Pub Date : 2022-10-26DOI: 10.1142/s0218339022500292
Biswajit Paul, Bapin Mondal, J. Ghosh, U. Ghosh
In this paper, we investigate the behavior of a predator–prey model with cooperation and Allee effect considering both deterministic and stochastic approaches. The main aim of this paper is to investigate the effect of environmental fluctuation in a deterministic predator–prey model. During the analysis of the deterministic model, it is shown that the system has saddle-node point of co-dimension 1, Hopf bifurcation and Bogdanov–Takens bifurcation of co-dimension 2. To study the effect of environmental fluctuation, we use perturbation to the birth rate of prey and death rate of predator density by Gaussian white noise. The persistence of the model and the stationary distribution is shown by forming a suitable Lyapunov function. Finally, numerical simulations are performed to validate the theoretical findings.
{"title":"DYNAMIC INTERACTIONS BETWEEN PREY AND PREDATOR WITH COOPERATION AND ALLEE EFFECT: DETERMINISTIC AND STOCHASTIC APPROACH","authors":"Biswajit Paul, Bapin Mondal, J. Ghosh, U. Ghosh","doi":"10.1142/s0218339022500292","DOIUrl":"https://doi.org/10.1142/s0218339022500292","url":null,"abstract":"In this paper, we investigate the behavior of a predator–prey model with cooperation and Allee effect considering both deterministic and stochastic approaches. The main aim of this paper is to investigate the effect of environmental fluctuation in a deterministic predator–prey model. During the analysis of the deterministic model, it is shown that the system has saddle-node point of co-dimension 1, Hopf bifurcation and Bogdanov–Takens bifurcation of co-dimension 2. To study the effect of environmental fluctuation, we use perturbation to the birth rate of prey and death rate of predator density by Gaussian white noise. The persistence of the model and the stationary distribution is shown by forming a suitable Lyapunov function. Finally, numerical simulations are performed to validate the theoretical findings.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44660902","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 : 2022-10-21DOI: 10.1142/s0218339022500280
Qing Han
An age-structured deterministic model with multiple infections that accounts for decaying maternal antibody, waning infection-acquired and vaccine-induced immunity is formulated to study the transmission dynamics of pertussis and the effect of childhood DTaP and adolescent Tdap vaccines. The expression of the reproduction number [Formula: see text] is derived for the ODE model in the case of proportionate mixing. Estimated age-dependent transmission probability and empirical contact data are used in the simulation of the ODE model from which the basic reproduction number [Formula: see text] is estimated to be around 15. The combination of DTaP and Tdap vaccines fails to bring [Formula: see text] under one and thus pertussis remains endemic despite sustained high coverage of vaccination. While both DTaP and Tdap vaccines have remarkable effect on reducing the incidences of the age groups being directly vaccinated, the adolescent booster dose Tdap is also found to provide some indirect protection for infants though very limited ([Formula: see text] incidence reduction).
{"title":"AN AGE-STRUCTURED MODEL FOR PERTUSSIS TRANSMISSION WITH MULTIPLE INFECTIONS STUDYING THE EFFECTS OF CHILDHOOD DTAP AND ADOLESCENT TDAP VACCINES","authors":"Qing Han","doi":"10.1142/s0218339022500280","DOIUrl":"https://doi.org/10.1142/s0218339022500280","url":null,"abstract":"An age-structured deterministic model with multiple infections that accounts for decaying maternal antibody, waning infection-acquired and vaccine-induced immunity is formulated to study the transmission dynamics of pertussis and the effect of childhood DTaP and adolescent Tdap vaccines. The expression of the reproduction number [Formula: see text] is derived for the ODE model in the case of proportionate mixing. Estimated age-dependent transmission probability and empirical contact data are used in the simulation of the ODE model from which the basic reproduction number [Formula: see text] is estimated to be around 15. The combination of DTaP and Tdap vaccines fails to bring [Formula: see text] under one and thus pertussis remains endemic despite sustained high coverage of vaccination. While both DTaP and Tdap vaccines have remarkable effect on reducing the incidences of the age groups being directly vaccinated, the adolescent booster dose Tdap is also found to provide some indirect protection for infants though very limited ([Formula: see text] incidence reduction).","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45638802","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 : 2022-10-21DOI: 10.1142/s0218339022500309
L. L. Obsu
In this paper, an optimal control theory was applied to the tuberculosis (TB) model governed by system of nonlinear ordinary differential equations. The aim is to investigate the impact of treatment failure on the TB epidemic. An optimal control strategy is proposed to minimize the disease effect and cost incurred due to treatment failure. The existence and uniqueness of optimal controls are proved. The characterization of optimal paths is analytically derived using Pontryagin’s Minimum Principle. The control-induced model is then fitted using TB infected cases reported from the year 2010–2019 in East Shewa zone Oromia regional state, Ethiopia. Different simulation cases were performed to compare with analytical results. The simulation results show that the combined effect of awareness via various mass media and continuous supervision during the treatment period helps to reduce treatment failure and hence reduced the TB epidemic in the community.
