Modelling the Control of the Impact of Fall Armyworm (Spodoptera frugiperda) Infestations on Maize Production

Abstract

In this paper, we propose and analyze a stage-structured mathematical model for modelling the control of the impact of Fall Armyworm infestations on maize production. Preliminary analysis of the model in the vegetative and reproductive stages revealed that the two systems had a unique and positively bounded solution for all time <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>t</a:mi> <a:mo>≥</a:mo> <a:mn>0</a:mn> </a:math> . Numerical analysis of the model in both stages under two different cases was also considered: Case 1: different number of the adult moths in the field assumed at <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mi>t</c:mi> <c:mo>=</c:mo> <c:mn>0</c:mn> </c:math> and Case 2: the existence of exogenous factors that lead to the immigration of adult moths in the field at time <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M3"> <e:mi>t</e:mi> <e:mo>&gt;</e:mo> <e:mn>0</e:mn> </e:math> . The results indicate that the destruction of maize biomass which is accompanied by a decrease in maize plants to an average of 160 and 142 in the vegetative and reproductive stages, respectively, was observed to be higher in Case 2 than in Case 1 due to subsequent increase in egg production and density of the caterpillars in first few (10) days after immigration. This severe effect on maize plants caused by the unprecedented number of the pests influenced the extension of the model in both stages to include controls such as pesticides and harvesting. The results further show that the pest was significantly suppressed, resulting in an increase in maize plants to an average of 467 and 443 in vegetative and reproductive stages, respectively.