Pub Date : 2023-05-06DOI: 10.1142/s0218339023500195
E. Bellavere, E. Venturino
In this paper we present a model for a possible containment way of alien species invasions. It relies on the application of one or more stripes on the ground for which the survival conditions are harsher. After reviewing a number of possible threats for biodiversity that are the main motivation of this study, as well as a few instances of landscape disruption, we present a reaction–diffusion model and report the simulations results in various conditions. The inferences indicate that the diffusion process can be delayed, through the use of multiple obstacles, thereby allowing the possibility of taking alternative measures in order to contain the invasion, at least for some time. We discuss the diffusion delay in terms of the level of hostility, the length and the number of consecutive repetitions of the harsh environments. Comparisons on the parameter space show that the harshness and structural characteristics of the stripes are intertwined in a non-trivial way. Alternatively, the model can be used to ascertain the situations in which a population living in a territory can still thrive when its habitat is broken by artifacts, whether human-built or resulting from natural causes. Examples of this sort are presented in the final discussion.
{"title":"CROSSING THE DESERT: A MODEL FOR ALIEN SPECIES INVASION CONTAINMENT OR TO LESSEN HABITAT DISRUPTION EFFECTS","authors":"E. Bellavere, E. Venturino","doi":"10.1142/s0218339023500195","DOIUrl":"https://doi.org/10.1142/s0218339023500195","url":null,"abstract":"In this paper we present a model for a possible containment way of alien species invasions. It relies on the application of one or more stripes on the ground for which the survival conditions are harsher. After reviewing a number of possible threats for biodiversity that are the main motivation of this study, as well as a few instances of landscape disruption, we present a reaction–diffusion model and report the simulations results in various conditions. The inferences indicate that the diffusion process can be delayed, through the use of multiple obstacles, thereby allowing the possibility of taking alternative measures in order to contain the invasion, at least for some time. We discuss the diffusion delay in terms of the level of hostility, the length and the number of consecutive repetitions of the harsh environments. Comparisons on the parameter space show that the harshness and structural characteristics of the stripes are intertwined in a non-trivial way. Alternatively, the model can be used to ascertain the situations in which a population living in a territory can still thrive when its habitat is broken by artifacts, whether human-built or resulting from natural causes. Examples of this sort are presented in the final discussion.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41290373","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 : 2023-05-06DOI: 10.1142/s0218339023500262
T. Vilches, G. B. de Almeida, C.M.C.B. Fortaleza, C. Ferreira
The efficacy of infection prevention and control on several hospital networks is assessed. We tested two kinds of strategy, a network-topology-based allocation and a [Formula: see text]-based allocation, where [Formula: see text] is the basic reproduction number of the infection. For this, a multi-patch deterministic model simulates the spread of carbapenemase-producing Enterobacteriaceae in several theoretical hospital networks parametrized by data from Brazil. Our results show that: (i) the allocation methods based on the [Formula: see text] of the hospitals may work better than the network-topology-based allocations; (ii) results from control efficacy for a specific hospital network cannot be generalized to other types of networks. Putting together the global network topology with local factors that drive pathogens transmission, the [Formula: see text]-based allocation method seems to be enough to control of healthcare-associated infections. Overall, the obtained results emphasize the importance of data collection on infection transmission and patient transfers.
