Mathematical Biosciences最新文献

{"title":"Fractional modelling of COVID-19 transmission incorporating asymptomatic and super-spreader individuals","authors":"Moein Khalighi ,&nbsp;Leo Lahti ,&nbsp;Faïçal Ndaïrou ,&nbsp;Peter Rashkov ,&nbsp;Delfim F.M. Torres","doi":"10.1016/j.mbs.2024.109373","DOIUrl":"10.1016/j.mbs.2024.109373","url":null,"abstract":"<div><div>The COVID-19 pandemic has presented unprecedented challenges worldwide, necessitating effective modelling approaches to understand and control its transmission dynamics. In this study, we propose a novel approach that integrates asymptomatic and super-spreader individuals in a single compartmental model. We highlight the advantages of utilizing incommensurate fractional order derivatives in ordinary differential equations, including increased flexibility in capturing disease dynamics and refined memory effects in the transmission process. We conduct a qualitative analysis of our proposed model, which involves determining the basic reproduction number and analysing the disease-free equilibrium’s stability. By fitting the proposed model with real data from Portugal and comparing it with existing models, we demonstrate that the incorporation of supplementary population classes and fractional derivatives significantly improves the model’s goodness of fit. Sensitivity analysis further provides valuable insights for designing effective strategies to mitigate the spread of the virus.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"380 ","pages":"Article 109373"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142928951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Chemotaxis effects on the vascular tumor growth: Phase-field model and simulations","authors":"Soroosh Arshadi ,&nbsp;Ahmadreza Pishevar ,&nbsp;Mahdi Javanbakht ,&nbsp;Shaghayegh Haghjooy Javanmard","doi":"10.1016/j.mbs.2024.109366","DOIUrl":"10.1016/j.mbs.2024.109366","url":null,"abstract":"<div><div>In this paper, we propose a vascular tumor growth model that combines a phase-field tumor model with a phase-field angiogenesis model. By incorporating various tumor cell species, we capture the instabilities of the tumor in the presence of evolving neovasculature. The model not only considers different dynamics of tumor cell phase conversions, movement, and pressure effects but also provides a comprehensive representation of angiogenesis, encompassing chemotaxis of endothelial cells, sprouting, anastomoses, and blood flow in capillaries. This study evaluates the impact of chemotaxis on tumor cell movement in both avascular and vascular tumor growth scenarios. The results highlight the acceleration of tumor growth when angiogenesis is stimulated. Additionally, the investigation explores various initial distances of the tumor from neighboring vessels, revealing a critical threshold distance beyond which the angiogenesis factor fails to stimulate angiogenesis, resulting in the tumor maintaining a stable state. The integration of chemotaxis into the growth model induces instabilities, leading to increased nutrient availability and faster growth for the tumor. Furthermore, the study considers anti-angiogenesis therapy as an ideal approach, assuming complete inhibition of angiogenesis from the early stages. In this scenario, the tumor persists in a steady state, adhering to the avascular size limit in the absence of neovasculature. Conversely, when considering chemotaxis, anti-angiogenesis therapy loses efficiency, enabling unrestrained tumor growth towards neighboring vessels. This work sheds light on the intricate interplay among chemotaxis, angiogenesis, and anti-angiogenesis therapy in the context of vascular tumor growth, providing valuable insights for the development of targeted treatment strategies.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"380 ","pages":"Article 109366"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142840715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A simple model of coupled individual behavior and its impact on epidemic dynamics","authors":"Jiangzhuo Chen ,&nbsp;Baltazar Espinoza ,&nbsp;Jingyuan Chou ,&nbsp;Abba B. Gumel ,&nbsp;Simon A. Levin ,&nbsp;Madhav Marathe","doi":"10.1016/j.mbs.2024.109345","DOIUrl":"10.1016/j.mbs.2024.109345","url":null,"abstract":"<div><div>Containing infectious disease outbreaks is a complex challenge that usually requires the deployment of multiple intervention strategies. While mathematical modeling of infectious diseases is a widely accepted tool to evaluate intervention strategies, most models and studies overlook the interdependence between individuals’ reactions to simultaneously implemented interventions. Intervention modeling efforts typically assume that individual adherence decisions are independent of each other. However, in the real world, individuals who are willing to comply with certain interventions may be more or less likely to comply with another intervention. The combined effect of interventions may depend on the correlation between adherence