Mathematical Biosciences最新文献

{"title":"A geometric approach to the impact of immigration of people infected with communicable diseases","authors":"Sofía Guarello ,&nbsp;Nicolás González ,&nbsp;Isabel Flores ,&nbsp;Pablo Aguirre","doi":"10.1016/j.mbs.2024.109320","DOIUrl":"10.1016/j.mbs.2024.109320","url":null,"abstract":"<div><div>We construct a set of new epidemiological thresholds to address the general problem of spreading and containment of a transmissible disease with influx of infected individuals (i.e., when the classic <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is no longer meaningful). We provide analytical properties of these indices and illustrate their usefulness in a compartmental model of COVID-19 with data taken from Chile showing a good predictive potential when contrasted with the recorded disease behavior. This geometric approach and the associated analytical and numerical results break new ground in that they allow us to quantify the severity of an immigration of infectious individuals into a community, and identification of the key parameters that are capable of changing or reversing the spread of an infectious disease in specific models.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"378 ","pages":"Article 109320"},"PeriodicalIF":1.9,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142515514","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":"On the necessity of accounting for age structure in human malaria transmission modeling","authors":"Quentin Richard ,&nbsp;Marc Choisy ,&nbsp;Thierry Lefèvre ,&nbsp;Ramsès Djidjou-Demasse","doi":"10.1016/j.mbs.2024.109319","DOIUrl":"10.1016/j.mbs.2024.109319","url":null,"abstract":"<div><div>Malaria is one of the most common mosquito-borne diseases widespread in tropical and subtropical regions, causing thousands of deaths every year in the world. In a previous paper, we formulated an age-structured model containing three structural variables: (i) the chronological age of human and mosquito populations, (ii) the time since they are infected, and (iii) humans waning immunity (i.e. the progressive loss of protective antibodies after recovery). In the present paper, we expand the analysis of this age-structured model and focus on the derivation of entomological and epidemiological results commonly used in the literature, following the works of Smith and McKenzie. We generalize their results to the age-structured case. In order to quantify the impact of neglecting structuring variables such as chronological age, we assigned values from the literature to our model parameters. While some parameters values are readily accessible from the literature, at least those about the human population, the parameters concerning mosquitoes are less commonly documented and the values of a number of them (<em>e.g.</em> mosquito survival in the presence or in absence of infection) can be discussed extensively. Our analysis, informed by parameter values from the literature, demonstrates that overlooking those structural variables of human and mosquito populations may result in inaccurate epidemiological predictions and suboptimal control strategies. We highlight the epidemiological implications of these findings and emphasize the necessity of considering age structure in future malaria control programs.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"378 ","pages":"Article 109319"},"PeriodicalIF":1.9,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142515515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A mathematical model of Cheyne-Stokes or periodic breathing","authors":"John B. Delos","doi":"10.1016/j.mbs.2024.109318","DOIUrl":"10.1016/j.mbs.2024.109318","url":null,"abstract":"<div><div>Cheyne-Stokes Breathing is a periodic cycle of apnea followed by hyperventilation. A theory of this phenomenon is developed based on a minimal set of physiological assumptions. The rate of loss of CO₂ from venous blood is proportional to the CO₂ concentration in the lungs times the respiration rate; the respiration rate is a linear function of arterial CO₂ concentration above a threshold, and zero below that threshold. A time delay between blood in lungs and respiratory response allows the system to go into oscillation. These assumptions lead to a single nonanalytic delay-differential equation containing only three parameters, which we call respiratory recovery coefficients, <span><math><mrow><mo>(</mo><mi>α</mi><mo>,</mo><mi>β</mi><mo>,</mo><mi>γ</mi><mo>)</mo></mrow></math></span>. A detailed study of the solutions to this equation is presented here. For <span><math><mi>β</mi></math></span> below a first threshold, breathing becomes steady, and any disturbance recovers exponentially to the steady state (∼overdamped oscillator). Above the first threshold, breathing recovers to the steady state by decaying oscillations (∼underdamped