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Modelling the dynamics of dengue real epidemics. (English) Zbl 1211.37116
Summary: In this work, we use a mathematical model for dengue transmission with the aim of analysing and comparing two dengue epidemics that occurred in Salvador, Brazil, in 1995-1996 and 2002. Using real data, we obtain the force of infection, $$\Lambda$$, and the basic reproductive number, $$R_{0}$$, for both epidemics. We also obtain the time evolution of the effective reproduction number, $$R(t)$$, which results in a very suitable measure to compare the patterns of both epidemics. Based on the analysis of the behaviour of $$R_{0}$$ and $$R(t)$$ in relation to the adult mosquito control parameter of the model, we show that the control applied only to the adult stage of the mosquito population is not sufficient to stop dengue transmission, emphasizing the importance of applying the control to the aquatic phase of the mosquito.

MSC:
 37N25 Dynamical systems in biology 92D30 Epidemiology
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References:
 [1] J CHUNGCHEONG MATH SOC 21 pp 501– (2008) [2] Burattini, Epidemiology and Infection (Print) 136 (3) pp 309– (2008) [3] Coelho, Memorias do Instituto Oswaldo Cruz 103 (6) pp 535– (2008) · doi:10.1590/S0074-02762008000600004 [4] Dibo, Memorias do Instituto Oswaldo Cruz 103 (6) pp 554– (2008) · doi:10.1590/S0074-02762008000600008 [5] Esteva, Mathematical biosciences 198 (2) pp 132– (2005) · Zbl 1090.92048 · doi:10.1016/j.mbs.2005.06.004 [6] Favier, Tropical medicine & international health : TM & IH 11 (3) pp 332– (2006) · doi:10.1111/j.1365-3156.2006.01560.x [7] J BIOL SYSTEMS 16 pp 1– (2008) [8] Focks, Journal of medical entomology 30 (6) pp 1003– (1993) · doi:10.1093/jmedent/30.6.1003 [9] Transactions of The Royal Society of Tropical Medicine and Hygiene 95 (4) pp 370– (2001) · doi:10.1016/S0035-9203(01)90184-1 [10] Massad, Tropical medicine & international health : TM & IH 15 (1) pp 120– (2010) [11] McBride, Microbes and infection / Institut Pasteur 2 (9) pp 1041– (2000) · doi:10.1016/S1286-4579(00)01258-2 [12] Newton, The American Journal of Tropical Medicine and Hygiene 47 (6) pp 709– (1992) · doi:10.4269/ajtmh.1992.47.709 [13] PHYS REV E 80 pp 016102– (2009) [14] Cadernos de sa  de p  blica / Minist  rio da Sa  de, Funda    o Oswaldo Cruz, Escola Nacional de Sa  de P  blica 25 pp S7– (2009) · doi:10.1590/S0102-311X2009000100002 [15] van den Driessche, Mathematical biosciences 180 pp 29– (2002) · Zbl 1015.92036 · doi:10.1016/S0025-5564(02)00108-6 [16] Wallinga, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 274 (1609) pp 599– (2007) · doi:10.1098/rspb.2006.3754 [17] Whitehead, Nature reviews. Microbiology 5 (7) pp 518– (2007) · doi:10.1038/nrmicro1690 [18] APPL MATH COMPUT 198 pp 401– (2008) [19] Yang, Epidemiology and Infection (Print) 137 (8) pp 1179– (2009) [20] Yang, Epidemiology and Infection (Print) 137 (8) pp 1188– (2009)
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