{"title":"OPTIMAL CONTROL ANALYSIS OF A TUBERCULOSIS MODEL","authors":"L. L. Obsu","doi":"10.1142/s0218339022500309","DOIUrl":"https://doi.org/10.1142/s0218339022500309","url":null,"abstract":"In this paper, an optimal control theory was applied to the tuberculosis (TB) model governed by system of nonlinear ordinary differential equations. The aim is to investigate the impact of treatment failure on the TB epidemic. An optimal control strategy is proposed to minimize the disease effect and cost incurred due to treatment failure. The existence and uniqueness of optimal controls are proved. The characterization of optimal paths is analytically derived using Pontryagin’s Minimum Principle. The control-induced model is then fitted using TB infected cases reported from the year 2010–2019 in East Shewa zone Oromia regional state, Ethiopia. Different simulation cases were performed to compare with analytical results. The simulation results show that the combined effect of awareness via various mass media and continuous supervision during the treatment period helps to reduce treatment failure and hence reduced the TB epidemic in the community.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41737712","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 : 2022-08-31DOI: 10.1142/s0218339022500243
Hongquan Sun, Hong Li, Zhangsheng Zhu
Influenced by seasonal changes, the infection rate of many infectious diseases fluctuates in cycles. In this paper, we propose and investigate an SIRS model on a scale-free network. To model seasonality, we assume that the infection rate is periodic. The existence and positivity of solutions of the proposed model are proved and the basic reproduction number [Formula: see text] is defined. The global stability of steady states is determined by rigorous mathematical analysis. When [Formula: see text], the disease-free equilibrium [Formula: see text] is globally asymptotically stable. When [Formula: see text], the system has a unique positive periodic solution [Formula: see text], and [Formula: see text] is globally asymptotically stable. Numerical simulations are performed to support our theoretic results, and the effects of various parameters on the amplitude and mean of infected individuals are studied. The sensitivity of parameters of the basic reproduction number [Formula: see text] is solved by the Sobol global sensitivity analysis method, and the results show that the effects of the parameters [Formula: see text] and [Formula: see text] on [Formula: see text] are remarkable.
{"title":"DYNAMICS OF AN SIRS EPIDEMIC MODEL WITH PERIODIC INFECTION RATE ON A SCALE-FREE NETWORK","authors":"Hongquan Sun, Hong Li, Zhangsheng Zhu","doi":"10.1142/s0218339022500243","DOIUrl":"https://doi.org/10.1142/s0218339022500243","url":null,"abstract":"Influenced by seasonal changes, the infection rate of many infectious diseases fluctuates in cycles. In this paper, we propose and investigate an SIRS model on a scale-free network. To model seasonality, we assume that the infection rate is periodic. The existence and positivity of solutions of the proposed model are proved and the basic reproduction number [Formula: see text] is defined. The global stability of steady states is determined by rigorous mathematical analysis. When [Formula: see text], the disease-free equilibrium [Formula: see text] is globally asymptotically stable. When [Formula: see text], the system has a unique positive periodic solution [Formula: see text], and [Formula: see text] is globally asymptotically stable. Numerical simulations are performed to support our theoretic results, and the effects of various parameters on the amplitude and mean of infected individuals are studied. The sensitivity of parameters of the basic reproduction number [Formula: see text] is solved by the Sobol global sensitivity analysis method, and the results show that the effects of the parameters [Formula: see text] and [Formula: see text] on [Formula: see text] are remarkable.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46647134","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 : 2022-08-31DOI: 10.1142/s021833902250022x
Bei Sun, K. Okosun, Xue Zhang
This paper studies an SIS-type Lyme transmission model incorporating insecticides spraying and vaccination as interventions. We obtain the positivity and boundedness of solutions, calculate the basic reproduction number, and discuss the global stability of disease-free and endemic equilibria when the basic reproduction number [Formula: see text] and [Formula: see text], respectively. We apply Pontryagin’s maximum principle to explore an optimal control strategy to minimize the number of infected ticks and hosts and the cost of using insecticides and vaccination. We design numerical simulations to illustrate the effectiveness of theoretical analysis.
