4.2.2. Numerical simulations

Figure 4. Numerical simulations of primary and secondary infections in the absence of Wolbachia-carrying mosquitoes. The

Figure 5. Numerical simulations of primary and secondary infections in the presence of Wolbachia-carrying mosquitoes.

1 <sup>H</sup>ð Þ¼ 0 I 2

1 <sup>H</sup>ð Þ¼ 0 I 2

<sup>H</sup>ð Þ¼ <sup>0</sup> 1 and NH <sup>¼</sup> <sup>10</sup>5. ANð Þ¼ <sup>0</sup> SNð Þ¼ <sup>0</sup> <sup>3</sup> � NH.

<sup>H</sup>ð Þ¼ <sup>0</sup> 1 and NH <sup>¼</sup> 105. ANð Þ¼ <sup>0</sup> SNð Þ¼ <sup>0</sup>

parameters values used are given in Table 2. Initial conditions are I

122 Dengue Fever - a Resilient Threat in the Face of Innovation

The parameters values used are given in Table 2. Initial conditions are I

AW ð Þ¼ 0 SW ð Þ¼ 0 1:5 � NH.

This section presents numerical simulations of the model. Figures 4 and 5 show the numerical simulations of primary and secondary infections in the absence and presence of Wolbachia, respectively.

Figures 4 and 5 show that Wolbachia can reduce dengue transmission. The number of infections in the presence of Wolbachia-carrying mosquitoes (see Figure 5) is smaller than that in the absence of Wolbachia-carrying mosquitoes (see Figure 4). This means that the Wolbachia can


Table 2. Parameter descriptions, values, and sources. Note that W and N are used to indicate Wolbachia-carrying and non-Wolbachia mosquitoes in the parameter descriptions, respectively. NH <sup>¼</sup> 105 .

potentially be used to break the cycle of dengue transmission. Note that the parameter values are largely uncertain. Therefore, large data set is needed to validate the model against data.

received funding from Ministry of Research, Technology and Higher Education of Indonesia (Grant No: 3/E/KPT/2018). NA received Academic Leadership Grant from Padjadjaran University (Grant No: 2297 /UN6.D/KS/2018) and Penelitian Dasar Unggulan Perguruan Tinggi

Mathematical Model as a Tool for the Control of Vector-Borne Diseases: *Wolbachia* Example

http://dx.doi.org/10.5772/intechopen.79754

125

1 Department of Mathematics, Faculty of Sciences and Engineering, University of Nusa

2 Department of Mathematics, Faculty of Mathematics and Natural Sciences, State University

[1] Gubler DJ. Dengue and dengue hemorrhagic fever. Clinical Microbiology Reviews. 1998;

[2] Bhatt S, Gething PW, Brady OJ, Messina JP, Farlow AW, et al. The global distribution and

[3] World Health Organisation. Dengue and Severe Dengue, Fact Sheet No. 117 [Online]. February 2018. Available from: http://www.who.int/news-room/fact-sheets/detail/dengue-

[4] Shepard DS, Undurraga EA, Halasa YA, Stanaway JD. The global economic burden of dengue: A systematic analysis. The Lancet Infectious Diseases. 2016;16(8):935-941

[5] Dorigatti I, McCormack C, Nedjati-Gilani G, Ferguson NM. Using Wolbachia for dengue

[6] McMeniman CJ, Lane RV, Cass BN, Fong AWC, Sidhu M, Wang Y-F, O'Neill SL. Stable introduction of a life-shortening Wolbachia infection into the mosquito Aedes aegypti. Science.

[7] Sinkins SP. Wolbachia and cytoplasmic incompatibility in mosquitoes. Insect Biochemistry

[8] Hoffmann AA, Iturbe-Ormaetxe I, Callahan AG, Phillips BL, Billington K, Axford JK, Montgomery B, Turley AP, O'Neill SL. Stability of the WMel Wolbachia infection following invasion into Aedes aegypti populations. PLoS Neglected Tropical Diseases. 2014;8:e3115

control: Insights from modelling. Trends in Parasitology. 2018;34(2):102-113

3 Department of Mathematics, Faculty of Mathematics and Natural Sciences, Padjadjaran

, Nursanti Anggriani<sup>3</sup> and Asep K. Supriatna<sup>3</sup>

(Grant No: 1126/UN6.D/LT/2018).

Cendana, Kupang NTT, Indonesia

of Jakarta, Jakarta DKI, Indonesia

University, Jawa Barat, Indonesia

2009;323(5910):141-144

\*, Eti D. Wiraningsih<sup>2</sup>

burden of dengue. Nature. 2013;496:1476-4687

and-severe-dengue [Accessed: June 1, 2018]

and Molecular Biology. 2004;34(7):723-729

\*Address all correspondence to: meksianis.ndii@staf.undana.ac.id

Author details

Meksianis Z. Ndii<sup>1</sup>

References

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