mbs.2025.109485
Paolo Climaco , Noelle M. Mitchell , Matthew J. Tyler , Kyungae Yang , Anne M. Andrews , Andrea L. Bertozzi
Aptamers are oligonucleotide receptors that bind to their targets with high affinity. Here, we consider aptamers comprised of single-stranded DNA that undergo target-binding-induced conformational changes, giving rise to unique secondary and tertiary structures. Given a specific aptamer primary sequence, there are well-established computational tools (notably mfold) to predict the secondary structure via free energy minimization algorithms. While mfold generates secondary structures for individual sequences, there is a need for a high-throughput process whereby thousands of DNA structures can be predicted in real-time for use in an interactive setting, when combined with aptamer selections that generate candidate pools that are too large to be experimentally interrogated. We developed a new Python code for high-throughput aptamer secondary structure determination (GMfold). GMfold uses subgraph matching methods to group aptamer candidates by secondary structure similarities. We also improve an open-source code, SeqFold, to incorporate subgraph matching concepts. We represent each secondary structure as a lowest-energy bipartite subgraph matching of the DNA graph to itself. These new tools enable thousands of DNA sequences to be compared based on their secondary structures, using machine-learning algorithms. This process is advantageous when analyzing sequences that arise from aptamer selections via systematic evolution of ligands by exponential enrichment (SELEX). This work is a building block for future machine-learning-informed DNA-aptamer selection processes to identify aptamers with improved target affinity and selectivity and advance aptamer biosensors and therapeutics.
{"title":"GMFOLD: Subgraph matching for high-throughput DNA-aptamer secondary structure classification and machine learning interpretability","authors":"Paolo Climaco , Noelle M. Mitchell , Matthew J. Tyler , Kyungae Yang , Anne M. Andrews , Andrea L. Bertozzi","doi":"10.1016/j.mbs.2025.109485","DOIUrl":"10.1016/j.mbs.2025.109485","url":null,"abstract":"<div><div>Aptamers are oligonucleotide receptors that bind to their targets with high affinity. Here, we consider aptamers comprised of single-stranded DNA that undergo target-binding-induced conformational changes, giving rise to unique secondary and tertiary structures. Given a specific aptamer primary sequence, there are well-established computational tools (notably mfold) to predict the secondary structure via free energy minimization algorithms. While mfold generates secondary structures for individual sequences, there is a need for a high-throughput process whereby thousands of DNA structures can be predicted in real-time for use in an interactive setting, when combined with aptamer selections that generate candidate pools that are too large to be experimentally interrogated. We developed a new Python code for high-throughput aptamer secondary structure determination (GMfold). GMfold uses subgraph matching methods to group aptamer candidates by secondary structure similarities. We also improve an open-source code, SeqFold, to incorporate subgraph matching concepts. We represent each secondary structure as a lowest-energy bipartite subgraph matching of the DNA graph to itself. These new tools enable thousands of DNA sequences to be compared based on their secondary structures, using machine-learning algorithms. This process is advantageous when analyzing sequences that arise from aptamer selections via systematic evolution of ligands by exponential enrichment (SELEX). This work is a building block for future machine-learning-informed DNA-aptamer selection processes to identify aptamers with improved target affinity and selectivity and advance aptamer biosensors and therapeutics.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"387 ","pages":"Article 109485"},"PeriodicalIF":1.9,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144532101","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 : 2025-06-23DOI: 10.1016/j.mbs.2025.109483
Eymard Hernandez-Lopez, Xiunan Wang
In this work, we investigate the impact of the dual Allee effects on tumor-immune interactions using an ordinary differential equation model. We analyze how the strength of the Allee effect in both effector and cancer cell populations influences the stability of equilibrium points. Our results suggest that moderate positive values of Allee effects can promote rapid population growth and complex population dynamics. In contrast, larger values of the Allee effects reduce the system’s dynamical complexity. The model exhibits a rich bifurcation structure, including saddle–node and Hopf bifurcations (co-dimension one) as well as generalized Hopf and Bogdanov–Takens bifurcations (co-dimension two). These findings highlight the importance of identifying critical thresholds in tumor-immune interactions, which could be leveraged for personalized antitumor treatments.
