Martin Deosborns Arop, Henry Kasumba, Juma Kasozi, Fredrik Berntsson
In this paper, we are interested in finding an optimal control support design for controlling vibrations due to pedestrian-bridge interactions. Therefore, we derive the topological derivatives of the proposed functionals using the averaged adjoint approach. A numerical algorithm initialized by these sensitivities is used as a solution strategy. The algorithm is tested numerically for two different cases of initial conditions.
{"title":"Optimal actuator design for control of vibrations induced by pedestrian-bridge interactions","authors":"Martin Deosborns Arop, Henry Kasumba, Juma Kasozi, Fredrik Berntsson","doi":"10.5206/mase/16958","DOIUrl":"https://doi.org/10.5206/mase/16958","url":null,"abstract":"In this paper, we are interested in finding an optimal control support design for controlling vibrations due to pedestrian-bridge interactions. Therefore, we derive the topological derivatives of the proposed functionals using the averaged adjoint approach. A numerical algorithm initialized by these sensitivities is used as a solution strategy. The algorithm is tested numerically for two different cases of initial conditions.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141102574","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}
This study presents an innovative 2D spatio-temporal model that sheds light on the intricate formation of biofilms, incorporating two essential biomass decay pathways: cell lysis and endogenous respiration. The model encompasses heterotrophic bacteria (HB), anaerobic heterotrophic bacteria (AHB), and autotrophic bacteria (AB), offering a comprehensive understanding of multi-species biofilm development. Through meticulous simulations, we explore the primary mechanisms behind inert biomass formation in biofilms, revealing the key roles played by the lysis of HB, AHB, and AB, as well as the endogenous respiration of HB. Moreover, the simulations reveal how species of higher abundance contribute significantly to inert biomass generation, reshaping our understanding of biofilm dynamics. Crucially, this study highlights the indispensability of considering biofilm inert biomass when modeling the nitrification and denitrification behaviors of a membrane aerated biofilm reactor (MABR). The distribution of oxygen and acetate across biofilm thickness is remarkably different when inert biomass is factored in, underscoring the necessity for a more holistic approach to modeling biofilm behavior. With the introduction of the inert biomass inclusive biofilm model, our simulations explore the interactive effects of key process conditions - bulk concentrations of oxygen ($O_{infty}$), ammonium nitrogen ($N_{1infty}$), acetate ($A_{infty}$), and biofilm thickness - on the nitrification and denitrification performance of MABR. A compelling correlation emerges between higher bulk concentrations of oxygen and ammonium nitrogen and optimal nitrification rates, achieving an impressive range of 0.3 to 1.1 g ammonium/$m^{2}/d. Delving into denitrification, we observe that high $O_{infty}$, low $N_{1infty}$, and either high or low $A_{infty}$ levels impede AHB formation and consequently hinder denitrification. Our findings provide a roadmap for achieving simultaneous nitrification and denitrification, contingent on specific conditions: $10[gm^{-3}] < O_{infty} < 15[gm^{-3}]$, $12[gm^{-3}] < N_{1infty} < 20[gm^{-3}]$, $A_{infty}$ ranging from $3[gm^{-3}]$ to $12[gm^{-3}]$, and a biofilm thickness $> 1.4[mm]$. While our study reveals promising avenues for simultaneous nitrification and denitrification, denitrification rates still lag behind nitrification rates under the same conditions. As a result, we advocate for further investigations to devise strategies that can enhance denitrification in MABR systems. In conclusion, this study advances our knowledge of biofilm dynamics by introducing a comprehensive model and illuminating the key factors driving nitrification and denitrification performance in MABRs. These findings pave the way for improved biofilm engineering and wastewater treatment strategies, opening new horizons for sustainable environmental practices.
