Pub Date : 2024-11-06DOI: 10.1016/j.mbs.2024.109336
Maisha Islam Sejunti , Dane Taylor , Naoki Masuda
Many social and biological networks periodically change over time with daily, weekly, and other cycles. Thus motivated, we formulate and analyze susceptible-infectious-susceptible (SIS) epidemic models over temporal networks with periodic schedules. More specifically, we assume that the temporal network consists of a cycle of alternately used static networks, each with a given duration. We observe a phenomenon in which two static networks are individually above the epidemic threshold but the alternating network composed of them renders the dynamics below the epidemic threshold, which we refer to as a Parrondo paradox for epidemics. We find that network structure plays an important role in shaping this phenomenon, and we study its dependence on the connectivity between and number of subpopulations in the network. We associate such paradoxical behavior with anti-phase oscillatory dynamics of the number of infectious individuals in different subpopulations.
{"title":"A Parrondo paradox in susceptible-infectious-susceptible dynamics over periodic temporal networks","authors":"Maisha Islam Sejunti , Dane Taylor , Naoki Masuda","doi":"10.1016/j.mbs.2024.109336","DOIUrl":"10.1016/j.mbs.2024.109336","url":null,"abstract":"<div><div>Many social and biological networks periodically change over time with daily, weekly, and other cycles. Thus motivated, we formulate and analyze susceptible-infectious-susceptible (SIS) epidemic models over temporal networks with periodic schedules. More specifically, we assume that the temporal network consists of a cycle of alternately used static networks, each with a given duration. We observe a phenomenon in which two static networks are individually above the epidemic threshold but the alternating network composed of them renders the dynamics below the epidemic threshold, which we refer to as a Parrondo paradox for epidemics. We find that network structure plays an important role in shaping this phenomenon, and we study its dependence on the connectivity between and number of subpopulations in the network. We associate such paradoxical behavior with anti-phase oscillatory dynamics of the number of infectious individuals in different subpopulations.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"378 ","pages":"Article 109336"},"PeriodicalIF":1.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142635463","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}
Pub Date : 2024-11-05DOI: 10.1016/j.mbs.2024.109337
Alessandro De Gaetano , Alain Barrat , Daniela Paolotti
Individuals’ perceptions of disease influence their adherence to preventive measures, shaping the dynamics of disease spread. Despite extensive research on the interaction between disease spread, human behaviors, and interventions, few models have incorporated real-world behavioral data on disease perception, limiting their applicability. In this study, we propose an approach to integrate survey data on contact patterns and disease perception into a data-driven compartmental model, by hypothesizing that perceived severity is a determinant of behavioral change. We explore scenarios involving a competition between a COVID-19 wave and a vaccination campaign, where individuals’ behaviors vary based on their perceived severity of the disease. Results indicate that behavioral heterogeneities influenced by perceived severity affect epidemic dynamics, in a way depending on the interplay between two contrasting effects. On the one hand, longer adherence to protective measures by groups with high perceived severity provides greater protection to vulnerable individuals, while premature relaxation of behaviors by low perceived severity groups facilitates virus spread. Differences in behavior across different population groups may impact strongly the epidemiological curves, with a transition from a scenario with two successive epidemic peaks to one with only one (higher) peak and overall more numerous severe outcomes and deaths. The specific modeling choices for how perceived severity modulates behavior parameters do not strongly impact the model’s outcomes. Moreover, the study of several simplified models indicate that the observed phenomenology depends on the combination of data describing age-stratified contact patterns and of the feedback loop between disease perception and behavior, while it is robust with respect to the lack of precise information on the distribution of perceived severity in the population. Sensitivity analyses confirm the robustness of our findings, emphasizing the consistent impact of behavioral heterogeneities across various scenarios. Our study underscores the importance of integrating risk perception into infectious disease transmission models and gives hints on the type of data that further extensive data collection should target to enhance model accuracy and relevance.