{"title":"IMPROVING CONTROL STRATEGIES OF INFECTIONS BY RESISTANT PATHOGENS IN A HOSPITAL NETWORK","authors":"T. Vilches, G. B. de Almeida, C.M.C.B. Fortaleza, C. Ferreira","doi":"10.1142/s0218339023500262","DOIUrl":"https://doi.org/10.1142/s0218339023500262","url":null,"abstract":"The efficacy of infection prevention and control on several hospital networks is assessed. We tested two kinds of strategy, a network-topology-based allocation and a [Formula: see text]-based allocation, where [Formula: see text] is the basic reproduction number of the infection. For this, a multi-patch deterministic model simulates the spread of carbapenemase-producing Enterobacteriaceae in several theoretical hospital networks parametrized by data from Brazil. Our results show that: (i) the allocation methods based on the [Formula: see text] of the hospitals may work better than the network-topology-based allocations; (ii) results from control efficacy for a specific hospital network cannot be generalized to other types of networks. Putting together the global network topology with local factors that drive pathogens transmission, the [Formula: see text]-based allocation method seems to be enough to control of healthcare-associated infections. Overall, the obtained results emphasize the importance of data collection on infection transmission and patient transfers.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44595469","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 : 2023-04-27DOI: 10.1142/s0218339023500201
H. El-Metwally, A. Khan, M. Y. Hamada
In recent years, the stability of the predator–prey model subject to the Allee effect has become an interesting issue. This study investigates the effect of Allee effect on the stability of a discrete-time predator–prey model with Holling type-II functional response. Using equilibrium analysis, stability analysis and bifurcation theory, the mathematical characteristics of the proposed model are examined. Model experiences flip bifurcation and Neimark–Sacker bifurcation based on the center manifold theorem and bifurcation theory. Our analytical results are demonstrated by numerical simulations.
{"title":"ALLEE EFFECT IN A RICKER TYPE DISCRETE-TIME PREDATOR–PREY MODEL WITH HOLLING TYPE-II FUNCTIONAL RESPONSE","authors":"H. El-Metwally, A. Khan, M. Y. Hamada","doi":"10.1142/s0218339023500201","DOIUrl":"https://doi.org/10.1142/s0218339023500201","url":null,"abstract":"In recent years, the stability of the predator–prey model subject to the Allee effect has become an interesting issue. This study investigates the effect of Allee effect on the stability of a discrete-time predator–prey model with Holling type-II functional response. Using equilibrium analysis, stability analysis and bifurcation theory, the mathematical characteristics of the proposed model are examined. Model experiences flip bifurcation and Neimark–Sacker bifurcation based on the center manifold theorem and bifurcation theory. Our analytical results are demonstrated by numerical simulations.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47448579","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 : 2023-04-27DOI: 10.1142/s0218339023500225
Xiaojuan Liu, Shulin Sun
In this paper, we consider a stochastic food chain chemostat model with variable yields. First, we prove the stochastic model has a unique global positive solution. Second, by employing suitable Lyapunov functions, Itô[Formula: see text] formula and some other important inequalities, the existence of a unique ergodic stationary distribution of a stochastic food chain chemostat model is researched, which can help us better understand the statistical characteristics of stochastic food chain chemostat models. Second, we investigate the extinction of the microorganism and the bacteria. Moreover, the case of extinction for bacteria but persistence for microbial species is considered. Finally, some numerical simulations are carried out to illustrate our theoretical results and the influence of the variable yields on the microorganism and the bacteria.
{"title":"DYNAMICAL BEHAVIOR OF A STOCHASTIC FOOD CHAIN CHEMOSTAT MODEL WITH VARIABLE YIELDS","authors":"Xiaojuan Liu, Shulin Sun","doi":"10.1142/s0218339023500225","DOIUrl":"https://doi.org/10.1142/s0218339023500225","url":null,"abstract":"In this paper, we consider a stochastic food chain chemostat model with variable yields. First, we prove the stochastic model has a unique global positive solution. Second, by employing suitable Lyapunov functions, Itô[Formula: see text] formula and some other important inequalities, the existence of a unique ergodic stationary distribution of a stochastic food chain chemostat model is researched, which can help us better understand the statistical characteristics of stochastic food chain chemostat models. Second, we investigate the extinction of the microorganism and the bacteria. Moreover, the case of extinction for bacteria but persistence for microbial species is considered. Finally, some numerical simulations are carried out to illustrate our theoretical results and the influence of the variable yields on the microorganism and the bacteria.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44821204","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 : 2023-04-27DOI: 10.1142/s0218339023500237
A. Grishchenko, C. V. van Rijn, I. Sysoev