{"title":"Unraveling the role of inert biomass in membrane aerated biofilm reactors for simultaneous nitrification and denitrification","authors":"Maryam Ghasemi, Sheng Chang, Sivabal Sivaloganathan","doi":"10.5206/mase/17134","DOIUrl":"https://doi.org/10.5206/mase/17134","url":null,"abstract":"This study presents an innovative 2D spatio-temporal model that sheds light on the intricate formation of biofilms, incorporating two essential biomass decay pathways: cell lysis and endogenous respiration. The model encompasses heterotrophic bacteria (HB), anaerobic heterotrophic bacteria (AHB), and autotrophic bacteria (AB), offering a comprehensive understanding of multi-species biofilm development. Through meticulous simulations, we explore the primary mechanisms behind inert biomass formation in biofilms, revealing the key roles played by the lysis of HB, AHB, and AB, as well as the endogenous respiration of HB. Moreover, the simulations reveal how species of higher abundance contribute significantly to inert biomass generation, reshaping our understanding of biofilm dynamics. Crucially, this study highlights the indispensability of considering biofilm inert biomass when modeling the nitrification and denitrification behaviors of a membrane aerated biofilm reactor (MABR). The distribution of oxygen and acetate across biofilm thickness is remarkably different when inert biomass is factored in, underscoring the necessity for a more holistic approach to modeling biofilm behavior. With the introduction of the inert biomass inclusive biofilm model, our simulations explore the interactive effects of key process conditions - bulk concentrations of oxygen ($O_{infty}$), ammonium nitrogen ($N_{1infty}$), acetate ($A_{infty}$), and biofilm thickness - on the nitrification and denitrification performance of MABR. A compelling correlation emerges between higher bulk concentrations of oxygen and ammonium nitrogen and optimal nitrification rates, achieving an impressive range of 0.3 to 1.1 g ammonium/$m^{2}/d. Delving into denitrification, we observe that high $O_{infty}$, low $N_{1infty}$, and either high or low $A_{infty}$ levels impede AHB formation and consequently hinder denitrification. Our findings provide a roadmap for achieving simultaneous nitrification and denitrification, contingent on specific conditions: $10[gm^{-3}] < O_{infty} < 15[gm^{-3}]$, $12[gm^{-3}] < N_{1infty} < 20[gm^{-3}]$, $A_{infty}$ ranging from $3[gm^{-3}]$ to $12[gm^{-3}]$, and a biofilm thickness $> 1.4[mm]$. While our study reveals promising avenues for simultaneous nitrification and denitrification, denitrification rates still lag behind nitrification rates under the same conditions. As a result, we advocate for further investigations to devise strategies that can enhance denitrification in MABR systems. In conclusion, this study advances our knowledge of biofilm dynamics by introducing a comprehensive model and illuminating the key factors driving nitrification and denitrification performance in MABRs. These findings pave the way for improved biofilm engineering and wastewater treatment strategies, opening new horizons for sustainable environmental practices.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140378931","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}
Ecotoxicological models play a vital role in understanding the influence of toxicants on population dynamics in contaminated aquatic ecosystems. Traditional differential equation models describing interactions between populations and toxicants typically assume instantaneous population growth, overlooking potential time delays associated with reproductive and maturation processes. In this paper, we introduce two models with time delays to investigate the interaction between a population and a toxicant, where the population growth is governed by a delayed logistic equation. We mainly focus on the stability analysis of the steady states of the models. Our findings indicate that high toxicant concentrations result in population extinction, whereas moderate toxicant levels can potentially induce bistability, where the population's fate, whether persistence or extinction, depends on the initial densities of the population and toxicant. Furthermore, both our theoretical analysis and numerical simulations demonstrate that the time delay can lead to the destabilization of the coexistence steady states and the appearance of periodic solutions through Hopf bifurcation.
{"title":"Time-delayed models for the effects of toxicants on populations in contaminated aquatic ecosystems","authors":"Yuxing Liu, Qihua Huang","doi":"10.5206/mase/16981","DOIUrl":"https://doi.org/10.5206/mase/16981","url":null,"abstract":"Ecotoxicological models play a vital role in understanding the influence of toxicants on population dynamics in contaminated aquatic ecosystems. Traditional differential equation models describing interactions between populations and toxicants typically assume instantaneous population growth, overlooking potential time delays associated with reproductive and maturation processes. In this paper, we introduce two models with time delays to investigate the interaction between a population and a toxicant, where the population growth is governed by a delayed logistic equation. We mainly focus on the stability analysis of the steady states of the models. Our findings indicate that high toxicant concentrations result in population extinction, whereas moderate toxicant levels can potentially induce bistability, where the population's fate, whether persistence or extinction, depends on the initial densities of the population and toxicant. Furthermore, both our theoretical analysis and numerical simulations demonstrate that the time delay can lead to the destabilization of the coexistence steady states and the appearance of periodic solutions through Hopf bifurcation.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140379186","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}
In this paper, the Lyapunov-Schmidt reduction is used to investigate the bifurcation of periodic travelling wave solutions of a perturbed (1+1)−dimensional dispersive long wave equation. We demonstrate that the bifurcation equation corresponding to the original problem is supplied by a nonlinear system of two cubic algebraic equations. As the bifurcation parameters change, this system has only one, three, or five regular real solutions. The linear approximation of the solutions to the main problem has been discovered.
