Pub Date : 2022-12-01DOI: 10.1080/17513758.2022.2155717
Yongxin Gao, Shuyuan Yao
In this paper, we use a mean-reverting Ornstein-Uhlenbeck process to simulate the stochastic perturbations in the environment, and then a modified Leslie-Gower Holling-type II predator-prey stochastic model in a polluted environment with interspecific competition and pulse toxicant input is proposed. Through constructing V-function and applying formula, the sharp sufficient conditions including strongly persistent in the mean, persistent in the mean and extinction are established. In addition, the theoretical results are verified by numerical simulation.
{"title":"Dynamical analysis of a modified Leslie-Gower Holling-type II predator-prey stochastic model in polluted environments with interspecific competition and impulsive toxicant input.","authors":"Yongxin Gao, Shuyuan Yao","doi":"10.1080/17513758.2022.2155717","DOIUrl":"https://doi.org/10.1080/17513758.2022.2155717","url":null,"abstract":"<p><p>In this paper, we use a mean-reverting Ornstein-Uhlenbeck process to simulate the stochastic perturbations in the environment, and then a modified Leslie-Gower Holling-type II predator-prey stochastic model in a polluted environment with interspecific competition and pulse toxicant input is proposed. Through constructing V-function and applying <math><mi>It</mi><msup><mrow><mrow><mover><mi>o</mi><mo>^</mo></mover></mrow></mrow><mo>'</mo></msup><mi>s</mi></math> formula, the sharp sufficient conditions including strongly persistent in the mean, persistent in the mean and extinction are established. In addition, the theoretical results are verified by numerical simulation.</p>","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"16 1","pages":"840-858"},"PeriodicalIF":2.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10838564","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 : 2022-06-02DOI: 10.1080/17513758.2022.2079739
Yiyou Pang, Shuai Wang, Siyu Liu
In this paper, we study a stage-structured wild and sterile mosquito interaction impulsive model. The aim is to study the feasibility of controlling the population of wild mosquitoes by releasing sterile mosquitoes periodically. The existence of trivial periodic solutions is obtained, and the corresponding local stability and global stability conditions are proved by Floquet theory and Lyapunov stability theorem, respectively. And we prove the existence conditions of non-trivial periodic solutions and their local stability. We can find that the system has the bistable phenomenon in which the trivial periodic solution and the non-trivial periodic solution can coexist under certain threshold conditions. All the results show that the appropriate release period and release amount of sterile mosquitoes can control the wild mosquito population within a certain range and even make them extinct. Finally, numerical simulation verifies our theoretical results.
{"title":"Dynamics analysis of stage-structured wild and sterile mosquito interaction impulsive model","authors":"Yiyou Pang, Shuai Wang, Siyu Liu","doi":"10.1080/17513758.2022.2079739","DOIUrl":"https://doi.org/10.1080/17513758.2022.2079739","url":null,"abstract":"In this paper, we study a stage-structured wild and sterile mosquito interaction impulsive model. The aim is to study the feasibility of controlling the population of wild mosquitoes by releasing sterile mosquitoes periodically. The existence of trivial periodic solutions is obtained, and the corresponding local stability and global stability conditions are proved by Floquet theory and Lyapunov stability theorem, respectively. And we prove the existence conditions of non-trivial periodic solutions and their local stability. We can find that the system has the bistable phenomenon in which the trivial periodic solution and the non-trivial periodic solution can coexist under certain threshold conditions. All the results show that the appropriate release period and release amount of sterile mosquitoes can control the wild mosquito population within a certain range and even make them extinct. Finally, numerical simulation verifies our theoretical results.","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"16 1","pages":"464 - 479"},"PeriodicalIF":2.8,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46992426","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 : 2022-05-30DOI: 10.1080/17513758.2022.2081368
Birhan Getachew Bitew, J. Munganga, Adamu Shitu Hassan
In this study, a model for the spread of cyst echinococcosis with interventions is formulated. The disease-free and endemic equilibrium points of the model are calculated. The control reproduction number for the model is derived, and the global dynamics are established by the values of . The disease-free equilibrium is globally asymptotically stable if and only if . For , using Volterra–Lyapunov stable matrices, it is proven that the endemic equilibrium is globally asymptotically stable. Sensitivity analysis to identify the most influential parameters in the dynamics of CE is carried out. To establish the long-term behaviour of the disease, numerical simulations are performed. The impact of control strategies is investigated. It is shown that, whenever vaccination of sheep is carried out solely or in combination with cleaning or disinfecting of the environment, cyst echinococcosis can be wiped out.