Connectivity analysis using modern approaches like Granger causality, partial directed coherence and transfer entropy always demands additional statistical evaluation of the obtained measures for significance. Although for very simple linear autoregressive processes and quasilinear oscillatory activities theoretical estimates are available, the real biological signals are too complex for application of analytical approaches and surrogate data come into use. When pathological activity like epileptic seizures is studied, the question can also rise in a somewhat different way: one asks whether the studied activity is different from the normal one rather than whether connectivity exists. The similar question is also valid if one compares connectivity in different physiological states like sleep and wakefulness. Here, we study two different approaches to statistical evaluation of transfer entropy estimates in application to the study of spike–wave discharges (SWDs), the main encephalographic manifestation of absence epilepsy, registered in local field potentials of WAG/Rij rats (genetic models). The first approach is to compare distributions of the estimators for the baseline and different stages of pathological activity using traditional measures like t-test with additional corrections for multiple testing. The second approach is to make surrogate data and test whether the achieved estimators differ for surrogate series and for real ones. To support our findings and to understand the methods better, the series simulated using simple oscillatory models of epileptic activity are evaluated in the same way as the experimental data. We show that the most pronounced phenomena like bidirectional increase in coupling between frontal and parietal cortical areas during SWDs in comparison to baseline activity are considered to be significant by both approaches. But when the less expressed coupling changes are under consideration, the approach base on surrogate data provides less false positives. These results confirm that the primary outcomes of connectivity analysis for absence epilepsy (and not only it) achieved previously are valid although the statistical evaluation of the connectivity estimators was suboptimal.
{"title":"METHODS FOR STATISTICAL EVALUATION OF CONNECTIVITY ESTIMATES IN EPILEPTIC BRAIN","authors":"A. Grishchenko, C. V. van Rijn, I. Sysoev","doi":"10.1142/s0218339023500237","DOIUrl":"https://doi.org/10.1142/s0218339023500237","url":null,"abstract":"Connectivity analysis using modern approaches like Granger causality, partial directed coherence and transfer entropy always demands additional statistical evaluation of the obtained measures for significance. Although for very simple linear autoregressive processes and quasilinear oscillatory activities theoretical estimates are available, the real biological signals are too complex for application of analytical approaches and surrogate data come into use. When pathological activity like epileptic seizures is studied, the question can also rise in a somewhat different way: one asks whether the studied activity is different from the normal one rather than whether connectivity exists. The similar question is also valid if one compares connectivity in different physiological states like sleep and wakefulness. Here, we study two different approaches to statistical evaluation of transfer entropy estimates in application to the study of spike–wave discharges (SWDs), the main encephalographic manifestation of absence epilepsy, registered in local field potentials of WAG/Rij rats (genetic models). The first approach is to compare distributions of the estimators for the baseline and different stages of pathological activity using traditional measures like t-test with additional corrections for multiple testing. The second approach is to make surrogate data and test whether the achieved estimators differ for surrogate series and for real ones. To support our findings and to understand the methods better, the series simulated using simple oscillatory models of epileptic activity are evaluated in the same way as the experimental data. We show that the most pronounced phenomena like bidirectional increase in coupling between frontal and parietal cortical areas during SWDs in comparison to baseline activity are considered to be significant by both approaches. But when the less expressed coupling changes are under consideration, the approach base on surrogate data provides less false positives. These results confirm that the primary outcomes of connectivity analysis for absence epilepsy (and not only it) achieved previously are valid although the statistical evaluation of the connectivity estimators was suboptimal.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41860638","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 : 2023-04-25DOI: 10.1142/s0218339023500249
Prasenjit Mahato, Subhashis Das, S. Mahato
We propose and study the transmission dynamics of susceptible-exposed-infected-recovered [Formula: see text] epidemic model with saturated treatment function. We consider saturated treatment function in the epidemic system to understand the effect of delayed treatment on the disease transmission. The indiscriminately perturbation which is considered as a type of white noise is proportional to the distance of state variables from the values of endemic equilibria. Choosing the suitable Lyapunov function and using the It[Formula: see text]’s formula, the existence and the uniqueness of the positive solution of the system are examined. Stochastic boundedness, permanence and extinction of the epidemic model are investigated with proper conditions. Numerical simulations are performed to illustrate our results. The sensitivity analysis of the basic reproduction number is performed. The effect of control parameter is determined on the model dynamics. It is our main finding that the different intensities of white noises can fluctuate the susceptible, exposed, infected, recovered individuals around its equilibrium points.