{"title":"Lyapunov-Schmidt reduction in the study of bifurcation of periodic travelling wave solutions of a perturbed (1 + 1)−dimensional dispersive long wave equation","authors":"Mudhir A. Abdul Hussain","doi":"10.5206/mase/16957","DOIUrl":"https://doi.org/10.5206/mase/16957","url":null,"abstract":"In this paper, the Lyapunov-Schmidt reduction is used to investigate the bifurcation of periodic travelling wave solutions of a perturbed (1+1)−dimensional dispersive long wave equation. We demonstrate that the bifurcation equation corresponding to the original problem is supplied by a nonlinear system of two cubic algebraic equations. As the bifurcation parameters change, this system has only one, three, or five regular real solutions. The linear approximation of the solutions to the main problem has been discovered.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140229463","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}
In recent decades, intensive research has been devoted to the study of various operator entropies. In this work, we investigate the properties of the parameterized relative operator entropy Sp(A | B) acting on positive definite matrices with respect to weighted Hellinger and Alpha Procrustes distances. In particular, we investigate estimation of the distance between the entropy Sp(A | B) and certain standard means.
近几十年来，人们对各种算子熵进行了深入研究。 在这项工作中，我们研究了作用于正定矩阵的参数化相对算子熵 Sp(A | B) 在加权海灵格距离和阿尔法普罗克鲁斯距离方面的特性。特别是，我们研究了熵 Sp(A | B) 与某些标准均值之间距离的估计。
{"title":"Relative operator entropy properties related to some weighted metrics","authors":"Mohamed Chergui, Abdenbi El Hilali","doi":"10.5206/mase/16771","DOIUrl":"https://doi.org/10.5206/mase/16771","url":null,"abstract":"In recent decades, intensive research has been devoted to the study of various operator entropies. In this work, we investigate the properties of the parameterized relative operator entropy Sp(A | B) acting on positive definite matrices with respect to weighted Hellinger and Alpha Procrustes distances. In particular, we investigate estimation of the distance between the entropy Sp(A | B) and certain standard means.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139611496","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}
Sagar R. Khirsariya, Snehal Rao, Jignesh P. Chauhan
The present study examines a semi-analytical method known as the Fractional Residual Power Series Method for obtaining solutions to the non-linear, time-fractional Kawahara and modified Kawahara equations. These equations are fifth-order, non-linear partial differential equations that arise in the context of shallow water waves. The analytical process and findings are compared with those obtained from the well-known Variational Iteration Method (VIM) and Homotopy Perturbation Method (HPM). The results obtained from the Fractional Residual Power Series Method are found to be more efficient, reliable, and easier to implement compared to other analytical and semi-analytical methods.
{"title":"Solution of fractional modified Kawahara equation: a semi-analytic approach","authors":"Sagar R. Khirsariya, Snehal Rao, Jignesh P. Chauhan","doi":"10.5206/mase/16369","DOIUrl":"https://doi.org/10.5206/mase/16369","url":null,"abstract":"The present study examines a semi-analytical method known as the Fractional Residual Power Series Method for obtaining solutions to the non-linear, time-fractional Kawahara and modified Kawahara equations. These equations are fifth-order, non-linear partial differential equations that arise in the context of shallow water waves. The analytical process and findings are compared with those obtained from the well-known Variational Iteration Method (VIM) and Homotopy Perturbation Method (HPM). The results obtained from the Fractional Residual Power Series Method are found to be more efficient, reliable, and easier to implement compared to other analytical and semi-analytical methods.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138947280","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}
Under the Dirichlet boundary setting, Aryal and Karki (2022) studied an inverse problem of recovering an initial temperature profile from known temperature measurements at a fixed location of a one-dimensional body and at linearly growing finitely many later times within a bounded interval. This paper studies the problem under the Neumann boundary conditions. That is, under this boundary setting, we suitably select a fixed location x0 on the body of length π and construct finitely many times tk, k = 1, 2, 3, . . . , n that grow linearly with k and are in [0, T] such that from the temperature measurements taken at x0 and at these n times, we recover the initial temperature profile f(x) with a desired accuracy, provided f is in a suitable subset of L2[0, π].