oscillator). Above a second threshold, oscillations grow to reach a limit cycle, and when that cycle is sufficiently large, it represents the Cheyne-Stokes cycle of hyperventilation and apnea. Fourier analysis shows that the transition to growing oscillations is a forward or soft Hopf bifurcation. In the Cheyne-Stokes region (sufficiently large <span><math><mi>β</mi></math></span>), the equation predicts the shapes of the curves representing the time-dependence of arterial CO₂ and the respiration rate. From these shapes, we infer the values of the respiratory recovery coefficients for several groups of patients. With additional approximations, we infer the values of other physiological parameters, including cardiac output, CO₂ chemosensitivity, and volume of blood between lungs and detectors.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"378 ","pages":"Article 109318"},"PeriodicalIF":1.9,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142484528","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":"Optimal control for an SIR model with limited hospitalised patients","authors":"Rocío Balderrama ,&nbsp;Mariana Inés Prieto ,&nbsp;Constanza Sánchez de la Vega ,&nbsp;Federico Vázquez","doi":"10.1016/j.mbs.2024.109317","DOIUrl":"10.1016/j.mbs.2024.109317","url":null,"abstract":"<div><div>This paper analyses the optimal control of infectious disease propagation using a classic susceptible–infected–recovered (SIR) model characterised by permanent immunity and the absence of available vaccines. The control is performed over a time-dependent mean reproduction number, in order to minimise the cumulative number of ever-infected individuals (recovered), under different constraints. We consider constraints on non-pharmaceutical interventions ranging from partial lockdown to non-intervention, as well as the social and economic costs associated with such interventions, and the capacity limitations of intensive care units that limits the number of infected individuals to a maximum allowed value. We rigorously derive an optimal quarantine strategy based on necessary optimality conditions. The obtained optimal strategy is of a boundary-bang type, comprising three phases: an initial phase with no intervention, a second phase maintaining the infected population at its maximum possible value, and a final phase of partial lockdown applied over a single interval. The optimal policy is further refined by optimising the transition times between these phases. We show that these results are in excellent agreement with the numerical solution of the problem.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"378 ","pages":"Article 109317"},"PeriodicalIF":1.9,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142484529","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":"Unraveling autonomic cardiovascular control complexity during orthostatic stress: Insights from a mathematical model","authors":"Martin Miranda Hurtado ,&nbsp;Rafael Kaempfer ,&nbsp;Justen R. Geddes ,&nbsp;Mette S. Olufsen ,&nbsp;Maria Rodriguez-Fernandez","doi":"10.1016/j.mbs.2024.109306","DOIUrl":"10.1016/j.mbs.2024.109306","url":null,"abstract":"<div><div>Understanding cardiovascular control mediated by the autonomic system remains challenging due to its inherent complexity. Consequently, syndromes such as orthostatic intolerance continue to evoke debates regarding the underlying pathophysiological mechanisms. This study develops a comprehensive mathematical model simulating the control of the sympathetic branch of the cardiovascular system in individuals with normal and abnormal responses to the head-up-tilt test. We recruited four young women: one control, one with vasovagal syncope, one with orthostatic hypertension, and one with orthostatic hypotension, exposing them to an orthostatic head-up tilt test (HUTT) employing non-invasive methods to measure electrocardiography and continuous blood pressure.</div><div>Our work encompasses a compartmental model formulated using a system of ordinary differential equations. Using heart rate as input, we predict blood pressure, flow, and volume in compartments representing the veins, arteries, heart, and the sympathetic branch of the baroreflex control system. The latter is modulated by high- and low-pressure baroreceptor afferents activated by changes in blood pressure induced by the HUTT. Sensitivity analysis, parameter subset selection, and optimization are employed to estimate patient-specific parameters associated with autonomic performance. The model has seven sensitive and identifiable parameters with significant physiological relevance that can serve as biomarkers for patient classification.