Zhaoxuan Huo, Jicai Huang, Yang Kuang, Shigui Ruan, Yuyue Zhang
In this paper we consider a tumor-immune system interaction model with immune response delay, in which a nonmonotonic function is used to describe immune response to the tumor burden and a time delay is used to represent the time for the immune system to respond and take effect. It is shown that the model may have one, two or three tumor equilibria, respectively, under different conditions. Time delay can only affect the stability of the low tumor equilibrium and local Hopf bifurcation occurs when the time delay passes through a critical value. The direction and stability of the bifurcating periodic solutions are also determined. Moreover, the global existence of periodic solutions is established by using a global Hopf bifurcation theorem. We also observe the existence of relaxation oscillations and complex oscillating patterns driven by the time delay. Numerical simulations are presented to illustrate the theoretical results.
{"title":"Oscillations in a tumor-immune system interaction model with immune response delay","authors":"Zhaoxuan Huo, Jicai Huang, Yang Kuang, Shigui Ruan, Yuyue Zhang","doi":"10.1093/imammb/dqae016","DOIUrl":"https://doi.org/10.1093/imammb/dqae016","url":null,"abstract":"In this paper we consider a tumor-immune system interaction model with immune response delay, in which a nonmonotonic function is used to describe immune response to the tumor burden and a time delay is used to represent the time for the immune system to respond and take effect. It is shown that the model may have one, two or three tumor equilibria, respectively, under different conditions. Time delay can only affect the stability of the low tumor equilibrium and local Hopf bifurcation occurs when the time delay passes through a critical value. The direction and stability of the bifurcating periodic solutions are also determined. Moreover, the global existence of periodic solutions is established by using a global Hopf bifurcation theorem. We also observe the existence of relaxation oscillations and complex oscillating patterns driven by the time delay. Numerical simulations are presented to illustrate the theoretical results.","PeriodicalId":519218,"journal":{"name":"Mathematical Medicine and Biology","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Rim Adenane, Carlos Andreu-Vilarroig, Florin Avram, Rafael-Jacinto Villanueva
Influenza and influenza-like illnesses (ILI) pose significant challenges to healthcare systems globally. Mathematical models play a crucial role in understanding their dynamics, calibrating them to specific scenarios, and making projections about their evolution over time. This study proposes a calibration process for three different but well-known compartmental models - SIR, SEIR/SLIR, and SLAIR - using influenza data from the 2016-2017 season in the Valencian Community, Spain. The calibration process involves indirect calibration for the SIR and SLIR models, requiring post-processing to compare model output with data, while the SLAIR model is directly calibrated through direct comparison. Our calibration results demonstrate remarkable consistency between the SIR and SLIR models, with slight variations observed in the SLAIR model due to its unique design and calibration strategy. Importantly, all models align with existing evidence and intuitions found in the medical literature. Our findings suggest that at the onset of the epidemiological season, a significant proportion of the population (ranging from 29.08% to 43.75% of the total population) may have already entered the recovered state, likely due to immunization from the previous season. Additionally, we estimate that the percentage of infected individuals seeking healthcare services ranges from 5.7% to 12.2%. Through a well-founded and calibrated modeling approach, our study contributes to supporting, settling, and quantifying current medical issues despite the inherent uncertainties involved in influenza dynamics. The full Mathematica code can be downloaded from https://munqu.webs.upv.es/software.html.
