Spreading Speed in A Nonmonotone Equation with Dispersal and Delay

Abstract

This paper is concerned with the estimation of spreading speed of a nonmonotone equation, which involves time delay and nonlocal dispersal. Due to the time delay, this equation does not generate monotone semiflows when the positive initial value is given. By constructing an auxiliary monotone equation, we obtain the spreading speed when the initial value admits nonempty compact support. Moreover, by passing to a limit function, we confirm the existence of traveling wave solutions if the wave speed equals to the spreading speed, which states the minimal wave speed of traveling wave solutions and improves the known results.

Analysis and Nonstandard Numerical Design of a Discrete Three-Dimensional Hepatitis B Epidemic Model

“…Mathematically, there are various reports on the modeling of the propagation of diseases [13][14][15][16]. In addition to reports on the modeling of the transmission of hepatitis B [10,17], there are also studies on the co-dynamics of pneumonia and typhoid fever diseases with cost effective optimal control analysis [18], the mathematical modeling of hepatitis C treatment for injecting drug users [19] and the epidemiological modeling of the propagation of cholera with optimal control treatment [20].…”

Minimal Wave Speed in a Competitive Integrodifference System without Comparison Principle

“…When the temporal variable is discrete, the deficiency of monotonicity is also universal, e.g., the discrete logistic model may lead to rich dynamics ( [11], Chapter 2). When spatial propagation dynamics are considered, we may refer to some results on the propagation dynamics of non-monotone integrodifference systems by Hsu and Zhao [12], Li et al [13], Lin [14], Pan and Lin [15], Pan and Zhang [16], and very recent papers [17,18] and references cited therein for other non-monotone diffusion systems. In these works, to establish the minimal wave speed, a general recipe is to pass to a limit function from the results of large wave speeds.…”

Minimal Wave Speed in a Delayed Lattice Dynamical System with Competitive Nonlinearity

“…If a noncooperative system admits comparison principle in the sense of standard partial ordering in R , there are also some results on propagation thresholds, e.g., predator-prey systems [5][6][7] and competitive system [8,9]. For some delayed models, the dynamics may be very plentiful [10,11], and the propagation modes may be complex; see some by [12][13][14][15][16][17] and recent papers [18][19][20] and references cited therein.…”