Assessing health burden risk and control effect on dengue fever infection in the southern region of Taiwan

Figures & data

Figure 1 Schematic demonstrating the interactive transmission dynamics of (A) mosquito and (B) human population dynamics.

Table 1 Input parameters of DALYs estimations

Parameters	Values	References
Age-corrected constant, C	0.16243	Murray^Citation19
Age-weight factor, ß	0.04	Murray^Citation19
Discount rate, r	0.03	Murray^Citation19
Disability weight, D (DF)	0.197	who,^Citation48
Disability weight, D (DHF/Dss)	0.542	Anderson et al^Citation49
Disability duration due to DF cases (days) L	4.015	Shepard et al^Citation22
Disability duration due to DHF/Dss cases (days), L2	14.016	Shepard et al^Citation22

Abbreviations: DF, dengue fever; DHF, dengue hemorrhagic fever; DSS, dengue shock syndrome.

Figure 2 Monthly time-series estimates in temperature and total DALYs in 2001–2014, where the symbols diamond, square, and triangle represent monthly maximum, mean, and minimum temperatures, respectively.

Abbreviations: DALYs, disability-adjusted life years; T_max, maximum temperature; T_mean, mean temperature; T_min, minimum temperature.

Figure 3 Relationships showing temperature dependency for (A) extrinsic incubation rate, (B) female mosquito death rate, and (C) larvae survival percentage used in vector-host interactive transmission model.

Abbreviations: ν_m, extrinsic incubation rate; μ_m, female mosquito death rate; S_L, larvae survival percentage.

Table 2 Parameters and equations used to estimate temperature-dependent basic reproduction number (R₀)

Symbol	Interpretation	Values/equations
Mosquito-related parameters
βmh^a	Transmission probability from vector to	LN (0.71, 1.16)^b
	host (bite^−1)
B^c	Biting rate (d^−1)	LN (0.18, 1.85)
Human-related parameters
βhm^a	Transmission probability from host to	LN (0.71, 1.16)
	vector (bite^−1)
ηh^d	Recovery rate (d^−1)	LN (0.24, 1.38)
νh^e	Intrinsic incubation rate (d^−1)	LN (0.04, 1.17)
μh^f	Human mortality rate (d^−1)	LN (1.68×10^−8, 1.01)
Nh^f	Total population in Kaohsiung	2,778,992
m^g	Female mosquitoes per human	LN (4.15, 1.26)
Temperature-dependent parameters in mosquito
Sm(0)^h,i	Susceptible mosquitoes: m×SL(T) × Nh	$S_L(T)=4\times 89.41\frac{\exp \left(-(T-24.14)/4.33\right)}{{\left(1+\exp \left(-(T-24.14)/4.33\right)\right)}^3}$	(T1)
νm^j	Extrinsic incubation rate (d^−1)	$v_{\text{m}}(T)=0.02+4.39\times {10}^{-6}{T}^3$	(T2)
μm^k	Female mosquito death rate (d^−I)	${\mu }_{\text{m}}(T)=-0.15+0.004T+\frac{2.03}{T}$	(T3)
Vector-host transmission dynamic model
R0^h	Basic reproduction number	$R_0=\sqrt{\frac{v_{\text{m}}{v}_{\text{h}}{B}^2{\beta }_{\text{hm}}{\beta }_{\text{mh}}}{\left(v_{\text{h}}+{\mu }_{\text{h}}\right)\left({\eta }_{\text{h}}+{\mu }_{\text{h}}\right){\mu }_{\text{m}}\left({\mu }_{\text{m}}+v_{\text{m}}\right)}\frac{S_{\text{m}}(0)}{N_{\text{h}}}}$	(T4)

Notes: ^aEstimated from Newton and Reiter.⁵⁰

b Lognormal distribution with geometric mean and geometric SD.

c Estimated based on Focks et al.⁵¹

d Estimated from Harn.⁵²

e Estimated from Hsieh and Ma.⁵³

f Adopted from Department of Household Registration, Ministry of the Interior, Taiwan, Republic of China (https://www.moi.gov.tw/stat/node.aspx?cate_sn=&belong_sn=6463&sn=6465).

g Estimated from Padmanabha et al.⁵⁴

h Adopted from Dumont et al.²⁷

i S^L(T⁾ was estimated from Ruiz-Moreno et al.²⁹

j Estimated based on Focks.⁵

k Estimated based on Yang et al.²⁸

Abbreviations: LN, lognormal; gm, geometric mean; gsd, geometric SD.

Figure 4 Uncertainty and sensitivity analysis of fractional parameter contribution to variance of temperature-dependent R₀.

Abbreviations: B, biting rate; β_hm, transmission probability from host; β_mh, transmission probability from vector; ν_h, intrinsic incubation rate; ν_m, extrinsic incubation rate; μ_h, human mortality rate; μ_m, female mosquito death rate; η_h, human recovery rate; S_L, larvae survival percentage; m, the number of female mosquitoes surrounding a human.