decisions. In this study, we consider vaccination and non-pharmaceutical interventions, and study how the correlation between individuals’ behaviors towards these two interventions strategies affects the epidemiological outcomes. Furthermore, we integrate disease surveillance in our model to study the effects of interventions triggered by surveillance events. This allows us to model a realistic operational context where surveillance informs the timing of interventions deployment, thereby influencing disease dynamics. Our results demonstrate the diverse effects of coupled individual behavior and highlight the importance of robust surveillance systems. Our study yields the following insights: <span><math><mrow><mo>(</mo><mi>i</mi><mo>)</mo></mrow></math></span> there exists a correlation level that minimizes the initial prevalence peak size; <span><math><mrow><mo>(</mo><mi>i</mi><mi>i</mi><mo>)</mo></mrow></math></span> the optimal correlation level depends on the disease’s basic reproduction number; <span><math><mrow><mo>(</mo><mi>i</mi><mi>i</mi><mi>i</mi><mo>)</mo></mrow></math></span> disease surveillance modulates the impact of interventions on reducing the epidemic burden.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"380 ","pages":"Article 109345"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142857339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The impact of risk compensation adaptive behavior on the final epidemic size","authors":"Baltazar Espinoza ,&nbsp;Jiangzhuo Chen ,&nbsp;Mark Orr ,&nbsp;Chadi M. Saad-Roy ,&nbsp;Simon A. Levin ,&nbsp;Madhav Marathe","doi":"10.1016/j.mbs.2024.109370","DOIUrl":"10.1016/j.mbs.2024.109370","url":null,"abstract":"<div><div>Public health interventions reduce infection risk, while imposing significant costs on both individuals and the society. Interventions can also lead to behavioral changes, as individuals weigh the cost and benefits of avoiding infection. Aggregate epidemiological models typically focus on the population-level consequences of interventions, often not incorporating the mechanisms driving behavioral adaptations associated with interventions compliance. In this study, we use a behavior-epidemic model to analyze the consequences of detrimental behavioral responses driven by risk compensation. We analyze scenarios with varying levels of vaccine-acquired immunity and study the trade-off between risk compensation behaviors and reduced susceptibility. Our results reveal a trade-off between imperfect vaccine-acquired immunity and the potential risk compensation behavior of vaccinated individuals. We find that the impact of vaccination is ultimately influenced by the risk compensation behaviors of vaccinated individuals, which can either increase or decrease the size of the epidemic depending on the vaccine effectiveness. Moreover, we show that the behavioral response of the susceptible population modulates the impact of compensation behaviors by vaccinated individuals. Our results highlight that the distribution of highly protective vaccines can mitigate the observed effect. Additionally, they emphasize the importance of concurrently implementing non-pharmaceutical interventions in scenarios wherein vaccines have low efficacy. We extend our model by incorporating a model of disease surveillance, which drives a realistic operational course of action based on testing, analysis and response. Our results highlight the importance of robust surveillance systems in providing early warnings of disease outbreaks, which trigger early behavioral responses and timely interventions.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"380 ","pages":"Article 109370"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142928150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effects of nonlinear impulsive controls and seasonality on hantavirus infection","authors":"Yuhang Li,&nbsp;Yanni Xiao","doi":"10.1016/j.mbs.2025.109378","DOIUrl":"10.1016/j.mbs.2025.109378","url":null,"abstract":"<div><div>Hemorrhagic fever with renal syndrome (HFRS) caused by hantavirus is prevalent across China and causes a significant number of deaths every year. This study aims to examine the transmission dynamics of hantavirus and to suggest effective control measures. We extend a periodic model of HFRS infection including house/field mice, contaminated environments, and the human population by introducing nonlinear pulses used to describe impulsive interventions. In our model, the systemic period determined by natural factors may be inconsistent with the periods of control strategies for the two kinds of mice. We prove that the model is uniformly and ultimately bounded and discuss the existence and uniqueness of the disease-free periodic solution. We calculate the basic reproduction number for the house/field mouse subsystem denoted by <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>01</mn></mrow></msub></math></span>/<span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>02</mn></mrow></msub></math></span>. We