Impact of temperature change on the population dynamics of the maize pest

We provided in this work a theoretical framework to study and to simulate the population dynamics of Busseola fusca (B. fusca): maize pest. The aim is to simulate and predict the presence levels of Busseola fusca under the influence of temperature variations and control actions. Based on the life cycle of B. fusca), we first propose a mathematical model to study the population dynamics of this maize pest. Some parameters are taken to be temperature-dependent. This led to a system of non-autonomous differential equations. Also, the classical control strategies are incorporated in the model. We present the theoretical analysis of the model. For the model with constant parameters, we compute the basic offspring number 𝒩0 that determines the evolution of the population of this insect and establish that the trivial equilibrium is globally asymptotically stable whenever 𝒩0 < 1, while if 𝒩0 > 1, the non trivial equilibrium is globally asymptotically stable. For the model with temperature variations, we find two explicit thresholds parameters 𝒩max and 𝒩min that bound the basic offspring number 𝒩0 (such that 𝒩max ≤ 𝒩0 ≤ 𝒩min), and use them to prove the extinction and the persistence of the pest within a maize field. We prove analytically and by numerical simulations that B. fusca) persists uniformly within a maize field when 𝒩min > 1 and tends to disappears within a maize field when 𝒩max < 1. The theoretical results are illustrated by numerical simulations. They suggest further that spraying insecticides to kill larvae and destroying residues after harvest significantly reduce the population Busseola fusca more than other control actions.