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A stage structured model of malaria transmission and efficacy of mosquito larvicides in its control

Manju Agarwal

Department of Mathematics & Astronomy, Lucknow University, Lucknow 226007, Uttar Pradesh, India

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and

Archana S. Bhadauria

Department of Mathematics & Astronomy, Lucknow University, Lucknow 226007, Uttar Pradesh, India

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https://doi.org/10.1142/S1793962314500238Cited by:1 (Source: Crossref)

Abstract

In this paper, we analyze a stage structured mathematical model for the transmission of malaria and its control by killing mosquitoes in larvae (immature) stage. Both the Mosquito and human populations are divided into susceptible and infective class. Susceptible class of mosquito population is further divided into mature and immature. The model is analyzed by using stability theory of nonlinear ordinary differential equations. Basic reproduction ratio is derived which is found to be the decreasing function of maturation delay and larvicidal activity. In addition, it is observed that biting rate of mosquito, transmission efficiency of parasitic infection from infective human to mosquito and critical value of maturation delay are the key parameters determining the stability switch in the system. Numerical simulation is also carried out to confirm the analytical results obtained in the paper.

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References

R. W. Snow et al. , Nature 434 , 214 ( 2005 ) . Crossref, Web of Science, Google Scholar
M. Martcheva and F. Hoppensteadt, J. Biol. Syst. 18(4), 867 (2010). Link, Web of Science, Google Scholar
A. Anparthi , Times of India ( 2011 ) . Google Scholar
J. C. Beier , Annu. Rev. Entomol 43 , 519 ( 1998 ) . Crossref, Web of Science, Google Scholar
J. C. Hogg and H. Hurd , Parasitology 111 , 555 ( 1995 ) . Crossref, Web of Science, Google Scholar
J. C. Hogg and H. Hurd , Med. Vet. Entomol. 9 , 176 ( 1995 ) . Crossref, Web of Science, Google Scholar
A. M. Ahmed et al. , Invertebr. Reprod. Dev. 36 , 217 ( 1999 ) . Crossref, Web of Science, Google Scholar
J. A. Hopwood et al. , J. Exp. Biol. 204 , 2773 ( 2001 ) . Crossref, Web of Science, Google Scholar
N. Chitnis, J. M. Cushing and J. M. Hyman, Siam J. Appl. Math. 67(1), 24 (2006). Crossref, Web of Science, Google Scholar
F. I. Campbel , W. W. Sullivan and L. N. Smith , J. Econ. Entomol. 26 , 500 ( 1993 ) . Crossref, Google Scholar
M. B. Thomas and A. F. Read , Nat. Rev. Microbiol. 5 , 377 ( 2007 ) . Crossref, Web of Science, Google Scholar
R. Ross , The Prevention of Malaria ( John Murray , London , 1911 ) . Google Scholar
G. MacDonald , The Epidemiology and Control of Malaria ( Oxford Univ. Press , London , 1957 ) . Google Scholar
K. Dietz , L. Molineaux and A. Thomas , Bull. World Health Organ. 50 , 347 ( 1974 ) . Web of Science, Google Scholar
R. M. Anderson and R. M. May , Infectious Diseases of Humans ( Oxford Univ. Press , Oxford , 1991 ) . Crossref, Google Scholar
J. L. Aron , Math. Biosci. 90 , 385 ( 1988 ) . Crossref, Web of Science, Google Scholar
K. Dietz, Malaria: Principles and Practice of Malariology 2, eds. W. H. Wernsdorfer and S. I. McGregor (Churchill Livingstoe, Edinburgh, 1988) pp. 1091–1133. Google Scholar
J. Dusho , W. Huang and C. Castillo-Chavez , J. Math. Biol. 36 , 227 ( 1998 ) . Crossref, Web of Science, Google Scholar
S. Singh, P. Chandra and J. B. Shukla, J. Biol. Syst. 13(1), 1 (2005). Link, Web of Science, Google Scholar
W. G. Aiello and H. I. Freedman , Math. Biosci. 101 , 139 ( 1990 ) . Crossref, Web of Science, Google Scholar
J. Li, Math. Biosci. Eng. 8(3), 753 (2011). Crossref, Web of Science, Google Scholar
Y. Kuang , Delay Differential Equations with Applications in Population Dynamics ( Academic Press , London , 1993 ) . Google Scholar
O. Diekmann , J. Heesterbeek and J. Metz , J. Math. Biol. 28 , 356 ( 1990 ) . Crossref, Web of Science, Google Scholar
S. Ruan , Q. Appl. Math. 59 , 159 ( 2001 ) . Crossref, Web of Science, Google Scholar