zbMATH — the first resource for mathematics

The impact of maturation delay of mosquitoes on the transmission of West Nile virus. (English) Zbl 1204.92057
Summary: We formulate and analyze a delay differential equation model for the transmission of the West Nile virus between vector mosquitoes and avian hosts that incorporates maturation delay for mosquitoes. The maturation time from eggs to adult mosquitoes is sensitive to weather conditions, in particular the temperature, and the model allows us to investigate the impact of this maturation time on transmission dynamics of the virus among mosquitoes and birds. Numerical results of the model show that a combination of the maturation time and the vertical transmission of the virus in mosquitoes has substantial influence on the abundance and number of infection peaks of the infectious mosquitoes.

92D30 Epidemiology
65C20 Probabilistic models, generic numerical methods in probability and statistics
34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D40 Ecology
37N25 Dynamical systems in biology
Full Text: DOI
[1] Anderson, J.F.; Main, A.J., Importance of vertical and horizontal transmission of west nile virus by culex pipiens in the northeastern united states, J. infect. dis., 194, 11, 1577, (2006)
[2] Anderson, R.M.; May, R.M., Infectious diseases of humans, (1991), Oxford University London/New York
[3] Arino, J.; Brauer, F.; vanden Driessche, P.; Watmough, J.; Wu, J., A final size relation for epidemic models, Math. biosci. eng., 4, 2, 159, (2007) · Zbl 1123.92030
[4] Arino, J.; Wang, L.; Wolkowicz, G.S.K., An alternative formulation for a delayed logistic equation, J. theor. biol., 241, 1, 109, (2006)
[5] Bayoh, M.N.; Lindsay, S.W., Effect of temperature on the development of the aquatic stages of anopheles gambiae sensu stricto (diptera: culicidae), B. entomol. res., 93, 5, 375, (2003)
[6] Bowman, C.; Gumel, A.B.; van den Driessche, P.; Wu, J.; Zhu, H., A mathematical model for assessing control strategies against west nile virus, B. math. biol., 67, 5, 1107, (2005) · Zbl 1334.92392
[7] Brust, R., Weight and develpoment time of different stadia of mosquitoes reared at various constant temperature, Can. entomol., 99, 9, 986, (1967)
[8] Campbell, L.G.; Martin, A.A.; Lanciotti, R.S.; Guble, D.J., West nile virus, Lancet infect. dis., 2, 9, 519, (2002)
[9] Castillo-Chavez, C.; Thieme, H.R., Asympotically autonomous epidemic models, (), 33
[10] Cooke, K.L.; van den Driessche, P., Analysis of an SEIRS epidemic model with two delays, J. math. biol., 35, 2, 240, (1996) · Zbl 0865.92019
[11] Cooke, K.L.; van den Driessche, P.; Zou, X., Interaction of maturation delay and nonlinear birth in population and epidemic models, J. math. biol., 39, 332, (1999) · Zbl 0945.92016
[12] Cruz-Pacheco, G.; Esteva, L.; Montano-Hirose, J.A.; Vargas, C., Modelling the dynamics of west nile virus, B. math. biol., 67, 6, 1157, (2005) · Zbl 1334.92397
[13] Dohm, D.J.; Sardelis, M.R.; Turell, M.J., Experimental vertical transmission of west nile virus by culex pipiens (diptera: culicidae), J. med. entomol., 39, 4, 640, (2002)
[14] Garett-Jones, C., Prognosis for interruption of malaria transmission through assessment of mosquitoes vectorical capacity, Nature, 204, 1173, (1964)
[15] Goddard, L.B.; Roth, A.E.; Reisen, W.K.; Scott, T.W., Vertical transmission of west nile virus by three California culex (diptera: culicidae) species, J. med. entomol., 40, 6, 743, (2003)
[16] Gourley, S.A.; Liu, R.; Wu, J., Eradicating vector-borne disease via age-structured culling, J. math. biol., 54, 3, 309, (2007) · Zbl 1115.92041
[17] Gourley, S.A.; Liu, R.; Wu, J., Some vector borne disease with structured host populations: extinction and spatial spread, SIAM J. appl. math., 67, 2, 408, (2007) · Zbl 1123.35083
