Assessing the effect of dynamics of unpredictable locust invasive behavior and its effect on food security and community livelihood

Abstract

Locusts are a highly destructive type of pest within the grasshopper species worldwide. When there is an invasion at a specific location, they can cause severe damage to crops. This study presents a mathematical model that examines locust invasions in terms of their dynamic behavior in both the source and invaded zones. The model is formulated using differential equations and takes into account the parameters and variables identified from both zones. The parameters were estimated using the least squares method, with all parameters being normally distributed. The study thoroughly discusses the existence of solutions by identifying equilibrium points and establishing conditions for their stability using the Jacobian matrix, Routh-Hurwitz criteria, and Lyapunov function. The analytical solution suggests that the system is stable when the intrinsic growth rate (σi and σs) is higher. However, the numerical solution indicates that the presence of locust populations in the two zones is determined by the intrinsic growth rate (σi and σs) the locust population increases and stabilizes after a few days. Factors such as survival and invasion rates were found to be major contributors to the existence and dynamics of locusts in the two zones. Additionally, it was observed that the deterrent coefficient in the invaded and source zones (ηi and ηs) has a significant impact on controlling the dynamic behavior of locusts.

Keywords

• locust behavior
• mathematical modeling
• least square method (lsm)
• community livelihood
• stability analysis