在 Dirichlet 边界条件下，Aryal 和 Karki（2022 年）研究了一个逆问题，即从一维物体固定位置的已知温度测量值，以及在有界区间内线性增长的有限多次以后的温度测量值，恢复初始温度曲线。本文研究的是诺伊曼边界条件下的问题。也就是说，在这种边界条件下，我们在长度为 π 的体上适当选择一个固定位置 x0，并构建有限多次 tk, k = 1, 2, 3, ., n，这些时间与 k 呈线性增长，且位于 [0, T] 中，这样，只要 f 位于 L2[0, π] 的一个合适子集中，我们就能根据在 x0 和这 n 个时间测量到的温度，以理想的精度恢复初始温度曲线 f(x)。
{"title":"Recovery of an initial temperature of a one-dimensional body from finite time-observations","authors":"Ramesh Karki, Chava Shawn, Young You","doi":"10.5206/mase/16723","DOIUrl":"https://doi.org/10.5206/mase/16723","url":null,"abstract":"Under the Dirichlet boundary setting, Aryal and Karki (2022) studied an inverse problem of recovering an initial temperature profile from known temperature measurements at a fixed location of a one-dimensional body and at linearly growing finitely many later times within a bounded interval. This paper studies the problem under the Neumann boundary conditions. That is, under this boundary setting, we suitably select a fixed location x0 on the body of length π and construct finitely many times tk, k = 1, 2, 3, . . . , n that grow linearly with k and are in [0, T] such that from the temperature measurements taken at x0 and at these n times, we recover the initial temperature profile f(x) with a desired accuracy, provided f is in a suitable subset of L2[0, π].","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138958399","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}
Taye Faniran, M. O. Adewole, Catherine Chirouze, Antoine Perasso, Raluca Eftimie
Methicillin-Resistant Staphylococcus Aureus (MRSA) infection can occur alongside or following COVID-19, which is a concern in healthcare settings. The effectiveness of antiviral treatments for COVID-19 depends on a functioning immune response, but antibiotics used for bacterial infections like MRSA can disrupt the immune response and reduce the effectiveness of antiviral treatments. The emergence of MRSA due to excessive antibiotic usage has led to the widespread use of vancomycin as an alternative treatment. Immunomodulatory antibiotics like azithromycin may also be considered. To study the dynamics of these coinfections, a multiscale model was developed. Parameter estimation and sensitivity analysis were performed, revealing influential parameters affecting the reproduction number. Numerical simulations showed that methicillin may increase the population of co-infected cells, while azithromycin can improve the host immune response but has limited impact on MRSA proliferation. Increased efficacy of vancomycin can lead to MRSA eradication. Combination of immunomodulatory antibiotics and vancomycin has minimal effect on co-infected cell population, but increased vancomycin efficacy can reduce coinfection severity. This study emphasizes the importance of continuous research, surveillance, and the development of effective strategies to combat the complexities of COVID-19 and MRSA coinfection.
