Turing patterns in a reaction–diffusion system modeling hunting cooperation

Capone, Florinda; Carfora, Maria Francesca; Luca, Roberta De; Torcicollo, Isabella

doi:10.1016/j.matcom.2019.03.010

Cited by 32 publications

(31 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The initial disease transmission is directly related to R 0 ; for this reason, we calculate the sensitivity indices of the basic reproductive number R 0 . Let p a generic parameter of model (1)- (4). The normalized forward sensitivity index of R 0 (which is differentiable with respect to p) is defined as…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…The index modulus is an indicator of the size of the effect of changes in that parameter. As we have an explicit expression of R 0 , we derive an analytical expression for the sensitivity of R 0 to each of the different parameters of model (1)- (4). Precisely,…”

Section: Sensitivity Analysismentioning

confidence: 99%

“…A number of different approaches (mathematical modeling, analysis, simulation) have been used for modeling the disease transmission, and a large number of mathematical models have been published [10,12,20,21,24]. Such models provide challenges and ideas in many other fields of applied mathematics such as ecology, economics in which nonlinear mathematical models having a similar structure are considered [2][3][4][5]22,23,25]. The mathematical models allow to obtain an estimate for the behavior of epidemics and to predict the asymptotic behavior of infection in order to take suitable actions to control epidemics.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analysis of a model for waterborne diseases with Allee effect on bacteria

Capone

Carfora

Luca

et al. 2020

NAMC

View full text Add to dashboard Cite

A limitation of current modeling studies in waterborne diseases (one of the leading causes of death worldwide) is that the intrinsic dynamics of the pathogens is poorly addressed, leading to incomplete, and often, inadequate understanding of the pathogen evolution and its impact on disease transmission and spread. To overcome these limitations, in this paper, we consider an ODEs model with bacterial growth inducing Allee effect. We adopt an adequate functional response to significantly express the shape of indirect transmission. The existence and stability of biologically meaningful equilibria is investigated through a detailed discussion of both backward and Hopf bifurcations. The sensitivity analysis of the basic reproduction number is performed. Numerical simulations confirming the obtained results in two different scenarios are shown.

show abstract

Section: Sensitivity Analysismentioning

confidence: 99%

Section: Sensitivity Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Analysis of a model for waterborne diseases with Allee effect on bacteria

Capone

Carfora

Luca

et al. 2020

NAMC

View full text Add to dashboard Cite

show abstract

“…In the present paper we have extended [18], introducing self-and cross-diffusion terms. The spatial diffusion plays an important role in the process of population evolution, not only in ecology but also in many other fields of applied mathematics such as biochemistry or economics and the effect of self-and cross-diffusion on the population dynamics has been widely investigated theoretically by many mathematicians ( [19][20][21][22][23][24] and references therein). Self-diffusion terms model the random movement of individuals in both prey and predator populations.…”

Section: Introductionmentioning

confidence: 99%

Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense

Carfora

Torcicollo

2020

Mathematics

View full text Add to dashboard Cite

In this paper, a reaction-diffusion prey-predator system including the fear effect of predator on prey population and group defense has been considered. The conditions for the onset of cross-diffusion-driven instability are obtained by linear stability analysis. The technique of multiple time scales is employed to deduce the amplitude equation near Turing bifurcation threshold by choosing the cross-diffusion coefficient as a bifurcation parameter. The stability analysis of these amplitude equations leads to the identification of various Turing patterns driven by the cross-diffusion, which are also investigated through numerical simulations.

show abstract

“…In the present paper, we consider the following reactiondiffusion system [7][8][9], which is described as zη zt (η, u, v) are the known nonlinear functions of η, u, and v.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of a Class of Predator-Prey Systems with Complex Dynamics Characters Based on a Sinc Function Interpolation Collocation Method

Ning

Wang

2020

Complexity

View full text Add to dashboard Cite

Although many kinds of numerical methods have been announced for the predator-prey system, simple and efficient methods have always been the direction that scholars strive to pursue. Based on this problem, in this paper, a new interpolation collocation method is proposed for a class of predator-prey systems with complex dynamics characters. Some complex dynamics characters and pattern formations are shown by using this new approach, and the results have a good agreement with theoretical results. Simulation results show the effectiveness of the method.

show abstract

Turing patterns in a reaction–diffusion system modeling hunting cooperation

Cited by 32 publications

References 21 publications

Analysis of a model for waterborne diseases with Allee effect on bacteria

Analysis of a model for waterborne diseases with Allee effect on bacteria

Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense

Numerical Solution of a Class of Predator-Prey Systems with Complex Dynamics Characters Based on a Sinc Function Interpolation Collocation Method

Contact Info

Product

Resources

About