{"title":"Calibration and Comparison of SIR, SEIR/SLIR, and SLAIR Models for Influenza Dynamics: Insights from the 2016-2017 Season in the Valencian Community, Spain","authors":"Rim Adenane, Carlos Andreu-Vilarroig, Florin Avram, Rafael-Jacinto Villanueva","doi":"10.1093/imammb/dqae015","DOIUrl":"https://doi.org/10.1093/imammb/dqae015","url":null,"abstract":"Influenza and influenza-like illnesses (ILI) pose significant challenges to healthcare systems globally. Mathematical models play a crucial role in understanding their dynamics, calibrating them to specific scenarios, and making projections about their evolution over time. This study proposes a calibration process for three different but well-known compartmental models - SIR, SEIR/SLIR, and SLAIR - using influenza data from the 2016-2017 season in the Valencian Community, Spain. The calibration process involves indirect calibration for the SIR and SLIR models, requiring post-processing to compare model output with data, while the SLAIR model is directly calibrated through direct comparison. Our calibration results demonstrate remarkable consistency between the SIR and SLIR models, with slight variations observed in the SLAIR model due to its unique design and calibration strategy. Importantly, all models align with existing evidence and intuitions found in the medical literature. Our findings suggest that at the onset of the epidemiological season, a significant proportion of the population (ranging from 29.08% to 43.75% of the total population) may have already entered the recovered state, likely due to immunization from the previous season. Additionally, we estimate that the percentage of infected individuals seeking healthcare services ranges from 5.7% to 12.2%. Through a well-founded and calibrated modeling approach, our study contributes to supporting, settling, and quantifying current medical issues despite the inherent uncertainties involved in influenza dynamics. The full Mathematica code can be downloaded from https://munqu.webs.upv.es/software.html.","PeriodicalId":519218,"journal":{"name":"Mathematical Medicine and Biology","volume":"189 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142264900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Suliman Almansour, Joanne L Dunster, Jonathan J Crofts, Martin R Nelson
Macrophages play a wide range of roles in resolving the inflammatory damage that underlies many medical conditions, and have the ability to adopt different phenotypes in response to different environmental stimuli. Categorising macrophage phenotypes exactly is a difficult task, and there is disparity in the literature around the optimal nomenclature to describe these phenotypes; however, what is clear is that macrophages can exhibit both pro- and anti-inflammatory behaviours dependent upon their phenotype, rendering mathematical models of the inflammatory response potentially sensitive to their description of the macrophage populations that they incorporate. Many previous models of inflammation include a single macrophage population with both pro- and anti-inflammatory functions. Here, we build upon these existing models to include explicit descriptions of distinct macrophage phenotypes and examine the extent to which this influences the inflammatory dynamics that the models emit. We analyse our models via numerical simulation in Matlab and dynamical systems analysis in XPPAUT, and show that models that account for distinct macrophage phenotypes separately can offer more realistic steady state solutions than precursor models do (better capturing the anti-inflammatory activity of tissue resident macrophages), as well as oscillatory dynamics not previously observed. Finally, we reflect on the conclusions of our analysis in the context of the ongoing hunt for potential new therapies for inflammatory conditions, highlighting manipulation of macrophage polarisation states as a potential therapeutic target.
{"title":"A systematic evaluation of the influence of macrophage phenotype descriptions on inflammatory dynamics","authors":"Suliman Almansour, Joanne L Dunster, Jonathan J Crofts, Martin R Nelson","doi":"10.1093/imammb/dqae004","DOIUrl":"https://doi.org/10.1093/imammb/dqae004","url":null,"abstract":"Macrophages play a wide range of roles in resolving the inflammatory damage that underlies many medical conditions, and have the ability to adopt different phenotypes in response to different environmental stimuli. Categorising macrophage phenotypes exactly is a difficult task, and there is disparity in the literature around the optimal nomenclature to describe these phenotypes; however, what is clear is that macrophages can exhibit both pro- and anti-inflammatory behaviours dependent upon their phenotype, rendering mathematical models of the inflammatory response potentially sensitive to their description of the macrophage populations that they incorporate. Many previous models of inflammation include a single macrophage population with both pro- and anti-inflammatory functions. Here, we build upon these existing models to include explicit descriptions of distinct macrophage phenotypes and examine the extent to which this influences the inflammatory dynamics that the models emit. We analyse our models via numerical simulation in Matlab and dynamical systems analysis in XPPAUT, and show that models that account for distinct macrophage phenotypes separately can offer more realistic steady state solutions than precursor models do (better capturing the anti-inflammatory activity of tissue resident macrophages), as well as oscillatory dynamics not previously observed. Finally, we reflect on the conclusions of our analysis in the context of the ongoing hunt for potential new therapies for inflammatory conditions, highlighting manipulation of macrophage polarisation states as a potential therapeutic target.","PeriodicalId":519218,"journal":{"name":"Mathematical Medicine and Biology","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140603477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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