then examine the threshold dynamics and analyze the conditions for global asymptotic stability of the disease-free periodic solution. Additionally, we determine that the HFRS infection uniformly persists in the human population when <span><math><mrow><mo>max</mo><mrow><mo>{</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>01</mn></mrow></msub><mo>,</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>02</mn></mrow></msub><mo>}</mo></mrow><mo>&gt;</mo><mn>1</mn></mrow></math></span>. Further, the existence of nontrivial periodic solutions for subsystems is examined via bifurcation theory. In particular, we observe complicated dynamics in the proposed model with multiple periods and nonlinear pulses. By fitting data on HFRS cases, we estimate the unknown parameters and predict the trend of HFRS infection in the human population. Numerical simulations show that enhancing the intensity and frequency of culling mice could curb the spread of hantavirus. Our findings suggest that improving the vaccination rate and decreasing the number of rodents, especially wild mice, are crucial in reducing HFRS infection.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"380 ","pages":"Article 109378"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143019028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Competing mechanisms for the buckling of an epithelial monolayer identified using multicellular simulation","authors":"Phillip J. Brown ,&nbsp;J. Edward F. Green ,&nbsp;Benjamin J. Binder ,&nbsp;James M. Osborne","doi":"10.1016/j.mbs.2024.109367","DOIUrl":"10.1016/j.mbs.2024.109367","url":null,"abstract":"<div><div>A model using the rigid body multi-cellular framework (RBMCF) is implemented to investigate the mechanisms of buckling of an epithelial monolayer. Specifically, the deformation of a monolayer of epithelial cells which are attached to a basement membrane and the surrounding stromal tissue. The epithelial monolayer, supporting basement membrane and stromal tissue are modelled using two separate vertex dynamics models (one for the epithelial monolayer layer and one for the basement membrane and stromal tissue combined) and interactions between the two are considered using the RBMCF to ensure biologically realistic interactions. Model simulations are used to investigate the effects of cell–stromal attachment and membrane rigidity on buckling behaviour. We demonstrate that there are two competing modes of buckling, stromal deformation and stromal separation.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"380 ","pages":"Article 109367"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142901508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A constrained optimisation framework for parameter identification of the SIRD model","authors":"Andrés Miniguano–Trujillo ,&nbsp;John W. Pearson ,&nbsp;Benjamin D. Goddard","doi":"10.1016/j.mbs.2025.109379","DOIUrl":"10.1016/j.mbs.2025.109379","url":null,"abstract":"<div><div>We consider a numerical framework tailored to identifying optimal parameters in the context of modelling disease propagation. Our focus is on understanding the behaviour of optimisation algorithms for such problems, where the dynamics are described by a system of ordinary differential equations associated with the epidemiological SIRD model. Applying an optimise-then-discretise approach, we examine properties of the solution operator and determine existence of optimal parameters for the problem considered. Further, first-order optimality conditions are derived, the solution of which provides a certificate of goodness of fit, which is not always guaranteed with parameter tuning techniques. We then propose strategies for the numerical solution of such problems, based on projected gradient descent, Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), nonmonotone Accelerated Proximal Gradient (nmAPG), and limited memory BFGS trust-region approaches. We carry out a thorough computational study for a range of problems of interest, determining the relative performance of these numerical methods. Our results provide insights into the effectiveness of these strategies, contributing to ongoing research into optimising parameters for accurate and reliable disease spread modelling. Moreover, our approach paves the way for calibration of more intricate compartmental models.