{"title":"STABILITY ANALYSIS AND OPTIMAL CONTROL OF A LYME DISEASE MODEL WITH INSECTICIDES SPRAYING AND VACCINATION","authors":"Bei Sun, K. Okosun, Xue Zhang","doi":"10.1142/s021833902250022x","DOIUrl":"https://doi.org/10.1142/s021833902250022x","url":null,"abstract":"This paper studies an SIS-type Lyme transmission model incorporating insecticides spraying and vaccination as interventions. We obtain the positivity and boundedness of solutions, calculate the basic reproduction number, and discuss the global stability of disease-free and endemic equilibria when the basic reproduction number [Formula: see text] and [Formula: see text], respectively. We apply Pontryagin’s maximum principle to explore an optimal control strategy to minimize the number of infected ticks and hosts and the cost of using insecticides and vaccination. We design numerical simulations to illustrate the effectiveness of theoretical analysis.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44391241","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 : 2022-08-13DOI: 10.1142/s021833902250019x
Buddhi Pantha, Jemal Mohammed-Awel, N. Vaidya
Despite the significant progress in the development of vaccines, the COVID-19 pandemic still poses difficulty for its control because of many obstacles such as the proper implementation of vaccination, public hesitancy towards vaccines, dropping out from the second dose, and varying level of protection after the first and the second doses. In this study, we develop a novel mathematical model of COVID-19 transmission, including two separate vaccinated compartments (first dose and both doses). We parametrize and validate our model using data from Dougherty county of Georgia, USA, one of the most affected counties, where the transmission trend clearly is associated with various policies and public events. We analyze our model for stability of equilibria and persistence of the disease, and formulate expression for reproduction numbers. We estimate that the basic reproduction number in Dougherty county is 1.69, and the effective reproduction number during the study period ranges from 0.26 to 6.36. The number of daily undiagnosed cases peaked at 310 per day, resulting in the maximum number of active infectious individuals to be 2471. Our model predicts that in a high transmission scenario, the vaccination strategies should be combined with other non-pharmaceutical prevention strategies to ensure transmission control. Moreover, our results emphasize that completing both doses of vaccines on time is critical to achieve maximum benefits from the vaccination programs.
{"title":"EFFECTS OF VACCINATION ON THE TRANSMISSION DYNAMICS OF COVID-19 IN DOUGHERTY COUNTY OF GEORGIA, USA","authors":"Buddhi Pantha, Jemal Mohammed-Awel, N. Vaidya","doi":"10.1142/s021833902250019x","DOIUrl":"https://doi.org/10.1142/s021833902250019x","url":null,"abstract":"Despite the significant progress in the development of vaccines, the COVID-19 pandemic still poses difficulty for its control because of many obstacles such as the proper implementation of vaccination, public hesitancy towards vaccines, dropping out from the second dose, and varying level of protection after the first and the second doses. In this study, we develop a novel mathematical model of COVID-19 transmission, including two separate vaccinated compartments (first dose and both doses). We parametrize and validate our model using data from Dougherty county of Georgia, USA, one of the most affected counties, where the transmission trend clearly is associated with various policies and public events. We analyze our model for stability of equilibria and persistence of the disease, and formulate expression for reproduction numbers. We estimate that the basic reproduction number in Dougherty county is 1.69, and the effective reproduction number during the study period ranges from 0.26 to 6.36. The number of daily undiagnosed cases peaked at 310 per day, resulting in the maximum number of active infectious individuals to be 2471. Our model predicts that in a high transmission scenario, the vaccination strategies should be combined with other non-pharmaceutical prevention strategies to ensure transmission control. Moreover, our results emphasize that completing both doses of vaccines on time is critical to achieve maximum benefits from the vaccination programs.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43176669","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 : 2022-07-30DOI: 10.1142/s0218339022500218
A. Zewdie, S. Gakkhar, Shivmurti K Gupta
Anthrax is a disease caused by Bacillus anthracis, commonly affects animals as well as humans health. In this paper, a nonlinear deterministic anthrax model involving human and animal is proposed and analyzed. The reproduction number [Formula: see text] and equilibrium points are explored to study the dynamic behavior of the disease. The existence and stability of equilibrium points are discussed. For [Formula: see text], the disease-free equilibrium [Formula: see text] is globally stable. However, it is unstable when [Formula: see text] and a locally stable endemic equilibrium point [Formula: see text] exists. The model is then extended to optimal control model considering human vaccination, animal vaccination and proper removal of carcass. The vaccination class of human and animal population appears separately in a model. The existence and characterization of optimal control are discussed. The numerical simulations are carried out for the choice of parametric values and initial conditions. These illustrate scavengers in the suspected area which eat infected dead body of animals contributing to the effort of reducing the expansion of disease. In addition, numerical comparison analysis with four distinct control strategies is carried out. Our findings show that each control technique has its own influence on reducing the total number of infections in the human and animal populations. The cumulative impact of all control measures is found to be extremely effective in lowering the prevalence of the disease.