{"title":"STOCHASTIC PERMANENCE AND EXTINCTION OF AN EPIDEMIC MODEL WITH SATURATED TREATMENT","authors":"Prasenjit Mahato, Subhashis Das, S. Mahato","doi":"10.1142/s0218339023500249","DOIUrl":"https://doi.org/10.1142/s0218339023500249","url":null,"abstract":"We propose and study the transmission dynamics of susceptible-exposed-infected-recovered [Formula: see text] epidemic model with saturated treatment function. We consider saturated treatment function in the epidemic system to understand the effect of delayed treatment on the disease transmission. The indiscriminately perturbation which is considered as a type of white noise is proportional to the distance of state variables from the values of endemic equilibria. Choosing the suitable Lyapunov function and using the It[Formula: see text]’s formula, the existence and the uniqueness of the positive solution of the system are examined. Stochastic boundedness, permanence and extinction of the epidemic model are investigated with proper conditions. Numerical simulations are performed to illustrate our results. The sensitivity analysis of the basic reproduction number is performed. The effect of control parameter is determined on the model dynamics. It is our main finding that the different intensities of white noises can fluctuate the susceptible, exposed, infected, recovered individuals around its equilibrium points.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42301946","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 : 2023-04-25DOI: 10.1142/s0218339023500250
Shuping Li, Huafang Liu
We propose and analyze a TB transmission model with nonlinear incidence rate, immunization and medical treatment. First, the existences and stabilities of the equilibrium are studied. The results indicate the basic reproduction number [Formula: see text] is the threshold of disease extinction and persistence. The disease-free equilibrium is globally asymptotically stable when [Formula: see text], and the disease will gradually disappear. The unique positive equilibrium is local stability and the disease is uniformly persistent when [Formula: see text]. Second, optimal control is added to the original model because of limited resources. Finally, the stability of the equilibrium and the theoretical results of optimal control are verified by numerical simulations, and the sensitivity of the parameters is analyzed by the PRCC method.
{"title":"DYNAMICAL ANALYSIS OF TB MODEL WITH NONLINEAR INCIDENCE RATE AND OPTIMAL CONTROL","authors":"Shuping Li, Huafang Liu","doi":"10.1142/s0218339023500250","DOIUrl":"https://doi.org/10.1142/s0218339023500250","url":null,"abstract":"We propose and analyze a TB transmission model with nonlinear incidence rate, immunization and medical treatment. First, the existences and stabilities of the equilibrium are studied. The results indicate the basic reproduction number [Formula: see text] is the threshold of disease extinction and persistence. The disease-free equilibrium is globally asymptotically stable when [Formula: see text], and the disease will gradually disappear. The unique positive equilibrium is local stability and the disease is uniformly persistent when [Formula: see text]. Second, optimal control is added to the original model because of limited resources. Finally, the stability of the equilibrium and the theoretical results of optimal control are verified by numerical simulations, and the sensitivity of the parameters is analyzed by the PRCC method.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48306394","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 : 2023-04-21DOI: 10.1142/s0218339023500171
S. Khajanchi, J. Mondal, Pankaj Tiwari
Immunotherapy has become a rapidly developing approach in the treatment of cancer. Cancer immunotherapy aims at promoting the immune system response to react against the tumor. In view of this, we develop a mathematical model for immune–tumor interplays with immunotherapeutic drug, and strategies for optimally administering treatment. The tumor–immune dynamics are given by a system of five coupled nonlinear ordinary differential equations which represent the interaction among tumor-specific CD4+T cells, tumor-specific CD8+T cells, tumor cells, dendritic cells and the immuno-stimulatory cytokine interleukin-2 (IL-2), extended through the addition of a control function describing the application of a dendritic cell vaccination. Dynamical behavior of the system is studied from the analytical as well as numerical points of view. The main aim is to investigate the treatment regimens which minimize the tumor cell burden and the toxicity of dendritic cell vaccination. Our numerical simulations demonstrate that the optimal treatment strategies using dendritic cell vaccination reduce the tumor cell burden and increase the cell count of CD4+T cells, CD8+T cells, dendritic cells and IL-2. The most influential parameters having significant impacts on the tumor cells are identified by employing the approach of global sensitivity analysis.