</div><div>Results show that the model can reproduce a spectrum of blood pressure responses successfully, fitting the trajectory displayed by the experimental data. The controller exhibits behavior that emulates the operation of the sympathetic system. These encouraging findings underscore the potential of computational methods in evaluating pathologies associated with autonomic nervous system control, warranting further exploration and novel approaches.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"377 ","pages":"Article 109306"},"PeriodicalIF":1.9,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142484530","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":"Ecoepidemic modeling and dynamics of alveolar echinococcosis transmission","authors":"Xinmiao Rong ,&nbsp;Meng Fan","doi":"10.1016/j.mbs.2024.109304","DOIUrl":"10.1016/j.mbs.2024.109304","url":null,"abstract":"<div><div>Alveolar echinococcosis, transmitted between definitive hosts and intermediate hosts via predation, threatens the health of humans and causes great economic losses in western China. In order to explore the transmission mechanism of this disease, an eco-epidemiological lifecycle model is formulated to illustrate interactions between two hosts. The basic and demographic reproduction numbers are developed to characterize the stability of the disease-free and endemic equilibria as well as bifurcation dynamics. The existence of forward bifurcation and Hopf bifurcation are confirmed and are used to explain the threshold transmission dynamics. Numerical simulations and bifurcation diagrams are also presented to depict rich dynamics of the model. Numerical analysis suggests that improving the control rate of voles will reduce the risk of transmission, while the high predation rate of foxes may also lead to a lower transmission risk, which is different from the predictions of previous studies. The evaluation of three control measures on voles implies that, when the fox’s predation rate is low (high), the chemical (integrated) control will be more effective.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"377 ","pages":"Article 109304"},"PeriodicalIF":1.9,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142378683","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":"An in-silico approach to the dynamics of proliferation potential in stem cells and the study of different therapies in cases of ovarian dysfunction","authors":"A.M. Portillo ,&nbsp;J.A. García-Velasco ,&nbsp;E. Varela","doi":"10.1016/j.mbs.2024.109305","DOIUrl":"10.1016/j.mbs.2024.109305","url":null,"abstract":"<div><div>A discrete mathematical model based on ordinary differential equations and the associated continuous model formed by a partial differential equation, which simulate the generational and temporal evolution of a stem cell population, are proposed. The model parameters are the maximum proliferation potential and the rates of mitosis, death events and telomerase activity. The mean proliferation potential at each point in time is suggested as an indicator of population aging. The model is applied on hematopoietic stem cells (HSCs), with different telomerase activity rates, in a range of variation of maximum proliferation potential in healthy individuals, to study the temporal evolution of aging. HSCs express telomerase, however not at levels that are sufficient for maintaining constant telomere length with aging <span><span>[1]</span></span>, <span><span>[2]</span></span>. Women with primary ovarian insufficiency (POI) are known to have low telomerase activity in granulosa cells and peripheral blood mononuclear cells <span><span>[3]</span></span>. Extrapolating this to hematopoietic stem cells, the mathematical model shows the differences in proliferation potential of the cell populations when telomerase expression is activated using sexual steroids, though the endogenous promoter or with gene therapy using exogenous, stronger promoters within the adeno-associated virus. In the first case, proliferation potential of cells from POI condition increases, but when adeno-associated viruses are used, the proliferation potential reaches the levels of healthy cell populations.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"377 ","pages":"Article 109305"},"PeriodicalIF":1.9,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142376443","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 joint-threshold Filippov model describing the effect of intermittent androgen-deprivation therapy in controlling prostate cancer","authors":"Aili Wang ,&nbsp;Rong Yan ,&nbsp;Haixia Li ,&nbsp;Xiaodan Sun ,&nbsp;Weike Zhou ,&nbsp;Stacey R. Smith?","doi":"10.1016/j.mbs.2024.109301","DOIUrl":"10.1016/j.mbs.2024.109301","url":null,"abstract":"<div><div>Intermittent androgen-deprivation therapy (IADT) can be beneficial to delay the occurrence of treatment resistance and cancer relapse compared to the standard continuous therapy. To study the effect of IADT in controlling prostate cancer, we developed a Filippov prostate cancer model with