{"title":"MODEL FOR TRANSMISSION AND OPTIMAL CONTROL OF ANTHRAX INVOLVING HUMAN AND ANIMAL POPULATION","authors":"A. Zewdie, S. Gakkhar, Shivmurti K Gupta","doi":"10.1142/s0218339022500218","DOIUrl":"https://doi.org/10.1142/s0218339022500218","url":null,"abstract":"Anthrax is a disease caused by Bacillus anthracis, commonly affects animals as well as humans health. In this paper, a nonlinear deterministic anthrax model involving human and animal is proposed and analyzed. The reproduction number [Formula: see text] and equilibrium points are explored to study the dynamic behavior of the disease. The existence and stability of equilibrium points are discussed. For [Formula: see text], the disease-free equilibrium [Formula: see text] is globally stable. However, it is unstable when [Formula: see text] and a locally stable endemic equilibrium point [Formula: see text] exists. The model is then extended to optimal control model considering human vaccination, animal vaccination and proper removal of carcass. The vaccination class of human and animal population appears separately in a model. The existence and characterization of optimal control are discussed. The numerical simulations are carried out for the choice of parametric values and initial conditions. These illustrate scavengers in the suspected area which eat infected dead body of animals contributing to the effort of reducing the expansion of disease. In addition, numerical comparison analysis with four distinct control strategies is carried out. Our findings show that each control technique has its own influence on reducing the total number of infections in the human and animal populations. The cumulative impact of all control measures is found to be extremely effective in lowering the prevalence of the disease.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49458492","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 : 2022-06-25DOI: 10.1142/s0218339022500206
M. F. Jiménez, G. Blé, M. Falconi
In this work, the impact of a biological agent (Trichoderma spp.) on the dynamic of a plant–parasite model is analyzed. It is assumed that the plant–Trichoderma spp. relationship is mutualistic, the Trichoderma spp.–parasite relationship is that of predator–prey, and the parasite is specialist. Conditions for pest eradication and for species coexistence are shown.
{"title":"DYNAMICS OF A MATHEMATICAL MODEL FOR INTERACTION PLANT–PARASITE–TRICHODERMA","authors":"M. F. Jiménez, G. Blé, M. Falconi","doi":"10.1142/s0218339022500206","DOIUrl":"https://doi.org/10.1142/s0218339022500206","url":null,"abstract":"In this work, the impact of a biological agent (Trichoderma spp.) on the dynamic of a plant–parasite model is analyzed. It is assumed that the plant–Trichoderma spp. relationship is mutualistic, the Trichoderma spp.–parasite relationship is that of predator–prey, and the parasite is specialist. Conditions for pest eradication and for species coexistence are shown.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41763789","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 : 2022-05-12DOI: 10.1142/s0218339022500164
Tsegaye Kebede Irena, S. Gakkhar
A deterministic nonlinear mathematical model is developed for typhoid transmission dynamics in human hosts, coupled with multiple transmission routes. The model aims to examine the role of control interventions such as vaccination, environmental sanitation, and saturated treatment on the prevalence of typhoid. First, the qualitative analysis of the model with constant control interventions is performed. The model exhibits a backward bifurcation phenomenon. Sensitivity analysis is also conducted to identify impactful parameters for effective control of the disease. Then, the model is extended to a corresponding optimal control problem to investigate the optimum intervention strategies by assessing their effects on typhoid prevalence and economic load. The characterization of the optimal controls is determined using Pontryagin’s Maximum Principle, and the optimality system is developed. Numerical results suggest that, in the absence of treatment, the combination of vaccination and environmental sanitation controls plays an important role in reducing the typhoid burden and economic load. Moreover, the comprehensive use of the three control interventions is more effective than using any single or two combined control interventions. It reduces the number of infective humans and environmental bacteria as well as the cost burden associated with applied controls and opportunity loss. Thus, the comprehensive effect of the three control interventions is found to be more economical during typhoid outbreaks.
