Sterile insect release method as a control measure of insect pests: A mathematical model

Recently non-conventional approaches of pest control are getting much more importance in different parts of the world. The main reason behind this is the long list of side effects of conventional approaches (use of pesticides etc.). The present paper focuses on one such extremely useful method of insect pest control, namely the Sterile Insect Release Method (SIRM), by using a mathematical model. A blend of dynamical behaviours of the model is studied critically, which, in turn, indicates the relevance of the method. The effect of uncertain environmental fluctuations on both fertile and sterile insects is also investigated. Our analytical findings are verified through computer simulation. Some important restrictions on the parameters of the system are mentioned, which may be implemented for a better performance of SIRM.

[1]  Dmitriĭ Olegovich Logofet,et al.  Stability of Biological Communities , 1983 .

[2]  S. Navarro,et al.  Mode of action of low atmospheric pressures onEphestia cautella (Wlk.) pupae , 1979, Experientia.

[3]  E. F. Knipling.  The Basic Principles of Insect Population Suppression and Management , 2006 .

[4]  G. P. Samanta.  Stochastic analysis of a prey‐predator system , 1994 .

[5]  M C Baishya,et al.  Non-equilibrium fluctuation in Volterra-Lotka systems. , 1987, Bulletin of mathematical biology.

[6]  Paul R. Ehrlich,et al.  The "Balance of Nature" and "Population Control" , 1967, The American Naturalist.

[7]  Sandip Banerjee,et al.  Stability and bifurcation in a diffusive prey-predator system: Non-linear bifurcation analysis , 2002 .

[8]  P. Hartman.  Ordinary Differential Equations , 1965 .

[9]  G. P. Samanta.  Influence of environmental noises on the Gomatam model of interacting species , 1996 .

[10]  T. Miyatake,et al.  Eradication Programs of Two Sweetpotato Pests, Cylas formicarius and Euscepes postfasciatus, in Japan with Special Reference to their Dispersal Ability , 2001 .

[11]  G. Bécus.  Stochastic prey-predator relationships: A random differential equation approach , 1979 .

[12]  Ratio dependent predation :A bifurcation analysis , 1998 .

[13]  Irene Aleksanova,et al.  Applied problems in probability theory , 1986 .

[14]  Prajneshu.  A stochastic model for two interacting species , 1976 .

[15]  Alakes Maiti,et al.  Deterministic and stochastic analysis of a prey-dependent predator–prey system , 2005 .

[16]  A. Robinson,et al.  MEDFLY AREAWIDE STERILE INSECT TECHNIQUE PROGRAMMES FOR PREVENTION, SUPPRESSION OR ERADICATION: THE IMPORTANCE OF MATING BEHAVIOR STUDIES , 2002 .

[17]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[18]  Kiyosi Itô.  Stochastic Differential Equations , 2018, The Control Systems Handbook.

[19]  Malay Bandyopadhyay,et al.  Deterministic and stochastic analysis of a nonlinear prey-predator system , 2003 .

[20]  R. May,et al.  Stability and Complexity in Model Ecosystems , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[21]  R. L. Stratonovich.  Conditional Markov Processes and their Application to the Theory of Optimal Control , 1968 .

[22]  F. Arthur,et al.  Impact of physical and biological factors on susceptibility of Tribolium castaneum and Tribolium confusum (Coleoptera: Tenebrionidae) to new formulations of hydroprene , 2004 .

[23]  Alakes Maiti,et al.  Stochastic Gomatam Model of Interacting Species: Non-Equilibrium Fluctuation and Stability , 2003 .

[24]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[25]  G. Mbata,et al.  Some Physical and Biological Factors Affecting Oviposition by Plodia Interpunctella (Hubner) (Lepidoptera: Phycitidae) , 1985 .