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"380 ","pages":"Article 109379"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142981076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigating seasonal disease emergence and extinction in stochastic epidemic models","authors":"Mahmudul Bari Hridoy,&nbsp;Linda J.S. Allen","doi":"10.1016/j.mbs.2025.109383","DOIUrl":"10.1016/j.mbs.2025.109383","url":null,"abstract":"<div><div>Seasonal disease outbreaks are common in many infectious diseases such as seasonal influenza, Zika, dengue fever, Lyme disease, malaria, and cholera. Seasonal outbreaks are often due to weather patterns affecting pathogens or disease-carrying vectors or by social behavior. We investigate disease emergence and extinction in seasonal stochastic epidemic models. Specifically, we study disease emergence through seasonally varying parameters for transmission, recovery, and vector births and deaths in time-nonhomogeneous Markov chains for SIR, SEIR, and vector-host systems. A branching process approximation of the Markov chain is used to estimate the seasonal probabilities of disease extinction. Several disease outcome measures are used to compare the dynamics in seasonal and constant environments. Numerical investigations illustrate and confirm previous results derived from stochastic epidemic models. Seasonal environments often result in lower probabilities of disease emergence and smaller values of the basic reproduction number than in constant environments, and the time of peak emergence generally precedes the peak time of the seasonal driver. We identify some new results when both transmission and recovery vary seasonally. If the relative amplitude of the recovery exceeds that of transmission or if the periodicity is not synchronized in time, lower average probabilities of disease emergence occur in a constant environment than in a seasonal environment. We also investigate the timing of vector control. This investigation provides new methods and outcome measures to study seasonal infectious disease dynamics and offers new insights into the timing of prevention and control.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"381 ","pages":"Article 109383"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143124192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A numerical evaluation of the economic tradeoff of vaccination against chikungunya virus in Brazil","authors":"Vinicius V.L. Albani ,&nbsp;Eduardo Massad","doi":"10.1016/j.mbs.2025.109376","DOIUrl":"10.1016/j.mbs.2025.109376","url":null,"abstract":"<div><div>This article uses a compartmental model describing the dynamic of the chikungunya virus in populations of humans and mosquitoes with parameters fitted to the incidence in Brazil to estimate the economic trade-off of vaccination against the virus infection. The model uses time-dependent parameters to incorporate fluctuations in the transmission and the mosquito population across the years. Using the model predictions of symptomatic infections and literature data concerning the proportions of post-acute and chronic cases, the vaccination cost is compared with the disease cost. Numerical results considering different scenarios indicate that vaccination has a limited impact on reducing the disease cost assuming that vaccination is applied uniformly countrywide. We do not consider regional targets. In some scenarios, vaccinating about 10<span><math><mtext>%</mtext></math></span> of the population as early as possible can reduce the disease cost and is more economically efficient. Larger proportions make vaccination not viable.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"380 ","pages":"Article 109376"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142967434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A nonautonomous model for the impact of toxicants on size-structured aquatic populations: Well-posedness and long-term dynamics","authors":"Xiumei Deng ,&nbsp;Qihua Huang ,&nbsp;Hao Wang","doi":"10.1016/j.mbs.2025.109382","DOIUrl":"10.1016/j.mbs.2025.109382","url":null,"abstract":"<div><div>Mathematical models have played a crucial role in understanding and assessing the impacts of toxicants on populations. However, many existing population-toxicant interaction models are physically unstructured and represented by autonomous systems, assuming all individuals are identical and model parameters are constant over time. In this paper, we develop a nonautonomous model describing the interaction between a size-structured population and an unstructured toxicant in a polluted aquatic ecosystem. This model allows us to investigate the influence of size- and time-dependent individual vital rates (growth, reproduction, and mortality), time-varying toxicant input and degradation, and size-specific sensitivity of individuals to toxicants on population persistence. We establish the existence and uniqueness of solutions for this model using the monotone method, based on a comparison principle. We then analyze how time- and size-dependent parameters affect the long-term population dynamics. Specifically, we derive conditions on these parameters that lead to either extinction or persistence of the population. We provide a comparative analysis of numerical solutions between our size-structured model and an unstructured model with size-averaged parameters, emphasizing the significance of incorporating size structure when evaluating the effects of toxicants on populations.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"381 ","pages":"Article 109382"},"PeriodicalIF":1.9,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143082906","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}