Mathematical Biosciences最新文献

{"title":"Two-step global sensitivity analysis of a non-local integro-differential model for Cancer-on-Chip experiments","authors":"Elio Campanile ,&nbsp;Annachiara Colombi ,&nbsp;Gabriella Bretti","doi":"10.1016/j.mbs.2024.109330","DOIUrl":"10.1016/j.mbs.2024.109330","url":null,"abstract":"<div><div>The present work focuses on a non-local integro-differential model reproducing Cancer-on-chip experiments where tumor cells, treated with chemotherapy drugs, secrete chemical signals stimulating the immune response. The reliability of the model in reproducing the phenomenon of interest is investigated through a global sensitivity analysis, rather than a local one, to have global information about the role of parameters, and by examining potential non-linear effects in greater detail. Focusing on a region in the parameter space, the effect of 13 model parameters on the <em>in silico</em> outcome is investigated by considering 11 different target outputs, properly selected to monitor the spatial distribution and the dynamics of immune cells along the period of observation. In order to cope with the large number of model parameters to be investigated and the computational cost of each numerical simulation, a two-step global sensitivity analysis is performed. First, the screening Morris method is applied to rank the effect of the 13 model parameters on each target output and it emerges that all the output targets are mainly affected by the same 6 parameters. The extended Fourier Amplitude Sensitivity Test (eFAST) method is then used to quantify the role of these 6 parameters. As a result, the proposed analysis highlights the feasibility of the considered space of parameters, and indicates that the most relevant parameters are those related to the chemical field and cell-substrate adhesion. In turn, it suggests how to possibly improve the model description as well as the calibration procedure, in order to better capture the observed phenomena and, at the same time, reduce the complexity of the simulation algorithm. On one hand, the model could be simplified by neglecting cell–cell alignment effects unless clear empirical evidences of their importance emerge. On the other hand, the best way to increase the accuracy and reliability of our model predictions would be to have experimental data/information to reduce the uncertainty of the more relevant parameters.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142564636","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":"Self-financing model for cabbage crops with pest management","authors":"Aurelien Kambeu Youmbi ,&nbsp;Suzanne Touzeau ,&nbsp;Frédéric Grognard ,&nbsp;Berge Tsanou","doi":"10.1016/j.mbs.2024.109332","DOIUrl":"10.1016/j.mbs.2024.109332","url":null,"abstract":"<div><div>Smallholder farmers rely on their farm earnings to cover operating costs and generate income. That is not an easy task because of the pests, which reduce yields and generate plant protection costs. The farm yield and plant protection depend on the budget capacity of the farmer. In this work, we want to explore conditions for a sustainable and self-financing cabbage farm. We propose then a non-linear mathematical model for cabbage crops by considering the current account of the plantation as a dynamic variable. We assume that this variable increases due to the sale of cabbages, and provides for the seedling purchase, the plant protection costs, and the grower’s income. In the first part, we analyze the model without pest management. We determine how the budget must be spent and we show the existence of a double transcritical bifurcation. We quantify the seasonal yield and income, and estimate the damage due to pest herbivory. In the second part, we analyze a slightly simplified version of our model and obtain the existence of a backward bifurcation. Furthermore, we show that botanical pesticides can be used to prevent pest spread with relatively low plant protection costs.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142564563","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":"Fractional-order modeling of myocardium structure effects on atrial fibrillation electrograms","authors":"Juan P. Ugarte ,&nbsp;Catalina Tobón","doi":"10.1016/j.mbs.2024.109331","DOIUrl":"10.1016/j.mbs.2024.109331","url":null,"abstract":"<div><div>Atrial fibrillation (AF) is the most common cardiac arrhythmia with mechanisms of initiation and sustaining that are not fully understood. The clinical procedure for AF contemplates the analysis of the atrial electrograms, whose morphology has been correlated with the underlying structure of the atrial myocardium. This study employs a mathematical model incorporating fractional calculus to simulate cardiac electrical conduction, accounting for tissue structural inhomogeneities using complex-valued orders. Simulations of different wavefront propagation patterns were performed, and virtual electrograms were analyzed using an asymmetry factor. Our results evinced that the shapes of the action potential and the propagating wavefront can be modulated through the fractional order under both healthy and AF conditions. Moreover, the asymmetry factor changes with variations in the fractional order. For a given propagation pattern under AF conditions, variation intervals for the asymmetry factor can be generated by forming sets of simulations with different configurations for the fractional order, representing diverse samples of atrial tissue with varying degrees of structural heterogeneity. This approach successfully reproduces the electrogram negative deflection predominance seen in AF patients, which standard integer-order models cannot predict. Our fractional-order conduction model aligns with the effects of atrial structure on the electrical dynamics observed in clinical AF. Therefore, it offers a valuable tool for studying cardiac electrophysiology, encompassing both electrical and structural interactions of the tissue within a unified model.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142559892","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 stochastic model for the bacterial growth exhibiting staged growth, desynchronization, saturation and persistence","authors":"Eugene B. Postnikov ,&nbsp;Anant Pratap Singh ,&nbsp;Alexander V. Sychev ,&nbsp;Anastasia I. Lavrova ,&nbsp;Vineet Kumar Singh","doi":"10.1016/j.mbs.2024.109322","DOIUrl":"10.1016/j.mbs.2024.109322","url":null,"abstract":"<div><div>We consider a model of population growth based on the stochastic variation of the population size-controlled duplication of bacterial cells. It is shown that the proper choice of the control function allows for reproducing a variety of regimes: a logistic growth with saturation, a hindered growth typical for persistent bacterial systems, and a linear population growth detected for some mycobacterial populations. When supplied with the rectangular function having the width equal to the generation time, this approach represents the solution generalizing Rubinow’s age-maturity model reproducing systems with desynchronization and saturation. The model’s plausibility is confirmed by the direct comparison with real data for the growth of <em>M. tuberculosis</em> populations obtained with the BACTEC MGIT system under different conditions of growth synchronization.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552266","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 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}