Figure 5 Three-dimensional interactive diagrams demonstrating relationships among monthly average temperature, R₀, and DALYs in seasons (A) summer, (B) fall, (C) winter, and (D) all seasons, respectively.

Abbreviations: R₀, basic reproduction number; DALYs, disability-adjusted life years.

Table 3 Optimal fitted three-dimensional models describing temperature–R₀–DALYs relationship^a

Fittedvalues	Season
	Summer	Fall	Winter	All
a	0.78±1.13×10-^H b	299.11 ±4.01 × 10^-10	4.18±1.82×10^-13	143.96±1.08×10^-12
b	3.45× 10-^14±1.19×10-^Citation14	-1.26× 10^-9±4.22× 10^-10	-5.72×10^-13±1.90×10^-13	-3.41 ×10^-12± 1.14×10^-12
c	-8.81 × 10^-15±3.04× 10^-15	3.26× 10^-10± 1.09× 10^-10	1.45× 10^-13±4.83× 10^-14	8.79× 10^-13±2.94× 10^-13
d	271.09±2.04×10^-15	2.25×10^3±4.89×10^-11	291.99±3.73×10^-14	1.25×10^3±1.08×10^-13
e	29.21 ±6.10×10^-18	24.95±4.04×10^-14	20.21 ± 1.04× 10^-16	24.96±9.51×10^-17
f	-1.65×10^-2±1.77×10^-19	1.59×10^-2±8.05×10^-16	-0.024±4.22×10^-18	-0.02±2.31×10^-18
r^2	0.99*	0.99*	0.99*	0.99*

Notes: ^aOptimal three-dimensional model: DALY(T,R0) = a + bR0 + cR₀² + d exp(–0.5×ln(T/e)/f)², where DALY(T, R₀) is the dengue caused DALYs varied with temperature (T) and R₀, b and c are fitted parameters demonstrating the quadratic relationships between temperature and R₀, a, d, e, and f represent the fitted parameters to describe the lognormal relationships between temperature and DALY that demonstrate the baseline DALY, peak DALY, location of peak DALY, and the geometric SD of DALY, respectively. ^bMean±SE. *P<0.001.

Abbreviations: DALYs, disability-adjusted life years; SE, standard error; R₀, basic reproduction number.

Figure 6 Box-and-Whisker plots showing estimated median and range values for (A) season-varied temperature and (B) R₀. Exceedance risk profiles indicating season-based DALYs occurring with different risk probabilities in (C) summer, (D) fall, (E) winter, and (F) all seasons.

Abbreviations: R₀, basic reproduction number; DALY, disability-adjusted life years.

Table 4 Temperature and basic reproduction number (R₀) variations-based DALYs with exceedance risks at 0.8, 0.5, and 0.2

Seasons	Exceedance risks
	0.8(more likely)	0.5(likely)	0.2(less likely)
Summer	41.8	127.2	225.2
	(33.0-50.6)^a	(116.5-138.0)	(217.6-232.8)
Fall	273.8	322.8	1023.8
	(211.2-336.4)	(266.7-378.9)	(912.9-1134.7)
Winter	20.8	59.9	172.4
	(12.2-29.4)	(45.2-74.6)	(157.4-187.4)
All	126.9	148.1	418.5
	(90.7-163.2)	(115.4—180.7)	(358.2-478.8)

Notes: ^aMedian (95% CI).

Abbreviation: DALYs, disability-adjusted life years.

Figure 7 Multi-efficacy control curve constructed with R₀, the asymptomatic infectious proportion, as well as various control efficacies for dengue outbreak containment in different seasons (A) summer, (B) fall, (C) winter, and (D) all seasons. Rectangular boxes showing 95% CIs of R₀ and θ, respectively. (E) Control measure effectiveness was estimated based on combinations of different control efficacies for varied seasons.

Abbreviations: R₀, basic reproduction number; θ, asymptomatic infectious proportion; ε, control efficacies for dengue outbreak containment; R, repellent use; S, pesticide spray; C, water container clean-up; W, life-shortening Wolbachia infection.

Murray CJ. Quantifying the burden of disease: the technical basis for disability-adjusted life years. Bull World Health Organ. 1994;72(3):429–445.

 PubMed Web of Science ®Google Scholar

World Health Organization. The Global Burden of Disease: 2004 Update. Geneva: WHO Press; 2008.

 Google Scholar

Anderson KB, Chunsuttiwat S, Nisalak A, et al. Burden of symptomatic dengue infection in children at primary school in Thailand: a prospective study. Lancet. 2007;369(9571):1452–1459.

 PubMed Web of Science ®Google Scholar

Shepard DS, Undurraga EA, Halasa YA. Economic and disease burden of dengue in Southeast Asia. PLoS Negl Trop Dis. 2013;7(2): e2055.

 PubMed Web of Science ®Google Scholar

Barbazan P, Guiserix M, Boonyuan W, et al. Modelling the effect of temperature on transmission of dengue. Med Vet Entomol. 2010;24(1):66–73.

 PubMed Web of Science ®Google Scholar