{"title":"OPTIMAL TREATMENT STRATEGIES USING DENDRITIC CELL VACCINATION FOR A TUMOR MODEL WITH PARAMETER IDENTIFIABILITY","authors":"S. Khajanchi, J. Mondal, Pankaj Tiwari","doi":"10.1142/s0218339023500171","DOIUrl":"https://doi.org/10.1142/s0218339023500171","url":null,"abstract":"Immunotherapy has become a rapidly developing approach in the treatment of cancer. Cancer immunotherapy aims at promoting the immune system response to react against the tumor. In view of this, we develop a mathematical model for immune–tumor interplays with immunotherapeutic drug, and strategies for optimally administering treatment. The tumor–immune dynamics are given by a system of five coupled nonlinear ordinary differential equations which represent the interaction among tumor-specific CD4+T cells, tumor-specific CD8+T cells, tumor cells, dendritic cells and the immuno-stimulatory cytokine interleukin-2 (IL-2), extended through the addition of a control function describing the application of a dendritic cell vaccination. Dynamical behavior of the system is studied from the analytical as well as numerical points of view. The main aim is to investigate the treatment regimens which minimize the tumor cell burden and the toxicity of dendritic cell vaccination. Our numerical simulations demonstrate that the optimal treatment strategies using dendritic cell vaccination reduce the tumor cell burden and increase the cell count of CD4+T cells, CD8+T cells, dendritic cells and IL-2. The most influential parameters having significant impacts on the tumor cells are identified by employing the approach of global sensitivity analysis.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43374639","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 : 2023-04-17DOI: 10.1142/s0218339023500213
Soumitra Pal, Ashvini Gupta, A. Misra, B. Dubey
Depending on behavioral differences, reproductive capability and dependency, the life span of a species is divided mainly into two classes, namely immature and mature. In this paper, we have studied the dynamics of a predator–prey system considering stage structure in prey and the effect of predator-induced fear with two discrete time delays: maturation delay and fear response delay. We consider that predators cooperate during hunting of mature prey and also include its impact in fear term. The conditions for existence of different equilibria, their stability analysis are carried out for non-delayed system and bifurcation results are presented extensively. It is observed that the fear parameter has stabilizing effect whereas the cooperative hunting factor having destabilizing effect on the system via occurrence of supercritical Hopf-bifurcation. Further, we observe that the system exhibits backward bifurcation between interior equilibrium and predator free equilibrium and hence the situation of bi-stability occurs in the system. Thereafter, we differentiate the region of stability and instability in bi-parametric space. We have also studied the system’s dynamics with respect to maturation and fear response delay and observed that they also play a vital role in the system stability and occurrence of Hopf-bifurcation is shown with respect to both time delays. The system shows stability switching phenomenon and even higher values of fear response delay leads the system to enter in chaotic regime. The role of fear factor in switching phenomenon is discussed. Comprehensive numerical simulation and graphical presentation are carried out using MATLAB and MATCONT.