{"title":"Mathematical modelling of echinococcosis in human, dogs and sheep with intervention","authors":"Birhan Getachew Bitew, J. Munganga, Adamu Shitu Hassan","doi":"10.1080/17513758.2022.2081368","DOIUrl":"https://doi.org/10.1080/17513758.2022.2081368","url":null,"abstract":"In this study, a model for the spread of cyst echinococcosis with interventions is formulated. The disease-free and endemic equilibrium points of the model are calculated. The control reproduction number for the model is derived, and the global dynamics are established by the values of . The disease-free equilibrium is globally asymptotically stable if and only if . For , using Volterra–Lyapunov stable matrices, it is proven that the endemic equilibrium is globally asymptotically stable. Sensitivity analysis to identify the most influential parameters in the dynamics of CE is carried out. To establish the long-term behaviour of the disease, numerical simulations are performed. The impact of control strategies is investigated. It is shown that, whenever vaccination of sheep is carried out solely or in combination with cleaning or disinfecting of the environment, cyst echinococcosis can be wiped out.","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"16 1","pages":"439 - 463"},"PeriodicalIF":2.8,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47234122","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 : 2022-05-30DOI: 10.1080/17513758.2022.2078899
N. Tuncer, A. Timsina, M. Nuño, G. Chowell, M. Martcheva
We fit an SARS-CoV-2 model to US data of COVID-19 cases and deaths. We conclude that the model is not structurally identifiable. We make the model identifiable by prefixing some of the parameters from external information. Practical identifiability of the model through Monte Carlo simulations reveals that two of the parameters may not be practically identifiable. With thus identified parameters, we set up an optimal control problem with social distancing and isolation as control variables. We investigate two scenarios: the controls are applied for the entire duration and the controls are applied only for the period of time. Our results show that if the controls are applied early in the epidemic, the reduction in the infected classes is at least an order of magnitude higher compared to when controls are applied with 2-week delay. Further, removing the controls before the pandemic ends leads to rebound of the infected classes.
{"title":"Parameter identifiability and optimal control of an SARS-CoV-2 model early in the pandemic","authors":"N. Tuncer, A. Timsina, M. Nuño, G. Chowell, M. Martcheva","doi":"10.1080/17513758.2022.2078899","DOIUrl":"https://doi.org/10.1080/17513758.2022.2078899","url":null,"abstract":"We fit an SARS-CoV-2 model to US data of COVID-19 cases and deaths. We conclude that the model is not structurally identifiable. We make the model identifiable by prefixing some of the parameters from external information. Practical identifiability of the model through Monte Carlo simulations reveals that two of the parameters may not be practically identifiable. With thus identified parameters, we set up an optimal control problem with social distancing and isolation as control variables. We investigate two scenarios: the controls are applied for the entire duration and the controls are applied only for the period of time. Our results show that if the controls are applied early in the epidemic, the reduction in the infected classes is at least an order of magnitude higher compared to when controls are applied with 2-week delay. Further, removing the controls before the pandemic ends leads to rebound of the infected classes.","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"16 1","pages":"412 - 438"},"PeriodicalIF":2.8,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48722633","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 : 2022-05-09DOI: 10.1080/17513758.2022.2071489
M. Leite, B. Chen-Charpentier, F. Agusto, O. Gaoue, N. Hritonenko
Habitat loss and harvesting of non-timber forest products (NTFPs) significantly affect the population dynamics. In this paper, we propose a general mathematical modelling approach incorporating the impact of habitat size reduction and non-lethal harvesting of NTFP on population dynamics. The model framework integrates experimental data of Pentadesma butyracea in Benin. This framework allows us to determine the rational non-lethal harvesting level and habitat size to ensure the stability of the plant ecosystem, and to study the impacts of distinct levels of humidity. We suggest non-lethal harvesting policies that maximize the economic benefit for local populations.