{"title":"Modeling the interplay between disease spread, behaviors, and disease perception with a data-driven approach","authors":"Alessandro De Gaetano , Alain Barrat , Daniela Paolotti","doi":"10.1016/j.mbs.2024.109337","DOIUrl":"10.1016/j.mbs.2024.109337","url":null,"abstract":"<div><div>Individuals’ perceptions of disease influence their adherence to preventive measures, shaping the dynamics of disease spread. Despite extensive research on the interaction between disease spread, human behaviors, and interventions, few models have incorporated real-world behavioral data on disease perception, limiting their applicability. In this study, we propose an approach to integrate survey data on contact patterns and disease perception into a data-driven compartmental model, by hypothesizing that perceived severity is a determinant of behavioral change. We explore scenarios involving a competition between a COVID-19 wave and a vaccination campaign, where individuals’ behaviors vary based on their perceived severity of the disease. Results indicate that behavioral heterogeneities influenced by perceived severity affect epidemic dynamics, in a way depending on the interplay between two contrasting effects. On the one hand, longer adherence to protective measures by groups with high perceived severity provides greater protection to vulnerable individuals, while premature relaxation of behaviors by low perceived severity groups facilitates virus spread. Differences in behavior across different population groups may impact strongly the epidemiological curves, with a transition from a scenario with two successive epidemic peaks to one with only one (higher) peak and overall more numerous severe outcomes and deaths. The specific modeling choices for how perceived severity modulates behavior parameters do not strongly impact the model’s outcomes. Moreover, the study of several simplified models indicate that the observed phenomenology depends on the combination of data describing age-stratified contact patterns and of the feedback loop between disease perception and behavior, while it is robust with respect to the lack of precise information on the distribution of perceived severity in the population. Sensitivity analyses confirm the robustness of our findings, emphasizing the consistent impact of behavioral heterogeneities across various scenarios. Our study underscores the importance of integrating risk perception into infectious disease transmission models and gives hints on the type of data that further extensive data collection should target to enhance model accuracy and relevance.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"378 ","pages":"Article 109337"},"PeriodicalIF":1.9,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142607445","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}
Pub Date : 2024-11-02DOI: 10.1016/j.mbs.2024.109335
Ananth Vedururu Srinivas, Carmen C. Canavier
Phase Response Curves (PRCs) have been useful in determining and analyzing various phase-locking modes in networks of oscillators under pulse-coupling assumptions, as reviewed in Mathematical Biosciences, 226:77–96, 2010. Here, we update that review to include progress since 2010 on pulse coupled oscillators with conduction delays. We then present original results that extend the derivation of the criteria for stability of global synchrony in networks of pulse-coupled oscillators to include conduction delays. We also incorporate conduction delays to extend previous studies that showed how an alternating firing pattern between two synchronized clusters could enforce within-cluster synchrony, even for clusters unable to synchronize themselves in isolation. To obtain these results, we used self-connected neurons to represent clusters. These results greatly extend the applicability of the stability analyses to networks of pulse-coupled oscillators since conduction delays are ubiquitous and strongly impact the stability of synchrony. Although these analyses only strictly apply to identical oscillators with identical connections to other oscillators, the principles are general and suggest how to promote or impede synchrony in physiological networks of neurons, for example. Heterogeneity can be interpreted as a form of frozen noise, and approximate synchrony can be sustained despite heterogeneity. The pulse-coupled oscillator model can not only be used to describe biological neuronal networks but also cardiac pacemakers, lasers, fireflies, artificial neural networks, social self-organization, and wireless sensor networks.
