Mathematical modelling and estimation of seasonal variation of mosquito population: a real case study

Resumo

A mathematical model is proposed and analyzed for the understanding of growth pattern of mosquito vector looking into its life cycle. The objective of this study is to develop a mathematical model that can fit to the real data provided by DRDE scientist for different month at different stations so that the seasonal variation in population density of mosquitoes can be reported accurately to the estimated data obtained by the proposed mathematical model.  The aquatic class $(L)$ and adult stage is divided in two class, indoor population $(I)$ and outdoor population $(O)$. Here we estimated different parameters of our proposed continuous model and numerically simulation is done to compare the estimated data with the original data.

Downloads

Não há dados estatísticos.

Biografia do Autor

Joydip Dhar, ABV- Indian Institute of Information Technology and Management

Associate Professor
Department of Applied Sciences

Applied Mathematics Section

Manisha Chaudhary, ABV- Indian Institute of Information Technology and Management

Research Assistant,

Modelling and Simulation Lab

ABV- Indian Institute of Information Technology and Management

Randhir Singh Baghel, Pratap Institute of Technology and Science
Research Scholar, SOMAS, Jiwaji University, Gwalior
A. C. Pandey, Defense Research Development Establishment (DRDE)

Scientist-F,

DRDE, Gwalior, India

Referências

H. Charles, J. Godfray, Mosquito ecology and control of malaria, Journal of Animal Ecology 82, 15-25, (2013).

R. Ross, The possibility of reducing mosquitoes, Nature 72, 151, (1905).

M. C. D. Moulay, M.A. Aziz-Alaoui, The chikungunya disease: Modeling, vector and transmission global dynamics original research article, Mathematical Biosciences 229, 50ä1ñ7, (2011).

M. Otero, H. Solari, N. Schweigmann, A stochastic population dynamics model for aedes aegypti: formulation and application to a city with temperate climate, Bull. Math. Biol. 68, 1945-1974, (2006).

J. M. Cushing, An introduction to structured population dynamics, SIAM, (1998).

T. K. Sriram, J. Dhar, Prediction of Computer and Video Game Playing Population: An Age Structured Model, International Journal of Computer, Information Science and Engineering 8, 153-157, (2014).

J. Dhar, Population model with diffusion and supplementary forest resource in a two-patch habitat, Applied Mathematical Modelling 32, 1219-1235, (2008).

J. Li, Simple mathematical models for interacting wild and transgenic mosquito population, Mathematical Biosciences 189, 39ä1ñ7, (2004).

M. Rafikov, L.Bevilacqua, A.P.P.Wyse, Optimal control strategy of malaria vector using genetically modified mosquitoes, Journal of Theoretical Biology 258, 418-425, (2009).

P. Cailly, A. Tranc, T. Balenghiene, G. LAmbertf, C. Toty, P. Ezanno, A climate-driven abundance model to assess mosquito control strategies, Ecological Modelling 227, 7-17, (2012).

J. Li, Discrete-time models with mosquitoes carrying genetically modified bacteria, Mathematical Biosciences, (2012).

W. Geneva, World malaria report, World Health Orga-nization 44, (2009).

K. S. Jatav, J. Dhar, A. Nagar, Mathematical study of stage-structured pests control through impulsively released natural enemies with discrete and distributed delays, Applied Mathematics and Computation 238, 511-526, (2014).

J. Dhar, K.S. Jatav, Mathematical analysis of a delayed stage-structured predatorûprey model with impulsive diffusion between two predators territories, Ecological Complexity 16, 59-67, (2013).

G. P. Sahu, J. Dhar, Analysis of an SVEIS epidemic model with partial temporary immunity and saturation incidence rate, Applied Mathematical Modelling 36, 908-923, (2012).

R. Anguelov, Y. Dumontb, J. Lubumaa, Mathematical modeling of sterile insect technology for control of anopheles mosquito, Computers and Mathematics with Applications 64, 374-389, (2012).

C. Dufourda, Y. Dumontb, Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control, Computers and Mathematics with Applications 66, 1695-1715, (2013).

A. N. Gideon, On the population dynamics of the malaria vector, Bulletin of Mathematical Biology 68, 2161ä1ñ789, (2006).

J. Ahumada, D. Lapoinite, M. Samuel, Modeling the population dynamics of culex quiquefasciatus (diptera: Culicidae), along an elevational gradient in hawaii, J. Med. Entomol. 41, 1157-1170, (2004).

B. Schaeffer, B. Mondet, S. Touzeau, Using a climate-dependent model to predict mosquito abundance: Application to aedes (stegomyia) africanus and aedes (diceromyia) furcifer (diptera: Culicidae), Infect. Genet. Evol 8, 422-432, (2008).

A. P. P.Wyse, Optimal control for malaria vector for a seasonal mathematical model, petropolis, rj, brazil" Thesis, National Laboratory for Scientific Computing.

A. M. Lutambi, M. A. Penny, T. Smith, N. Chitnis, Mathematical modelling of mosquito dispersal in a heterogeneous environment, Mathematical Biosciences 241, 198-216, (2013).

A. N. Clements, The Biology of Mosquitoes, Volume 3: Transmission of Viruses and Interactions with Bacteria, Vol. 3, Cabi, (2011).

L. Eddey, Destruction of adult mosquitoes by residual ddt methods, Transactions of the Royal Society of Tropical Medicine and Hygiene 40, 567-588, (1947).

F. B. Agusto, S. Bewick, R. D. Parshad, Mosquito management in the face of natural selection, Mathematical Biosciences 239, 154-168, (2012).

Publicado
2014-08-19
Seção
Artigos