Mathematical modeling of fall armyworm spodoptera frugiperda infestations in maize crops and its impact on final maize biomass

A Dissertation Submitted in Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy in Mathematical and Computer Sciences and Engineering of the Nelson Mandela African Institution of Science and TechnologyFall armyworm (FAW-Spodoptera frugiperda), a highly destructive and fast spreading agricul tural pest native to North and South America, poses a real threat to global food security. It is estimated that intermittent FAW outbreaks could cause up to $US 13 billion per annum in crop losses throughout sub-Saharan Africa. Considering this projected loss it is imperative that various tools and techniques be utilized to infer on the various factors that affect FAW maize in teraction and in-turn affect the final maize biomass. Mathematical modeling has proved to be an important tool that is capable of shedding light on the FAW-maize interaction dynamics. In this study, three mathematical models were proposed to evaluate the impact of memory effects and controls, seasonality and Integrated Pest Management strategy (farming awareness and larvae predation) on FAW infestations in maize crops and on final maize biomass. Firstly, to evaluate the impact of memory effects and control, a new dynamical system for FAW-maize biomass interaction via Caputo fractional-order operator was proposed and analyzed. In the proposed model, four equilibrium points which revealed the existence of a threshold parameter defined by R0 were computed and analyzed. Further, it was observed that, R0, the average number of newborns produced by one individual female moth during its life span was an integral compo nent for stability of the aforementioned model equilibria. Secondly, to evaluate the implications of seasonality on FAW maize interaction and on the final maize biomass, a non-autonomous mathematical model was proposed and analyzed. The analysis revealed that the model solution was non-negative, unique, permanent and bounded admitting global asymptotic and continuous periodic function. Further, the model was extended into an optimal control problem with the aim of determining optimal pesticides and traditional methods that are capable of minimizing FAW egg and larvae populations at minimum cost. Results from the study demonstrated that a combination of pesticides use at low intensity with traditional methods at higher intensity could eradicate FAW in a maize field in a period less than half the life span of the crop in the field. Thirdly, to evaluate the impact of farming awareness campaigns and larvae predation, a fractional-order model that incorporated farming awareness campaigns and larvae predation was proposed and analysed. Overall, the study highlighted that, non-time dependent farming awareness campaigns should be close to 100% all the time to eradicate the FAW. However, when time-dependent farming awareness was implemented, it was observed that even less than 50% intensity level could lead to eradication of FAW. In all the proposed models, comprehen sive numerical simulations were carried out in MATLAB programming language to support the analytical findings. In a nutshell, the results of this study showed that mathematical models can be important tools to evaluate FAW and maize interaction dynamics

A mathematical model for fall armyworm management on maize biomass

This research article published by Springer Nature, 2021Fall armyworm (Spodoptera frugiperda), a highly destructive and fast spreading agricultural pest native to North and South America, poses a real threat to global food security. In this paper, to explore the dynamics and implications of fall armyworm outbreak in a field of maize biomass, we propose a new dynamical system for maize biomass and fall armyworm interaction via Caputo fractional-order operator, which is not only a nonlocal operator but also contains all characteristics concerned with memory of the dynamical system. We define the basic reproduction number, which represents the average number of newborns produced by one individual female moth during its life span. We establish that the basic reproduction number is a threshold quantity, which determines persistence and extinction of the pest. Finally, we simulate the Caputo system using the Adam–Bashforth–Moulton method to illustrate the main results

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

This research article published by Hindawi, 2021In 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 . 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 and Case 2: the existence of exogenous factors that lead to the immigration of adult moths in the field at time . 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

Predatory effects on the dynamics of Spodoptera Frugiperda infestations in maize

Maize remains in demand due to its nutritive value, capacity to provide food for a growing world population, contribution to food security, and increase in worldwide investments in ethanol as a biofuel. However, the invasion and widespread infestation of Spodoptera frugiperda result in significant maize yield losses, leading to a lower standard of living and a weakened economy for maize producers. This study builds differentiable equations to simulate the behavior of the Spodoptera frugiperda-maize biomass model, incorporating predators and best farming practices. The model exhibits six points of equilibrium, all of which are locally asymptotically stable if the necessary requirements are met. Latin Hypercube Sampling (LHS) and PRCC multivariate analysis were employed to identify the sensitive parameters affecting the pest. Numerical simulations suggest that, in the early stages, integrating natural enemies with best farming practices proves to be an effective intervention as it directly reduces the pest population and promotes sustainable pest control

Modeling the dynamics of Diamondback Moth infestations on cabbage biomass

The Diamondback Moth (Plutella xylostella) is a notorious agricultural pest that poses significant challenges to cabbage production. In this study, we formulated and analyzed the deterministic differential equations to capture the infestations dynamics of diamondback moth in a cabbages biomass, taking into account the use of environmentally friendly pesticides. To study its dynamics we computed the threshold number, ℛ∗, based on the pest-free equilibrium point. The results indicate that when ℛ∗≤1, the equilibrium point ξ1 is both locally and globally stable. Conversely, when ℛ∗>1, the coexistence point becomes globally asymptotically stable. The stability of the equilibrium points were both Locally and globally assessed using Ruth Hurwitz’s criteria for local stability and Lyapunov functions for global analysis. A comprehensive numerical analysis was conducted, confirming the substantial support for the analytical findings. Finally, this research suggests that in order to reduce the impact of the diamondback moth, it is necessary to decrease the threshold value smaller than a unity through the adoption of effective inter-cropping techniques and the use of environmentally friendly pesticides