{"title":"CHAOTIC DYNAMICS OF A STAGE-STRUCTURED PREY–PREDATOR SYSTEM WITH HUNTING COOPERATION AND FEAR IN PRESENCE OF TWO DISCRETE DELAYS","authors":"Soumitra Pal, Ashvini Gupta, A. Misra, B. Dubey","doi":"10.1142/s0218339023500213","DOIUrl":"https://doi.org/10.1142/s0218339023500213","url":null,"abstract":"Depending on behavioral differences, reproductive capability and dependency, the life span of a species is divided mainly into two classes, namely immature and mature. In this paper, we have studied the dynamics of a predator–prey system considering stage structure in prey and the effect of predator-induced fear with two discrete time delays: maturation delay and fear response delay. We consider that predators cooperate during hunting of mature prey and also include its impact in fear term. The conditions for existence of different equilibria, their stability analysis are carried out for non-delayed system and bifurcation results are presented extensively. It is observed that the fear parameter has stabilizing effect whereas the cooperative hunting factor having destabilizing effect on the system via occurrence of supercritical Hopf-bifurcation. Further, we observe that the system exhibits backward bifurcation between interior equilibrium and predator free equilibrium and hence the situation of bi-stability occurs in the system. Thereafter, we differentiate the region of stability and instability in bi-parametric space. We have also studied the system’s dynamics with respect to maturation and fear response delay and observed that they also play a vital role in the system stability and occurrence of Hopf-bifurcation is shown with respect to both time delays. The system shows stability switching phenomenon and even higher values of fear response delay leads the system to enter in chaotic regime. The role of fear factor in switching phenomenon is discussed. Comprehensive numerical simulation and graphical presentation are carried out using MATLAB and MATCONT.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42869222","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 : 2023-03-30DOI: 10.1142/s0218339023500183
Dipesh Barman, Subarna Roy, Pankaj Tiwari, S. Alam
In this paper, we investigate the dynamics of a predator–prey system of an ecological community in which the fear instigated by the predators has an adverse effect on the reproduction rate of prey species, and also on the competition among themselves due to the limited environmental resources. To capture and handle the realistic scenario in a more meaningful way, we have mathematically built up the model system with the assumption that the predators predate on the prey items following Cosner functional response, which increases with increments in the prey and predator populations. The model system has been studied through noteworthy mathematical analysis and an extensive numerical simulation. Our simulation results demonstrate that the predator–prey system stabilizes due to predator’s induced fear suppressing/enhancing the birth/death of prey species. The competition among the predators for the available prey items also has a stabilizing role on the system’s dynamics. In contrast, the increasing growth rate of prey species or predation rate creates instability in the system by changing the stable phase to the limit cycle oscillations. Moreover, the effects of seasonality are also studied by extending the model system to its nonautonomous counterpart. Sufficient conditions are derived so that the seasonally driven system exhibits at least one positive periodic solution. Our numerical results show that the seasonally forced system exhibits periodic solution (globally attractive periodic solution), higher periodic solutions, bursting patterns and the extinction of predator species due to the seasonal variations of some parameters.
{"title":"TWO-FOLD IMPACTS OF FEAR IN A SEASONALLY FORCED PREDATOR–PREY SYSTEM WITH COSNER FUNCTIONAL RESPONSE","authors":"Dipesh Barman, Subarna Roy, Pankaj Tiwari, S. Alam","doi":"10.1142/s0218339023500183","DOIUrl":"https://doi.org/10.1142/s0218339023500183","url":null,"abstract":"In this paper, we investigate the dynamics of a predator–prey system of an ecological community in which the fear instigated by the predators has an adverse effect on the reproduction rate of prey species, and also on the competition among themselves due to the limited environmental resources. To capture and handle the realistic scenario in a more meaningful way, we have mathematically built up the model system with the assumption that the predators predate on the prey items following Cosner functional response, which increases with increments in the prey and predator populations. The model system has been studied through noteworthy mathematical analysis and an extensive numerical simulation. Our simulation results demonstrate that the predator–prey system stabilizes due to predator’s induced fear suppressing/enhancing the birth/death of prey species. The competition among the predators for the available prey items also has a stabilizing role on the system’s dynamics. In contrast, the increasing growth rate of prey species or predation rate creates instability in the system by changing the stable phase to the limit cycle oscillations. Moreover, the effects of seasonality are also studied by extending the model system to its nonautonomous counterpart. Sufficient conditions are derived so that the seasonally driven system exhibits at least one positive periodic solution. Our numerical results show that the seasonally forced system exhibits periodic solution (globally attractive periodic solution), higher periodic solutions, bursting patterns and the extinction of predator species due to the seasonal variations of some parameters.","PeriodicalId":54872,"journal":{"name":"Journal of Biological Systems","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43408049","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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