Dynamics of a Stage Structure Pest Control Model with Impulsive Effects at Different Fixed Time

Many existing pest control models, which control pests by releasing natural enemies, neglect the effect that natural enemies may get killed. From this point of view, we formulate a pest control model with stage structure for the pest with constant maturation time delay (through-stage time delay) and periodic releasing natural enemies and natural enemies killed at different fixed time and perform a systematic mathematical and ecological study. By using the comparison theorem and analysis method, we obtain the conditions for the global attractivity of the pest-eradication periodic solution and permanence of the system. We also present a pest management strategy in which the pest population is kept under the economic threshold level (ETL) when the pest population is uniformly permanent. We show that maturation time delay, impulsive releasing, and killing natural enemies can bring great effects on the dynamics of the system. Numerical simulations confirm our theoretical results

Chemical Control for Host-Parasitoid Model within the Parasitism Season and Its Complex Dynamics

In the present paper, we develop a host-parasitoid model with Holling type II functional response function and chemical control, which can be applied at any time of each parasitism season or pest generation, and focus on addressing the importance of the timing of application pesticide during the parasitism season or pest generation in successful pest control. Firstly, the existence and stability of both the host and parasitoid populations extinction equilibrium and parasitoid-free equilibrium have been investigated. Secondly, the effects of key parameters on the threshold conditions have been discussed in more detail, which shows the importance of pesticide application times on the pest control. Thirdly, the complex dynamics including multiple attractors coexistence, chaotic behavior, and initial sensitivity have been studied by using numerical bifurcation analyses. Finally, the uncertainty and sensitivity of all the parameters on the solutions of both the host and parasitoid populations are investigated, which can help us to determine the key parameters in designing the pest control strategy. The present research can help us to further understand the importance of timings of pesticide application in the pest control and to improve the classical chemical control and to make management decisions

A stage-structured predator-prey si model with disease in the prey and impulsive effects

This paper aims to develop a high-dimensional SI model with stage structure for both the prey (pest) and the predator, and then to investigate the dynamics of it. The model can be used for the study of Integrated Pest Management (IPM) which is a combination of constant pulse releasing of animal enemies and diseased pests at two different fixed moments. Firstly, we use analytical techniques for impulsive delay differential equations to obtain the conditions for global attractivity of the ‘pest-free’ periodic solution and permanence of the population model. It shows that the conditions strongly depend on time delay, impulsive release of animal enemies and infective pests. Secondly, we present a pest management strategy in which the pest population is kept under the economic threshold level (ETL) when the pest population is permanent. Finally, numerical analysis is presented to illustrate our main conclusion

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

2006 Annual Research Symposium Abstract Book

2006 annual volume of abstracts for science research projects conducted by students at Trinity College