{"title":"Bifurcation analysis of tumor-immune dynamics under the dual Allee effects","authors":"Eymard Hernandez-Lopez, Xiunan Wang","doi":"10.1016/j.mbs.2025.109483","DOIUrl":"10.1016/j.mbs.2025.109483","url":null,"abstract":"<div><div>In this work, we investigate the impact of the dual Allee effects on tumor-immune interactions using an ordinary differential equation model. We analyze how the strength of the Allee effect in both effector and cancer cell populations influences the stability of equilibrium points. Our results suggest that moderate positive values of Allee effects can promote rapid population growth and complex population dynamics. In contrast, larger values of the Allee effects reduce the system’s dynamical complexity. The model exhibits a rich bifurcation structure, including saddle–node and Hopf bifurcations (co-dimension one) as well as generalized Hopf and Bogdanov–Takens bifurcations (co-dimension two). These findings highlight the importance of identifying critical thresholds in tumor-immune interactions, which could be leveraged for personalized antitumor treatments.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"387 ","pages":"Article 109483"},"PeriodicalIF":1.9,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144499929","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 : 2025-06-21DOI: 10.1016/j.mbs.2025.109480
Tianyu Cheng, Jianhong Wu
We introduce a coupled system of a disease transmission differential equation and a behavioral adaptation algebraic renewal equation to understand the mechanisms of nonlinear oscillations post-acute phase of a pandemic. This extends the Zhang–Scarabel–Murty–Wu model, which was formulated and analyzed to describe multi-wave patterns observed at the early stage during the acute phase of the COVID-19 pandemic. Our extension involves the depletion of susceptible population due to infection and contains a nonlinear disease transmission term to reflect the recovery and temporal immunity in the infected population past the acute phase of the pandemic. Examining whether and how incorporating this depletion of susceptible population impacts interwoven disease transmission dynamics and behavioral adaptation is the objective of our current research. We introduce some prototypical risk aversion functions to characterize behavioral responses to perceived risks and show how the risk aversion behaviors and the logistic delay in implementation of behavioral adaptation combined contribute to a dynamic equilibrium state described by a periodic oscillatory wave. We also link the period between two consecutive peaks to basic epidemic parameters, the community flexibility to behavioral change, and the population’s tolerance to perceived risks.
{"title":"Recurrent patterns of disease spread post the acute phase of a pandemic: Insights from a coupled system of a differential equation for disease transmission and a delayed algebraic equation for behavioral adaptation","authors":"Tianyu Cheng, Jianhong Wu","doi":"10.1016/j.mbs.2025.109480","DOIUrl":"10.1016/j.mbs.2025.109480","url":null,"abstract":"<div><div>We introduce a coupled system of a disease transmission differential equation and a behavioral adaptation algebraic renewal equation to understand the mechanisms of nonlinear oscillations post-acute phase of a pandemic. This extends the Zhang–Scarabel–Murty–Wu model, which was formulated and analyzed to describe multi-wave patterns observed at the early stage during the acute phase of the COVID-19 pandemic. Our extension involves the depletion of susceptible population due to infection and contains a nonlinear disease transmission term to reflect the recovery and temporal immunity in the infected population past the acute phase of the pandemic. Examining whether and how incorporating this depletion of susceptible population impacts interwoven disease transmission dynamics and behavioral adaptation is the objective of our current research. We introduce some prototypical risk aversion functions to characterize behavioral responses to perceived risks and show how the risk aversion behaviors and the logistic delay in implementation of behavioral adaptation combined contribute to a dynamic equilibrium state described by a periodic oscillatory wave. We also link the period between two consecutive peaks to basic epidemic parameters, the community flexibility to behavioral change, and the population’s tolerance to perceived risks.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"387 ","pages":"Article 109480"},"PeriodicalIF":1.9,"publicationDate":"2025-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144478349","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 : 2025-06-21DOI: 10.1016/j.mbs.2025.109500
Atsushi Yamauchi
The colonization model, also known as the Levins model, has been developed to understand the mechanisms that drive species coexistence under interspecific competition. Previous simulation studies have shown that the dynamic properties of the model significantly depend on the encounter mode between propagules and colonization sites. Perfect mass action encounters result in convergence towards equilibrium, while perfect ratio-dependent encounters lead to multiple continuously transient trajectories that depend on the initial condition. In the present study, I investigate the properties of the dynamics by transforming the colonization model into a Lotka-Volterra model. I show that the eigenvalues of the Jacobian matrix indicate stability of the equilibrium under perfect mass action encounters, while the Lyapunov function shows the existence of an infinite number of continuously transient trajectories under perfect ratio-dependent encounters. These results highlight new properties of Lotka-Volterra systems and the colonization model, and provide new insights into the mechanisms and dynamic processes involved in the coexistence of multiple species.