{"title":"Multiscale modeling approach to assess the impact of antibiotic treatment for COVID-19 on MRSA transmission and alternative immunotherapy treatment options","authors":"Taye Faniran, M. O. Adewole, Catherine Chirouze, Antoine Perasso, Raluca Eftimie","doi":"10.5206/mase/16685","DOIUrl":"https://doi.org/10.5206/mase/16685","url":null,"abstract":"Methicillin-Resistant Staphylococcus Aureus (MRSA) infection can occur alongside or following COVID-19, which is a concern in healthcare settings. The effectiveness of antiviral treatments for COVID-19 depends on a functioning immune response, but antibiotics used for bacterial infections like MRSA can disrupt the immune response and reduce the effectiveness of antiviral treatments. The emergence of MRSA due to excessive antibiotic usage has led to the widespread use of vancomycin as an alternative treatment. Immunomodulatory antibiotics like azithromycin may also be considered. To study the dynamics of these coinfections, a multiscale model was developed. Parameter estimation and sensitivity analysis were performed, revealing influential parameters affecting the reproduction number. Numerical simulations showed that methicillin may increase the population of co-infected cells, while azithromycin can improve the host immune response but has limited impact on MRSA proliferation. Increased efficacy of vancomycin can lead to MRSA eradication. Combination of immunomodulatory antibiotics and vancomycin has minimal effect on co-infected cell population, but increased vancomycin efficacy can reduce coinfection severity. This study emphasizes the importance of continuous research, surveillance, and the development of effective strategies to combat the complexities of COVID-19 and MRSA coinfection.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138967406","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}
Biological invasion has become an important element of global changes. In this paper, we use a reaction-diffusion system to discuss the minimal invasion speed of two competing species in the homogeneous environment. The general condition for the minimum invasion speed is obtained by applying the theory of propagation dynamics. Then the explicit conditions are derived by constructing upper solutions. The analytical results are corroborated by simulations of the considered reaction-diffusion system. Our results reveal the impact of the diffusion rate, growth rate, competitiveness of the species, as well as the carrying capacity of the environment, on the invasion speed, which provides an effective method for preventing biological invasion and controlling existing biological invasion.
{"title":"The minimal invasion speed of two competing species in homogeneous environment","authors":"Xu Li, Tingting Zhang, Qiming Zhang","doi":"10.5206/mase/16801","DOIUrl":"https://doi.org/10.5206/mase/16801","url":null,"abstract":"Biological invasion has become an important element of global changes. In this paper, we use a reaction-diffusion system to discuss the minimal invasion speed of two competing species in the homogeneous environment. The general condition for the minimum invasion speed is obtained by applying the theory of propagation dynamics. Then the explicit conditions are derived by constructing upper solutions. The analytical results are corroborated by simulations of the considered reaction-diffusion system. Our results reveal the impact of the diffusion rate, growth rate, competitiveness of the species, as well as the carrying capacity of the environment, on the invasion speed, which provides an effective method for preventing biological invasion and controlling existing biological invasion.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139233195","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}
This paper discusses a mathematical model describing the formation of tuberculosis(TB) granulomas. The main purpose is to analyze the change trend of Mtb and immune cells in different stages after Mtb invaded the host. The theoretical analysis indicates that the existence and global stability of bacteria-free equilibrium and bacteria-present equilibrium under different conditions. In addition, the sensitivity analysis is performed on the parameters, which determines the parameters that have the greatest impact on Mtb invading the host. The stage of no infection, the latent TB infection(LTBIs) and active TB corresponding to the clearance, survival or growth and reproduction of Mtb are displayed by the numerical simulations. The results suggest that whether the individuals infected with Mtb will be progressed to the active TB depends on the immune system of individuals.
{"title":"Analysis of a simple mathematical model describing tuberculous granuloma","authors":"Yuqi Jin, Hui Cao, Xiaxia Xu","doi":"10.5206/mase/16678","DOIUrl":"https://doi.org/10.5206/mase/16678","url":null,"abstract":"This paper discusses a mathematical model describing the formation of tuberculosis(TB) granulomas. The main purpose is to analyze the change trend of Mtb and immune cells in different stages after Mtb invaded the host. The theoretical analysis indicates that the existence and global stability of bacteria-free equilibrium and bacteria-present equilibrium under different conditions. In addition, the sensitivity analysis is performed on the parameters, which determines the parameters that have the greatest impact on Mtb invading the host. The stage of no infection, the latent TB infection(LTBIs) and active TB corresponding to the clearance, survival or growth and reproduction of Mtb are displayed by the numerical simulations. The results suggest that whether the individuals infected with Mtb will be progressed to the active TB depends on the immune system of individuals.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135392986","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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