{"title":"Existence and stability criteria for global synchrony and for synchrony in two alternating clusters of pulse-coupled oscillators updated to include conduction delays","authors":"Ananth Vedururu Srinivas, Carmen C. Canavier","doi":"10.1016/j.mbs.2024.109335","DOIUrl":"10.1016/j.mbs.2024.109335","url":null,"abstract":"<div><div>Phase Response Curves (PRCs) have been useful in determining and analyzing various phase-locking modes in networks of oscillators under pulse-coupling assumptions, as reviewed in Mathematical Biosciences, 226:77–96, 2010. Here, we update that review to include progress since 2010 on pulse coupled oscillators with conduction delays. We then present original results that extend the derivation of the criteria for stability of global synchrony in networks of pulse-coupled oscillators to include conduction delays. We also incorporate conduction delays to extend previous studies that showed how an alternating firing pattern between two synchronized clusters could enforce within-cluster synchrony, even for clusters unable to synchronize themselves in isolation. To obtain these results, we used self-connected neurons to represent clusters. These results greatly extend the applicability of the stability analyses to networks of pulse-coupled oscillators since conduction delays are ubiquitous and strongly impact the stability of synchrony. Although these analyses only strictly apply to identical oscillators with identical connections to other oscillators, the principles are general and suggest how to promote or impede synchrony in physiological networks of neurons, for example. Heterogeneity can be interpreted as a form of frozen noise, and approximate synchrony can be sustained despite heterogeneity. The pulse-coupled oscillator model can not only be used to describe biological neuronal networks but also cardiac pacemakers, lasers, fireflies, artificial neural networks, social self-organization, and wireless sensor networks.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"378 ","pages":"Article 109335"},"PeriodicalIF":1.9,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142570795","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 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 in silico 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.
{"title":"Two-step global sensitivity analysis of a non-local integro-differential model for Cancer-on-Chip experiments","authors":"Elio Campanile , Annachiara Colombi , 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":"378 ","pages":"Article 109330"},"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}
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.
{"title":"Self-financing model for cabbage crops with pest management","authors":"Aurelien Kambeu Youmbi , Suzanne Touzeau , Frédéric Grognard , 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":"378 ","pages":"Article 109332"},"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}
Pub Date : 2024-10-29DOI: 10.1016/j.mbs.2024.109331
Juan P. Ugarte , Catalina Tobón
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.
{"title":"Fractional-order modeling of myocardium structure effects on atrial fibrillation electrograms","authors":"Juan P. Ugarte , 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":"378 ","pages":"Article 109331"},"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}
Pub Date : 2024-10-29DOI: 10.1016/j.mbs.2024.109321
Arsène Jaurès Ouemba Tassé , Berge Tsanou , Jean Louis Woukeng , Jean M-S Lubuma
We construct a new metapopulation model for the transmission dynamics and control of the Ebola Virus Disease (EVD) in an environment characterized by considerable migrations and travels of people. It is an extended SEIR model modified by the addition of Quarantine and Isolated compartments to account for travelers who undergo the exit screening. The model is well-fitted by using the reported cases from the neighboring countries Guinea, Liberia and Sierra Leone where the 2014–2016 Ebola outbreak simultaneously arose. We show that the unique disease-free equilibrium (DFE) of the model is unstable or locally asymptotically stable (LAS) depending on whether the control reproduction number is larger or less than unity. In the latter case, we prove that the DFE is globally asymptotically stable (GAS) provided that the exit screening is 100% negative. We also prove the GAS of the DFE by introducing more explicit thresholds, thanks to which the existence of at least one boundary equilibrium is established. We design two new nonstandard finite difference (NSFD) schemes, which preserve the dynamics of the continuous model. Numerical simulations that support the theory highlight that exit screening is useful to mitigate the infection. They also suggest that the disease is controlled or the explicit threshold is less than unity provided that the migration and the exit screening parameters are above a critical value.
