International Journal of Recent Technology and Engineering (IJRTE) ISSN: 2277-3878, Volume-8 Issue-3, September 2019 5316 Published By: Blue Eyes Intelligence Engineering & Sciences Publication Retrieval Number: C6876098319/2019©BEIESP DOI:10.35940/ijrte.C6876.098319 Abstract: In this paper, using Mathematical model to control the life cycle of Feminine Anopheles mosquitoes is derived. The Feminine Anopheles mosquito life cycle controlling by backstepping strategy. The backstepping control technique provides the scientific procedure for choosing a controller in Feminine Anopheles life cycle. The Feminine Anopheles mosquito life cycle models are derived using Lyapunov stability theory. Keywords: Mathematical model, Feminine Anopheles mosquito, Malaria, Back stepping, Lyapunov function. I. INTRODUCTION Malaria is transmitted in humans by Feminine Anopheles mosquito genus. Feminine Anopheles mosquito genus takes blood meals, to carry out egg production, that link between the human and also the Anopheles insect. Anopheles genus life cycle depends on many natural factors however temperature and humidness measure the foremost sensitive natural factors in their life cycle. Normally 30−40 Feminine Anopheles species transmit infection in nature. The life stage of the Feminine Anopheles mosquito is categorised into 4 stages like egg, larva, pupa and adult. The primary 3 stages except adult are in floating [1–4] . These 3 stages principally rely upon aquatic temperature [5–7] . Once adult Feminine Anopheles mosquitoes have emerged, the temperature and humidness might transmit malaria with success. In recent years, a backstepping approach has been produced for arranging controllers to manage the stimulating frameworks [8, 9] . A standard develop of the methodology is that the style of an all around stable control dynamical framework. The backstepping strategy is predicated on the numerical model of the analyzed framework, bringing new factors into it during a sort depending on the state factors, predominant parameters, and supportive capacities. The extreme work of an accommodating stage space is to dispose of nonlinearities tired the framework and impacting the consistent quality Revised Manuscript Received on September 15, 2019 Naresh Kumar Jothi, Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, Avadi, Chennai, Tamilnadu, INDIA. nareshsastra@yahoo.co.in M.L. Suresh, Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, Avadi, Chennai, Tamilnadu, INDIA. mukunthusuresh@gmail.com T N M Malini Mai, Department of Mathematics, Jeppiaar SRR Engineering College, Padur, Chennai. malinitnm2008@yahoo.com , of its activity [10–15] . The work of backstepping procedure makes an additional non-linearity and eliminates with unwanted nonlinearities from the framework. In this paper, the elements of Feminine Anopheles mosquito life cycle is displayed and backstepping the board style is planned to control the Feminine Anopheles mosquito life cycle. The backstepping method is applied in every stage of the Feminine Anopheles mosquito life cycle. Lyapunov function is used to work out the backstepping method. This paper is sorted out as pursues, In segment two, the arrangement of differential condition is demonstrated. This differential condition speaks to the existence cycle of Feminine Anopheles mosquito. In segment three, existence life cycle control using backstepping method is demonstrated. In section four, the simulation work is demonstrated and In section five, the account of the results obtained during this paper is explained. II. MATHEMATICAL MODEL FORMULATION The absolute populace of Feminine Anopheles mosquito life cycle comprises of four structures, for example, grown-up, egg, hatchling and pupa. Fig 1 Stream Diagram of Feminine Anopheles life cycle Mathematical Model for the control of Life cycle of Feminine Anopheles Mosquitoes Naresh Kumar Jothi, M.L. Suresh, T N M Malini Mai