Dengue in the Philippines: model and analysis of parameters affecting transmission

Figures & data

Figure 1. Model diagram depicting the dengue transmission dynamics.

Table 1. Parameters values used in the dengue transmission model.

Parameter	Description	Value per week	Range	References
$b_{\mathrm{h}}$	Birth rate of humans	0.00085	–	Data fitted^a
${\mu }_{\mathrm{h}}$	Mortality rate of humans	0.00045	–	Data fitted^a
B	Vector biting rate	1	[0,4]	[15,37]
$C_{\mathrm{hv}}$	Transmission probability from human to vector	0.75	[0,1]	[15,37]
$C_{\mathrm{vh}}$	Transmission probability from vector to human	0.375	[0,1]	[15,37]
γ	Non-seeking healthcare recovery rate	0.5	[0.5,1.75]	[37]
θ	Healthcare-seeking recovery rate	1	[0.5,1.75]	[37]
$b_{\mathrm{v}}$	Per capita oviposition rate	75	[55,165]	[37]
${\mu }_{\mathrm{v}}$	Mortality rate of vectors	0.1	[0.06,0.20]	[37]
K	Vector carrying capacity	300,000,000	–	Estimated
α	Transition rate from infected to hospitalized humans	0.2	–	Estimated

^aEstimated from the Philippine population data.

Table 2. Initial conditions used in the dengue transmission model.

Parameter	Description	Value
$S_{\mathrm{h}}\left(0\right)$	Initial condition for susceptible humans	50,000,000
$I_{\mathrm{h}}\left(0\right)$	Initial condition for infected humans	15,000
$J_{\mathrm{h}}\left(0\right)$	Initial condition for healthcare-seeking humans	1500
$R_{\mathrm{h}}\left(0\right)$	Initial condition for recovered humans	5000
$S_{\mathrm{v}}\left(0\right)$	Initial condition for susceptible mosquitoes	20,000,000
$I_{\mathrm{v}}\left(0\right)$	Initial condition for infected mosquitoes	2,000,000

Figure 2. Dynamics of the healthcare-seeking class under varying model parameters. (a) Effect of varying α on the healthcare-seeking class, $J_{\mathrm{h}}$. (b) Effect of varying B on the healthcare-seeking class, $J_{\mathrm{h}}$. (c) Effect of varying $C_{\mathrm{vh}}$ on the healthcare-seeking class, $J_{\mathrm{h}}$. (d) Effect of varying $C_{\mathrm{hv}}$ on the healthcare-seeking class, $J_{\mathrm{h}}$.

Figure 3. (a) Bar graphs and (b) time course plots of the partial rank correlation coefficients (PRCCs) of the model parameters at 14 different time points (week 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22.5, 25, 27.5, 30) having the healthcare-seeking class as the reference model output. Model parameters were sampled 1000 times. (a) PRCC of the model parameters. (b) PRCC plotted over time.

Figure 4. Scatter plots of the residuals of linear regressions of the parameter ($\alpha ,B,C_{\mathrm{vh}},C_{\mathrm{hv}}$) versus all the parameters of the dengue model (abscissa) and the residuals of the regression of the model output ($J_h$) versus the parameter ($\alpha ,B,C_{\mathrm{vh}},C_{\mathrm{hv}}$) (ordinate). Corresponding PRCCs and p-values are obtained at different time points (week 4, 8, 12, 20). (a) Residual scatter plots for α. (b) Residual scatter plots for B. (c) Residual scatter plots for $C_{\mathrm{vh}}$. (d) Residual scatter plots for $C_{\mathrm{hv}}$.

Table 3. Partial rank correlation coefficients (PRCCs) of the model parameters at different time points (week 4, 8, 12, 20) having the healthcare-seeking class as the reference model output.

Parameter	Week 4	Week 8	Week 12	Week 20
$b_{\mathrm{h}}$	0.03326074	0.02634555	0.08166479	0.72440299
${\mu }_{\mathrm{h}}$	−0.01840611	0.01096615	−0.01404464	−0.01795374
B	0.97627901	−0.82145934	−0.95667317	−0.54733113
$C_{\mathrm{hv}}$	0.85555312	−0.40982824	−0.78205065	−0.28843513
$C_{\mathrm{vh}}$	0.93318314	−0.62412762	−0.87934455	−0.35750878
γ	−0.44204164	0.13901939	0.47879786	0.09163382
θ	−0.61020623	−0.62432293	−0.78287610	−0.77245147
$b_{\mathrm{v}}$	0.01916402	−0.05545822	−0.00994370	0.03836683
${\mu }_{\mathrm{v}}$	−0.23054657	0.09739979	0.21898691	−0.16647739
K	0.86682594	−0.46992403	−0.82512793	−0.28395440
α	0.65139711	0.59061355	0.58288276	0.75708901
Dummy	0.03317500	−0.02123174	−0.05246864	−0.01376391

Figure 5. The reported Philippine dengue cases by morbidity week in 2014 and 2015.

Figure 6. The reported dengue cases by morbidity week and cumulative sum in the Philippines from week 16 to 52 of 2014 and the corresponding model identification. (a) The reported 2014 Philippine dengue cases by morbidity week and the model estimation. (b) The reported 2014 cumulative Philippine dengue cases and the model estimation.

Figure 7. The reported dengue cases by morbidity week and cumulative sum in the Philippines from week 16 to 52 of 2015 and the corresponding model identification. (a) The reported 2015 Philippine dengue cases by morbidity week and the model estimation. (b) The reported 2015 cumulative Philippine dengue cases and the model estimation.

Figure 8. Bootstrap distributions of the parameter estimates $\alpha ,B,C_{\mathrm{vh}},$ and $C_{\mathrm{hv}}$ obtained from 1000 resampling Poisson distribution of 2014 Philippine dengue data by morbidity week.

Figure 9. Bootstrap distributions of the parameter estimates $\alpha ,B,C_{\mathrm{vh}},$ and $C_{\mathrm{hv}}$ obtained from 1000 resampling Poisson distribution of 2015 Philippine dengue data by morbidity week.

Table 4. Estimated parameter values obtained using 2014 and 2015 Philippine dengue data by morbidity week.

Year	Parameter	Initial	Estimated	Mean	Std. dev.	Conf. int.
2014	α	0.2000	0.0026	0.002608	0.000013	$(0.002584,0.002633)$
	B	1.0000	0.3438	0.342435	0.005263	$(0.332120,0.352750)$
	$C_{\mathrm{vh}}$	0.3750	0.6133	0.615811	0.010432	$(0.595365,0.636256)$
	$C_{\mathrm{hv}}$	0.7500	0.3228	0.324225	0.005208	$(0.314017,0.334433)$
2015	α	0.2000	0.0043	0.004336	0.000011	$(0.004313,0.004358)$
	B	1.0000	0.5176	0.489219	0.031219	$(0.428030,0.550408)$
	$C_{\mathrm{vh}}$	0.3750	0.2069	0.219819	0.016182	$(0.188103,0.251536)$
	$C_{\mathrm{hv}}$	0.7500	0.5713	0.607557	0.044691	$(0.519964,0.695150)$

M. Derouich, A. Boutayeb, and E. Twizell, A model of dengue fever, BioMed. Eng. OnLine 2 (2003), pp. 4–4. doi: 10.1186/1475-925X-2-4

 Google Scholar

D.P. Lizarralde-Bejarano, S. Arboleda-Snchez, and M.E. