IJPAM: Volume 101, No. 4 (2015)

A MOSQUITOES POPULATION DYNAMICS MODEL
WITH PESTICIDE CONTROL

A.C. Panday$^1$, D.N. Goswami$^2$, Joydip Dhar$^3$, Shriprakash$^4$, G.P. Sahu$^5$
$^{1,4}$Defense Research Development Establishment
Jhanshi Road
Gwalior, 474009, M.P., INDIA
$^2$Jiwaji University
Gwalior, 474009, M.P., INDIA
$^{3,5}$ABV-Indian Institute of Information Technology and Management
Gwalior, 474010, M.P., INDIA


Abstract. A deterministic differential equation model for the population dynamics of the mosquito vector is derived and studied. The life cycle of mosquito involves four stages Egg, Larva, Pupa & Adult. The mosquito population is divided into 3 compartments; larvae (L), indoor population (I) and outdoor population (O). The effect of pesticide applied to control the vector, is incorporated in the model with both periodic application and constant application. Taking mean effectiveness $\beta_0$ of pesticide as constant rate of pesticide control, the dynamical behaviour is studied. The system is bounded. Conditions for the existence and stability of a non-zero steady-state vector population density are derived. Numerical simulation is performed to verify the analytical result.

Received: October 31, 2015

AMS Subject Classification: 92B05, 34D20, 34N05

Key Words and Phrases: mosquito dynamics, mathematical model, stability analysis, periodic control

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DOI: 10.12732/ijpam.v101i4.12 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 101
Issue: 4
Pages: 595 - 604


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