a joint threshold function: therapy is implemented once the total population of androgen-dependent cells (AC-Ds) and androgen-independent cells (AC-Is) is greater than the threshold value <span><math><mrow><mi>E</mi><mi>T</mi></mrow></math></span>, and it is suspended once the population is less than <span><math><mrow><mi>E</mi><mi>T</mi></mrow></math></span>. As the parameters vary, our model undergoes a series of sliding bifurcations, including boundary node, focus, saddle, saddle-node and tangency bifurcations. We also obtained the coexistence of one, two or three real equilibria and the bistability of two equilibria. Our results demonstrate that the population of AC-Is can be contained at a predetermined level if the initial population of AC-Is is less than this level, and we choose a suitable threshold value.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"377 ","pages":"Article 109301"},"PeriodicalIF":1.9,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142305091","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":"Adolescent vaping behaviours: Exploring the dynamics of a social contagion model","authors":"Sarah I. Machado-Marques,&nbsp;Iain R. Moyles","doi":"10.1016/j.mbs.2024.109303","DOIUrl":"10.1016/j.mbs.2024.109303","url":null,"abstract":"<div><p>Vaping, or the use of electronic cigarettes (e-cigarettes), is an ongoing issue for public health. The rapid increase in e-cigarette usage, particularly among adolescents, has often been referred to as an epidemic. Drawing upon this epidemiological analogy between vaping and infectious diseases as a theoretical framework, we present a deterministic compartmental model of adolescent e-cigarette smoking which accounts for social influences on initiation, relapse, and cessation behaviours. We use results from a sensitivity analysis of the model’s parameters on various response variables to identify key influences on system dynamics and simplify the model into one that can be analysed more thoroughly. We identify a single feasible endemic equilibrium for the proportion of smokers that decreases as social influence on cessation increases. Through steady state and stability analyses, as well as simulations of the model, we conclude that social influences from and on temporary quitters are not important in overall model dynamics, and that social influences from permanent quitters can have a significant impact on long-term system dynamics. In particular, we show that social influence on cessation can induce persistent recurrent smoking outbreaks.</p></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"377 ","pages":"Article 109303"},"PeriodicalIF":1.9,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0025556424001639/pdfft?md5=a3403f8b7858cb1615546af170478764&pid=1-s2.0-S0025556424001639-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142270742","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":"Modeling virus-stimulated proliferation of CD4+ T-cell, cell-to-cell transmission and viral loss in HIV infection dynamics","authors":"Jiawei Deng ,&nbsp;Hongying Shu ,&nbsp;Lin Wang ,&nbsp;Xingfu Zou","doi":"10.1016/j.mbs.2024.109302","DOIUrl":"10.1016/j.mbs.2024.109302","url":null,"abstract":"<div><p>Human immunodeficiency virus (HIV) can persist in infected individuals despite prolonged antiretroviral therapy and it may spread through two modes: virus-to-cell and cell-to-cell transmissions. Understanding viral infection dynamics is pivotal for elucidating HIV pathogenesis. In this study, we incorporate the loss term of virions, and both virus-to-cell and cell-to-cell infection modes into a within-host HIV model, which also takes into consideration the proliferation of healthy target cells stimulated by free viruses. By constructing suitable Lyapunov function and applying geometric methods, we establish global stability results of the infection free equilibrium and the infection persistent equilibrium, respectively. Our findings highlight the crucial role of the basic reproduction number in the threshold dynamics. Moreover, we use the loss rate of virions as the bifurcation parameter to investigate stability switches of the positive equilibrium, local Hopf bifurcation, and its global continuation. Numerical simulations validate our theoretical results, revealing rich viral dynamics including backward bifurcation, saddle–node bifurcation, and bistability phenomenon in the sense that the infection free equilibrium and a limit cycle are both locally asymptotically stable. These insights contribute to a deeper understanding of HIV dynamics and inform the development of effective therapeutic strategies.</p></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"377 ","pages":"Article 109302"},"PeriodicalIF":1.9,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142242387","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}