Next Article in Journal
Effect of Ti on the Structure and Mechanical Properties of TixZr2.5-xTa Alloys
Next Article in Special Issue
The Retentivity of Four Kinds of Shadowing Properties in Non-Autonomous Discrete Dynamical Systems
Previous Article in Journal
Theory of Non-Equilibrium Heat Transport in Anharmonic Multiprobe Systems at High Temperatures
Previous Article in Special Issue
Extension of Operational Matrix Technique for the Solution of Nonlinear System of Caputo Fractional Differential Equations Subjected to Integral Type Boundary Constrains
Article

Impulsive Reaction-Diffusion Delayed Models in Biology: Integral Manifolds Approach

by 1,†,‡, 2,*,‡ and 1,‡
1
Department of Mathematical Physics, Technical University of Sofia, 8800 Sliven, Bulgaria
2
Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
*
Author to whom correspondence should be addressed.
Current address: Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA.
These authors contributed equally to this work.
Academic Editor: Helena Reis
Entropy 2021, 23(12), 1631; https://doi.org/10.3390/e23121631
Received: 22 October 2021 / Revised: 27 November 2021 / Accepted: 30 November 2021 / Published: 3 December 2021
(This article belongs to the Special Issue Dynamical Systems, Differential Equations and Applications)
In this paper we study an impulsive delayed reaction-diffusion model applied in biology. The introduced model generalizes existing reaction-diffusion delayed epidemic models to the impulsive case. The integral manifolds notion has been introduced to the model under consideration. This notion extends the single state notion and has important applications in the study of multi-stable systems. By means of an extension of the Lyapunov method integral manifolds’ existence, results are established. Based on the Lyapunov functions technique combined with a Poincarè-type inequality qualitative criteria related to boundedness, permanence, and stability of the integral manifolds are also presented. The application of the proposed impulsive control model is closely related to a most important problems in the mathematical biology—the problem of optimal control of epidemic models. The considered impulsive effects can be used by epidemiologists as a very effective therapy control strategy. In addition, since the integral manifolds approach is relevant in various contexts, our results can be applied in the qualitative investigations of many problems in the epidemiology of diverse interest. View Full-Text
Keywords: reaction-diffusion equations; delays; impulses; integral manifolds; stability reaction-diffusion equations; delays; impulses; integral manifolds; stability
MDPI and ACS Style

Stamov, G.; Stamova, I.; Spirova, C. Impulsive Reaction-Diffusion Delayed Models in Biology: Integral Manifolds Approach. Entropy 2021, 23, 1631. https://doi.org/10.3390/e23121631

AMA Style

Stamov G, Stamova I, Spirova C. Impulsive Reaction-Diffusion Delayed Models in Biology: Integral Manifolds Approach. Entropy. 2021; 23(12):1631. https://doi.org/10.3390/e23121631

Chicago/Turabian Style

Stamov, Gani, Ivanka Stamova, and Cvetelina Spirova. 2021. "Impulsive Reaction-Diffusion Delayed Models in Biology: Integral Manifolds Approach" Entropy 23, no. 12: 1631. https://doi.org/10.3390/e23121631

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop