Pest regulation by means of impulsive controls Paul Georgescu * , Gheorghe Moros ßanu Department of Mathematics and Its Applications, Central European University, Nador u. 9, 1051 Budapest, Hungary Abstract In this paper, we consider an integrated pest management model which is impulsively controlled by means of biological and chemical controls. These controls are assumed to act in a periodic fashion, a nonlinear incidence rate being used to account for the dynamics of the disease caused by the application of the biological control. The Floquet theory for impul- sive ordinary differential equations is employed to obtain a condition in terms of an inequality involving the total action of the nonlinear force of infection in a period, under which the susceptible pest-eradication solution is globally asymptotically stable. If the opposite inequality is satisfied, then it is shown that the system under consideration becomes uniformly per- sistent. A biological interpretation of the persistence condition is also provided. Ó 2007 Elsevier Inc. All rights reserved. Keywords: Pest management; Impulsive controls; Nonlinear infection rate; Stability; Persistence 1. Introduction Lately, it has been widely noticed that pesticide abuse has unwelcomed long-term environmental conse- quences and ultimately damages human health. In some instances, the persistent use of pesticides has increased the incidence of pest varieties which are resistant to chemicals, rendering chemical controls almost ineffective, while in other situations the use of such products changed for the worse the balance between the beneficial and the harmful insects. Consequently, sophisticated and multifaceted ecosystem-based strategies have been constructed in order to minimize the use of hazardous chemicals. Integrated pest management (IPM) is an ecological approach which represents a synthesis of techniques of various natures to control pests, with an accent on those which are potentially less damaging to the environ- ment. Further, techniques specifically suited to the target pests are preferred, in order to avoid harmful effects on non-target organisms. Specifically, natural predators, parasites or pathogens of pests may be used, together with genetically-engineered pest-resistant varieties of crops, mechanical methods of pest control such as traps or insect barriers and habitat manipulation. In this approach, pesticides are used only as a last resort, when deemed an absolute necessity. For a historical perspective on the evolution of IPM definitions, see [2]. 0096-3003/$ - see front matter Ó 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2007.01.079 * Corresponding author. E-mail addresses: vpgeo@go.com (P. Georgescu), Morosanug@ceu.hu (G. Moros ßanu). Applied Mathematics and Computation 190 (2007) 790–803 www.elsevier.com/locate/amc