A discrete tick population dynamics model with continuous and seasonal birth breeding

Abstract

In this paper, we formulate a discrete two-stage model with two types of birth mechanisms, continuous and seasonal. We divide tick population into two subgroups, i.e. immature and mature. We also consider diapause as an important adaptive process for ticks in respond to climate change in both stages. We derive a formula for the inherent net reproductive numbers and explore their stability analysis. When breeding is continuous, there exists a unique globally asymptotically stable positive fixed point provided that the inherent net reproductive number is larger than one; the extinction fixed point is globally asymptotically stable if the inherent net reproductive number is less than one. When breeding is seasonal with 2-periodic birth function, there exists a unique globally asymptotically stable periodic solution provided that the inherent net reproductive number is larger than one, while the population goes to extinction if this value is less than one. For the cases with multi-periodic birth function, we use numerical simulation to compare their complex behaviors.

Periodic solution analysis of a population dynamics system model for pulsating organisms

“…Fig. 1 shows the state trajectory lines of system (67) under different impulse dynamics, (a)~(c) are the trajectory lines of X1 (1) , X2 (2) and X3 (3) , respectively, and combining with the theorem, we can get that the state trajectory lines of system (67) all converge to 0 eventually, and X3 (3) has already arrived at the zero value around 0.02.…”

“…Biomathematics is a cross-discipline between biology and mathematics, mainly through the use of mathematical methods to study and analyze as well as to solve biological problems, and for biologyrelated mathematical methods [1][2]. Biomathematics plays an indispensable role in promoting modern science and technology and has been widely used in many fields such as ecology, environment, population, epidemiology, and agricultural production [3][4].…”