{"title":"Viability of Pentadesma in reduced habitat ecosystems within two climatic regions with fruit harvesting","authors":"M. Leite, B. Chen-Charpentier, F. Agusto, O. Gaoue, N. Hritonenko","doi":"10.1080/17513758.2022.2071489","DOIUrl":"https://doi.org/10.1080/17513758.2022.2071489","url":null,"abstract":"Habitat loss and harvesting of non-timber forest products (NTFPs) significantly affect the population dynamics. In this paper, we propose a general mathematical modelling approach incorporating the impact of habitat size reduction and non-lethal harvesting of NTFP on population dynamics. The model framework integrates experimental data of Pentadesma butyracea in Benin. This framework allows us to determine the rational non-lethal harvesting level and habitat size to ensure the stability of the plant ecosystem, and to study the impacts of distinct levels of humidity. We suggest non-lethal harvesting policies that maximize the economic benefit for local populations.","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"16 1","pages":"207 - 235"},"PeriodicalIF":2.8,"publicationDate":"2022-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49324637","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 : 2022-04-25DOI: 10.1080/17513758.2022.2066729
Ming Chen, Jimin Zhang, Satlykova Ejegul
A mathematical model with the intraguild predation structure is proposed to describe the interactions of autotrophs and mixotrophs containing light and nutrients in a well-mixed aquatic ecosystem. The dissipation, existence and stability of equilibria of the model are proved, and the ecological reproductive indexes for the extinction, survival and coexistence of autotrophs and mixotrophs are established. We also consider the influence of Holling type functional responses and abiotic factors on the coexistence and biomass of autotrophs and mixotrophs. It is shown that the intraguild predation structure is beneficial to phytoplankton biodiversity and provides an explanation for the phytoplankton paradox.
{"title":"Dynamics of autotroph–mixotroph interactions with the intraguild predation structure","authors":"Ming Chen, Jimin Zhang, Satlykova Ejegul","doi":"10.1080/17513758.2022.2066729","DOIUrl":"https://doi.org/10.1080/17513758.2022.2066729","url":null,"abstract":"A mathematical model with the intraguild predation structure is proposed to describe the interactions of autotrophs and mixotrophs containing light and nutrients in a well-mixed aquatic ecosystem. The dissipation, existence and stability of equilibria of the model are proved, and the ecological reproductive indexes for the extinction, survival and coexistence of autotrophs and mixotrophs are established. We also consider the influence of Holling type functional responses and abiotic factors on the coexistence and biomass of autotrophs and mixotrophs. It is shown that the intraguild predation structure is beneficial to phytoplankton biodiversity and provides an explanation for the phytoplankton paradox.","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"16 1","pages":"186 - 206"},"PeriodicalIF":2.8,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41495816","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 : 2022-04-11DOI: 10.1080/17513758.2022.2061614
Ivy J Hindle, L. Forbes, S. Carver
Understanding the spread of pathogens through the environment is critical to a fuller comprehension of disease dynamics. However, many mathematical models of disease dynamics ignore spatial effects. We seek to expand knowledge around the interaction between the bare-nosed wombat (Vombatus ursinus) and sarcoptic mange (etiologic agent Sarcoptes scabiei), by extending an aspatial mathematical model to include spatial variation. S. scabiei was found to move through our modelled region as a spatio-temporal travelling wave, leaving behind pockets of localized host extinction, consistent with field observations. The speed of infection spread was also comparable with field research. Our model predicts that the inclusion of spatial dynamics leads to the survival and recovery of affected wombat populations when an aspatial model predicts extinction. Collectively, this research demonstrates how environmentally transmitted S. scabiei can result in travelling wave dynamics, and that inclusion of spatial variation reveals a more resilient host population than aspatial modelling approaches.
{"title":"The effect of spatial dynamics on the behaviour of an environmentally transmitted disease","authors":"Ivy J Hindle, L. Forbes, S. Carver","doi":"10.1080/17513758.2022.2061614","DOIUrl":"https://doi.org/10.1080/17513758.2022.2061614","url":null,"abstract":"Understanding the spread of pathogens through the environment is critical to a fuller comprehension of disease dynamics. However, many mathematical models of disease dynamics ignore spatial effects. We seek to expand knowledge around the interaction between the bare-nosed wombat (Vombatus ursinus) and sarcoptic mange (etiologic agent Sarcoptes scabiei), by extending an aspatial mathematical model to include spatial variation. S. scabiei was found to move through our modelled region as a spatio-temporal travelling wave, leaving behind pockets of localized host extinction, consistent with field observations. The speed of infection spread was also comparable with field research. Our model predicts that the inclusion of spatial dynamics leads to the survival and recovery of affected wombat populations when an aspatial model predicts extinction. Collectively, this research demonstrates how environmentally transmitted S. scabiei can result in travelling wave dynamics, and that inclusion of spatial variation reveals a more resilient host population than aspatial modelling approaches.","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"16 1","pages":"144 - 159"},"PeriodicalIF":2.8,"publicationDate":"2022-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42169563","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 : 2022-04-11DOI: 10.1080/17513758.2022.2061615