{"title":"A metapopulation model with exit screening measure for the 2014–2016 West Africa Ebola virus outbreak","authors":"Arsène Jaurès Ouemba Tassé , Berge Tsanou , Jean Louis Woukeng , Jean M-S Lubuma","doi":"10.1016/j.mbs.2024.109321","DOIUrl":"10.1016/j.mbs.2024.109321","url":null,"abstract":"<div><div>We construct a new metapopulation model for the transmission dynamics and control of the Ebola Virus Disease (EVD) in an environment characterized by considerable migrations and travels of people. It is an extended SEIR model modified by the addition of Quarantine and Isolated compartments to account for travelers who undergo the exit screening. The model is well-fitted by using the reported cases from the neighboring countries Guinea, Liberia and Sierra Leone where the 2014–2016 Ebola outbreak simultaneously arose. We show that the unique disease-free equilibrium (DFE) of the model is unstable or locally asymptotically stable (LAS) depending on whether the control reproduction number is larger or less than unity. In the latter case, we prove that the DFE is globally asymptotically stable (GAS) provided that the exit screening is 100% negative. We also prove the GAS of the DFE by introducing more explicit thresholds, thanks to which the existence of at least one boundary equilibrium is established. We design two new nonstandard finite difference (NSFD) schemes, which preserve the dynamics of the continuous model. Numerical simulations that support the theory highlight that exit screening is useful to mitigate the infection. They also suggest that the disease is controlled or the explicit threshold is less than unity provided that the migration and the exit screening parameters are above a critical value.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"378 ","pages":"Article 109321"},"PeriodicalIF":1.9,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142559891","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}
Pub Date : 2024-10-29DOI: 10.1016/j.mbs.2024.109338
Anita T. Layton
Mathematical models of whole-body dynamics have advanced our understanding of human integrative systems that regulate physiological processes such as metabolism, temperature, and blood pressure. For most of these whole-body models, baseline parameters describe a 35-year-old young adult man who weighs 70 kg. As such, even among adults those models may not accurately represent half of the population (women), the older population, and those who weigh significantly more than 70 kg. Indeed, sex, age, and weight are known modulators of physiological function. To more accurately simulate a person who does not look like that “baseline person,” or to explain the mechanisms that yield the observed sex or age differences, these factors should be incorporated into mathematical models of physiological systems. Another key modulator is the time of day, because most physiological processes are regulated by the circadian clocks. Thus, ideally, mathematical models of integrative physiological systems should be specific to either a man or woman, of a certain age and weight, and a given time of day. We illustrate the importance of capturing these individual differences, using the blood pressure regulatory system as an example, and explain how that such models can be built.
{"title":"We are all different: Modeling key individual differences in physiological systems","authors":"Anita T. Layton","doi":"10.1016/j.mbs.2024.109338","DOIUrl":"10.1016/j.mbs.2024.109338","url":null,"abstract":"<div><div>Mathematical models of whole-body dynamics have advanced our understanding of human integrative systems that regulate physiological processes such as metabolism, temperature, and blood pressure. For most of these whole-body models, baseline parameters describe a 35-year-old young adult man who weighs 70 kg. As such, even among adults those models may not accurately represent half of the population (women), the older population, and those who weigh significantly more than 70 kg. Indeed, sex, age, and weight are known modulators of physiological function. To more accurately simulate a person who does not look like that “baseline person,” or to explain the mechanisms that yield the observed sex or age differences, these factors should be incorporated into mathematical models of physiological systems. Another key modulator is the time of day, because most physiological processes are regulated by the circadian clocks. Thus, ideally, mathematical models of integrative physiological systems should be specific to either a man or woman, of a certain age and weight, and a given time of day. We illustrate the importance of capturing these individual differences, using the blood pressure regulatory system as an example, and explain how that such models can be built.</div></div>","PeriodicalId":51119,"journal":{"name":"Mathematical Biosciences","volume":"378 ","pages":"Article 109338"},"PeriodicalIF":1.9,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142559893","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}
Pub Date : 2024-10-26DOI: 10.1016/j.mbs.2024.109322
Eugene B. Postnikov , Anant Pratap Singh , Alexander V. Sychev , Anastasia I. Lavrova , Vineet Kumar Singh
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 M. tuberculosis populations obtained with the BACTEC MGIT system under different conditions of growth synchronization.
{"title":"A stochastic model for the bacterial growth exhibiting staged growth, desynchronization, saturation and persistence","authors":"Eugene B. Postnikov , Anant Pratap Singh , Alexander V. Sychev , Anastasia I. Lavrova , 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":"378 ","pages":"Article 109322"},"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}
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 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.
{"title":"A geometric approach to the impact of immigration of people infected with communicable diseases","authors":"Sofía Guarello , Nicolás González , Isabel Flores , 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}
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