Two‐compartment age‐structured model of solitarious and gregarious locust population dynamics

Abstract

Communicated by: R Anguelov MSC Classification: 92D25, 35L04, 37C75We study a nonlinear age-structured model of locust population dynamics with variable time of egg incubation that describes the phase shifting and behavior of desert locust, Schistocerca gregaria. The model is based on the 2compartment system of transport equations with nonlinear density-dependent fertility rates with time delay in boundary conditions. It describes the dynamics of the density of 2 phases of locust's population-solitarious and gregarious.Such system is studied both theoretically and numerically. The analysis of asymptotical stability of the trivial and nontrivial equilibria of the autonomous system allows to understand the conditions and the particularities of bidirectional phase shifts between solitarious and gregarious S gregaria. We found that the parameter of maturation age was very important in the 2-phase dynamics.We extrapolate that a rapid change in environmental conditions that may trigger the maturation process of dormant solitarious population may also decrease, overall, the maturation age and hence destabilize the solitarious subpopulation from a near zero population size towards much larger populations and hence initiate quickly good conditions for gregarization. We also observed that the most realistic population dynamics of locusts was when the attraction point of a stable solitarious population size was above the gregarization threshold. This means that solitarious populations may last through time only near a zero size, but as soon as environmental conditions become favorable to population increase, the gregarization may happen. This outlines the intrinsic character of outbreaking dynamics that a species such as desert locust displays.

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“…, and time t system (1) -(4) is reduced to the Cauchy problem for the linear ODE system described propagation of "travelling wave" fronts along the characteristics v m = const [18], [19]:…”

“…given by Eqs. (12), (13), (14), (17), (19), (20) -(23) exists if the coefficients of system (1)- (4) and initial values (2), (4) satisfy the conditions:…”