Dimitrios Voulgarelis, K. Bulusu, J. Yates
In this study we compare seven mathematical models of tumour growth using nonlinear mixed-effects which allows for a simultaneous fitting of multiple data and an estimation of both mean behaviour and variability. This is performed for two large datasets, a patient-derived xenograft (PDX) dataset consisting of 220 PDXs spanning six different tumour types and a cell-line derived xenograft (CDX) dataset consisting of 25 cell lines spanning eight tumour types. Comparison of the models is performed by means of visual predictive checks (VPCs) as well as the Akaike Information Criterion (AIC). Additionally, we fit the models to 500 bootstrap samples drawn from the datasets to expand the comparison of the models under dataset perturbations and understand the growth kinetics that are best fitted by each model. Through qualitative and quantitative metrics the best models are identified the effectiveness and practicality of simpler models is highlighted
{"title":"Comparison of classical tumour growth models for patient derived and cell-line derived xenografts using the nonlinear mixed-effects framework","authors":"Dimitrios Voulgarelis, K. Bulusu, J. Yates","doi":"10.1080/17513758.2022.2061615","DOIUrl":"https://doi.org/10.1080/17513758.2022.2061615","url":null,"abstract":"In this study we compare seven mathematical models of tumour growth using nonlinear mixed-effects which allows for a simultaneous fitting of multiple data and an estimation of both mean behaviour and variability. This is performed for two large datasets, a patient-derived xenograft (PDX) dataset consisting of 220 PDXs spanning six different tumour types and a cell-line derived xenograft (CDX) dataset consisting of 25 cell lines spanning eight tumour types. Comparison of the models is performed by means of visual predictive checks (VPCs) as well as the Akaike Information Criterion (AIC). Additionally, we fit the models to 500 bootstrap samples drawn from the datasets to expand the comparison of the models under dataset perturbations and understand the growth kinetics that are best fitted by each model. Through qualitative and quantitative metrics the best models are identified the effectiveness and practicality of simpler models is highlighted","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"16 1","pages":"160 - 185"},"PeriodicalIF":2.8,"publicationDate":"2022-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45993923","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}
In this paper, we consider the dynamical behaviour of a stochastic coronavirus (COVID-19) susceptible-infected-removed epidemic model with the inclusion of the influence of information intervention and Lévy noise. The existence and uniqueness of the model positive solution are proved. Then, we establish a stochastic threshold as a sufficient condition for the extinction and persistence in mean of the disease. Based on the available COVID-19 data, the parameters of the model were estimated and we fit the model with real statistics. Finally, numerical simulations are presented to support our theoretical results.
{"title":"Impact of information and Lévy noise on stochastic COVID-19 epidemic model under real statistical data","authors":"Peijiang Liu, Lifang Huang, Anwarud Din, Xiangxiang Huang","doi":"10.1080/17513758.2022.2055172","DOIUrl":"https://doi.org/10.1080/17513758.2022.2055172","url":null,"abstract":"In this paper, we consider the dynamical behaviour of a stochastic coronavirus (COVID-19) susceptible-infected-removed epidemic model with the inclusion of the influence of information intervention and Lévy noise. The existence and uniqueness of the model positive solution are proved. Then, we establish a stochastic threshold as a sufficient condition for the extinction and persistence in mean of the disease. Based on the available COVID-19 data, the parameters of the model were estimated and we fit the model with real statistics. Finally, numerical simulations are presented to support our theoretical results.","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"16 1","pages":"236 - 253"},"PeriodicalIF":2.8,"publicationDate":"2022-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41930966","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 : 2022-03-14DOI: 10.1080/17513758.2022.2050313
Yongxin Gao, Fan Yang
This paper is concerned with a modified Leslie–Gower and Holling-type II two-predator one-prey model with Lévy jumps. First, we use an Ornstein–Uhlenbeck process to describe the environmental stochasticity and prove that there is a unique positive solution to the system. Moreover, sufficient conditions for persistence in the mean and extinction of each species are established. Finally, we give some numerical simulations to support the main results.
{"title":"Persistence and extinction of a modified Leslie–Gower Holling-type II two-predator one-prey model with Lévy jumps","authors":"Yongxin Gao, Fan Yang","doi":"10.1080/17513758.2022.2050313","DOIUrl":"https://doi.org/10.1080/17513758.2022.2050313","url":null,"abstract":"This paper is concerned with a modified Leslie–Gower and Holling-type II two-predator one-prey model with Lévy jumps. First, we use an Ornstein–Uhlenbeck process to describe the environmental stochasticity and prove that there is a unique positive solution to the system. Moreover, sufficient conditions for persistence in the mean and extinction of each species are established. Finally, we give some numerical simulations to support the main results.","PeriodicalId":48809,"journal":{"name":"Journal of Biological Dynamics","volume":"16 1","pages":"117 - 143"},"PeriodicalIF":2.8,"publicationDate":"2022-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42210217","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号