{"title":"Dynamic properties of Lotka–Volterra systems corresponding to the colonization model","authors":"Atsushi Yamauchi","doi":"10.1016/j.mbs.2025.109500","DOIUrl":"10.1016/j.mbs.2025.109500","url":null,"abstract":"<div><div>The colonization model, also known as the Levins model, has been developed to understand the mechanisms that drive species coexistence under interspecific competition. Previous simulation studies have shown that the dynamic properties of the model significantly depend on the encounter mode between propagules and colonization sites. Perfect mass action encounters result in convergence towards equilibrium, while perfect ratio-dependent encounters lead to multiple continuously transient trajectories that depend on the initial condition. In the present study, I investigate the properties of the dynamics by transforming the colonization model into a Lotka-Volterra model. I show that the eigenvalues of the Jacobian matrix indicate stability of the equilibrium under perfect mass action encounters, while the Lyapunov function shows the existence of an infinite number of continuously transient trajectories under perfect ratio-dependent encounters. These results highlight new properties of Lotka-Volterra systems and the colonization model, and provide new insights into the mechanisms and dynamic processes involved in the coexistence of multiple species.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"387 ","pages":"Article 109500"},"PeriodicalIF":1.9,"publicationDate":"2025-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144478348","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 time-to-recovery or time-to-death for various infectious diseases can vary significantly among individuals, influenced by several factors such as demographic differences, immune strength, medical history, age, pre-existing conditions, and infection severity. To capture these variations, time-since-infection dependent recovery and death rates offer a detailed description of the epidemic. However, obtaining individual-level data to estimate these rates is challenging, while aggregate epidemiological data (such as the number of new infections, number of active cases, number of new recoveries, and number of new deaths) are more readily available. In this article, a new methodology is proposed to estimate time-since-infection dependent recovery and death rates using easily available data sources, accommodating irregular data collection timings reflective of real-world reporting practices. The Nadaraya–Watson estimator is utilized to derive the number of new infections. This model improves the accuracy of epidemic progression descriptions and provides clear insights into recovery and death distributions. The proposed methodology is validated using COVID-19 data and its general applicability is demonstrated by applying it to some other diseases like measles and typhoid.
{"title":"Estimation of time-varying recovery and death rates from epidemiological data: A new approach","authors":"Samiran Ghosh , Malay Banerjee , Subhra Sankar Dhar , Siuli Mukhopadhyay","doi":"10.1016/j.mbs.2025.109479","DOIUrl":"10.1016/j.mbs.2025.109479","url":null,"abstract":"<div><div>The time-to-recovery or time-to-death for various infectious diseases can vary significantly among individuals, influenced by several factors such as demographic differences, immune strength, medical history, age, pre-existing conditions, and infection severity. To capture these variations, time-since-infection dependent recovery and death rates offer a detailed description of the epidemic. However, obtaining individual-level data to estimate these rates is challenging, while aggregate epidemiological data (such as the number of new infections, number of active cases, number of new recoveries, and number of new deaths) are more readily available. In this article, a new methodology is proposed to estimate time-since-infection dependent recovery and death rates using easily available data sources, accommodating irregular data collection timings reflective of real-world reporting practices. The Nadaraya–Watson estimator is utilized to derive the number of new infections. This model improves the accuracy of epidemic progression descriptions and provides clear insights into recovery and death distributions. The proposed methodology is validated using COVID-19 data and its general applicability is demonstrated by applying it to some other diseases like measles and typhoid.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"387 ","pages":"Article 109479"},"PeriodicalIF":1.9,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144277096","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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