{"title":"MODELING THE ROLE OF VACCINATION, ENVIRONMENTAL SANITATION, AND SATURATED TREATMENT ON THE SPREAD OF TYPHOID FEVER","authors":"Tsegaye Kebede Irena, S. Gakkhar","doi":"10.1142/s0218339022500164","DOIUrl":"https://doi.org/10.1142/s0218339022500164","url":null,"abstract":"A deterministic nonlinear mathematical model is developed for typhoid transmission dynamics in human hosts, coupled with multiple transmission routes. The model aims to examine the role of control interventions such as vaccination, environmental sanitation, and saturated treatment on the prevalence of typhoid. First, the qualitative analysis of the model with constant control interventions is performed. The model exhibits a backward bifurcation phenomenon. Sensitivity analysis is also conducted to identify impactful parameters for effective control of the disease. Then, the model is extended to a corresponding optimal control problem to investigate the optimum intervention strategies by assessing their effects on typhoid prevalence and economic load. The characterization of the optimal controls is determined using Pontryagin’s Maximum Principle, and the optimality system is developed. Numerical results suggest that, in the absence of treatment, the combination of vaccination and environmental sanitation controls plays an important role in reducing the typhoid burden and economic load. Moreover, the comprehensive use of the three control interventions is more effective than using any single or two combined control interventions. It reduces the number of infective humans and environmental bacteria as well as the cost burden associated with applied controls and opportunity loss. Thus, the comprehensive effect of the three control interventions is found to be more economical during typhoid outbreaks.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46510750","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 : 2022-05-12DOI: 10.1142/s0218339022500139
I. Trejo, Mehtap Lafci Büyükkahraman, H. Kojouharov
Innate immune system cells activate in response to infection and trigger an acute inflammatory reaction to restore tissue homeostasis and promote subsequent tissue repair. Their activation and functions must be very well regulated to avoid tissue damage, organ dysfunction, or even death. In this work, a new set of mathematical models is presented to examine the dynamics of the innate immune system response to tissue damage and provide further understanding of the role of the innate immune system during the early stages of an inflammatory response. Different damaged cells production functions are proposed to represent the effect of secondary tissue damage by the innate immune system. The stability and bifurcation analyses of the model reveal that there is an important threshold parameter that can be controlled in order to avoid sustained chronic inflammation and secure a successful healing outcome. A set of numerical simulations is also performed to support the presented theoretical results and demonstrate the medical applicability of the new mathematical model.
{"title":"MATHEMATICAL INSIGHTS INTO THE DYNAMICS OF INNATE IMMUNE RESPONSE DURING INFLAMMATION","authors":"I. Trejo, Mehtap Lafci Büyükkahraman, H. Kojouharov","doi":"10.1142/s0218339022500139","DOIUrl":"https://doi.org/10.1142/s0218339022500139","url":null,"abstract":"Innate immune system cells activate in response to infection and trigger an acute inflammatory reaction to restore tissue homeostasis and promote subsequent tissue repair. Their activation and functions must be very well regulated to avoid tissue damage, organ dysfunction, or even death. In this work, a new set of mathematical models is presented to examine the dynamics of the innate immune system response to tissue damage and provide further understanding of the role of the innate immune system during the early stages of an inflammatory response. Different damaged cells production functions are proposed to represent the effect of secondary tissue damage by the innate immune system. The stability and bifurcation analyses of the model reveal that there is an important threshold parameter that can be controlled in order to avoid sustained chronic inflammation and secure a successful healing outcome. A set of numerical simulations is also performed to support the presented theoretical results and demonstrate the medical applicability of the new mathematical model.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42723610","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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