Dynamics of a reaction-diffusion SIRI model with relapse and free boundary

Longtime behavior for solutions to a temporally discrete diffusion equation with a free boundary

“…A large amount of work related to continuous-time free boundary problems based on the Fisher-KPP equation has emerged. For example, extensions to equations with general nonlinear terms [10,17], time delay [4,33,26], and nonlocal diffusion [3,21], extensions to systems of population or epidemic models [5,8,11,27,30], and see more in a survey paper [6], with great progress has been made in relevant topics.…”

“…In the course of the proof for Proposition 2.4 by solving (5) step by step, one can generalize its equivalent integrodifference equation form…”

“…where G(x, y) acts as a kernel function, its symmetry as described in Lemma 2.2 reflects the non-advection diffusion of (5). While here F (u(n, x)) is the growth function that corresponds to the reaction term of (5).…”

“…where G(x, y) acts as a kernel function, its symmetry as described in Lemma 2.2 reflects the non-advection diffusion of (5). While here F (u(n, x)) is the growth function that corresponds to the reaction term of (5). The idea of such equivalence on bounded domains was first mentioned in [14], and the kernel function G(x, y) can be computed exactly according to different boundary conditions, which improves the deficiency of IDEs that cannot account for boundary.…”

A Deterministic Mathematical Model for the Control of Spread of Prosopis Juliflora Plants

“…to dissect endemic equilibrium for SIR, SIRS and SIS pestilence models. Vargas-De-Leon[21] set forward the composite quadratic Lyaponuv capacity to dissect solidness of endemic equilibrium for SIR, SIRS and SIS scourge models and later developed a composite-Volterra capacity to break down endemic equilibrium for the model with backslide. In this work we adopt Lyapunov work.…”