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Shiv Nadar University

The object of the present paper is to study an integrated pest management (IPM) problem in an agroecosystem (paddy-fish culture) through mathematical modeling and analysis, where release of sterile males and spraying of pesticide have been used as control measures for pest population. Using optimal analysis of the model, we have shown that restricted and proper use of control measures might enhance the crop production of the system in an economically viable way. The paper also considers the vulnerability of the underlined ecosystem due to the effect of temperature on the pest growth. Using Liapunov-like function, we have found out a suitable range of temperature, where this IPM strategy remains effective. Some important remarks have finally been made on the basis of numerical simulation. © 2006 Elsevier Inc. All rights reserved.

Mathematics

(SoNS) School of Natural Sciences

World University root node

Mathematical Biosciences

An improved integrated pest management model under 2-control parameters (sterile male and pesticide)

This paper deals with the mathematical modeling of pest management under viral infection (i.e. using viral pesticide) and analysis of its essential mathematical features. As the viral infection induces host lysis which releases more virus into the environment, on the average 'κ' viruses per host, κ∈(1,∞), the 'virus replication parameter' is chosen as the main parameter on which the dynamics of the infection depends. We prove that there exists a threshold value κ0 beyond which the endemic equilibrium bifurcates from the free disease one. Still for increasing κ values, the endemic equilibrium bifurcates towards a periodic solution. We further analyse the orbital stability of the periodic orbits arising from bifurcation by applying Poor's condition. A concluding discussion with numerical simulation of the model is then presented. © 2005 Elsevier Ltd. All rights reserved.

Journal of Theoretical Biology

Pest control through viral disease: Mathematical modeling and analysis

The paper deals with the effect of pesticide on the pest affecting a paddy field and also on the fishes living in the soil water. An objective function is formed in terms of projected loss of individual fish, the projected profit of killing a pest and the cost of spraying insecticide for a finite time period. Next the corresponding pest management model is formed by considering the growth equations of paddy, pest, and fish of the soil water. The model is analyzed by control theoretic means to determine the threshold limits of pesticide to be used. Lastly, the optimal value of pesticide is obtained. It is shown that the optimal value lies within the threshold limits. Finally corresponding to this optimal threshold value of pesticide, the optimal values of the biomass of paddy and that of the fish of the soil water are also obtained. The results are finally verified numerically by special choice of parameters compatible with the model. © World Scientific Publishing Company.