[18] Hagstrum, D.W.; Workman, E.B., Interaction of temperature and feeding rate in determining the rate of development of larval culex tarsalis, Ann. entomol. soc. am., 64, 3, 668, (1971)
[19] Hethcote, H., The mathematics of infectious diseases, SIAM rev., 42, 4, 599, (2000) · Zbl 0993.92033
[20] Huffaker, C., The temperature relations of the immature stages of the malarial mosquito an. quadrimaculatus say, with a comparison of the developmental power of constant and variable temperatures in insect metabolism, Ann. emtomol. soc. am., 37, 1, 1, (1944)
[21] Komar, N.; Langevin, S.; Nemeth, N.; Edwards, E.; Hettler, D.; Davis, B.; Bowen, R.; Bunning, M., Experimental infection of north American birds with the New York 1999 strain of west nile virus, Emerg. infect. dis., 9, 3, 11, (2003)
[22] Kuang, Y., Delay differential equation with applications in population dynamics, (1993), Academic Press Boston
[23] Langevin, S.A.; Bunning, M.; Davis, N.K.B., Experimental infection of chickens as candidate sentinels for west nile virus, Emerg. infect. dis., 7, 4, 726, (2001)
[24] Lassiter, M.; Apperson, C.; Roe, R., Juvenile hormone metabolism during the fourth stadium and pupal stage of the south house mosquito culex quinquefasciatus say, J. insect physiol., 41, 10, 869, (1995)
[25] Lewis, M.; Renclawowicz, J.; van den Driessche, P., Travelling waves and spread rates for a west nile virus model, B. math. biol., 68, 1, 3, (2006) · Zbl 1334.92414
[26] Lord, C.C.; Day, J.F., Simulation studies of St. Louis encephalitis and west nile viruses: the impact of bird mortality, Vector borne zoonotic dis., 1, 4, 317, (2001)
[27] Lyimo, E.O.; Takken, W., Effects of adult body size on fecundity and the pre-gravid rate of anopheles gambiae females in tanzania, Med. vet. entomol., 7, 4, 328, (1993)
[28] Mclean, R.G.; Ubico, S.R.; Docherty, D.E.; Hansen, W.R.; Sileo, L.; McNamara, T.S., West nile virus transmission and ecology in birds, Ann. NY acad. sci., 951, 54, (2001)
[29] Munga, S.; Minakawa, N.; Zhou, G., Survivorship of immature stages of anopheles gambiae s.l. (diptera: culicidae) in natural habitats in western kenya highlands, J. med. entomol., 44, 5, 758, (2007)
[30] Paaijmans, K.P.; Read, A.F.; Thomas, M.B., Understanding the link between malaria risk and climate, Proc. natl. acad. sci. USA, 106, 33, 13844, (2009)
[31] Shaman, J.; Spiegelman, M.; Cane, M.; Stieglitz, M., A hydrologically driven model of swamp water mosquito population dynamics, Ecol. model., 194, 395, (2006)
[32] Smith, H.J., Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, Mathematical surveys and monographs, vol. 41, (1995), American Mathematical Society Providence Rhode Island
[33] Thieme, H.R., Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations, J. math. biol., 30, 7, 755, (1992) · Zbl 0761.34039
[34] Tun-Lin, W.; Burkot, T.R.; Kay, B.H., Effect of temperature and larval diet on development rate and survival of the dengue vector aedes aegypti in north queensland, Australia, Med. vet. entomol., 14, 1, 31, (2000)
[35] Tuno, N.; Okeka, W.; Minakawa, N.; Takagi, M., Survivorship of anopheles gambiae sensu stricto (diptera: culicidae) larvae in western kenya highland forest, J. med. entomol., 42, 3, 270, (2005)
[36] Velasco-Hernández, J.X., A model for chagas disease involving transmission by vectors and blood transfusion, Theor. popul. biol., 46, 1, 1, (1994) · Zbl 0804.92024
[37] Wan, H.; Zhu, H., The backward bifurcation in compartmental models for west nile virus, Math. biosci., 227, 20, (2010) · Zbl 1194.92067
[38] Wonham, M.J.; de-Camino Beck, T.; Lewis, M.A., An epidemiological model for west nile virus: invasion analysis and control applications, Proc. roy. soc. lond. ser. B, 271, 1538, 501, (2004)
[39] <http://www.cdc.gov/ncidod/dvbid/westnile/>.
[40] <http://www.phac-aspc.gc.ca/wnv-vwn/index-eng.php>.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.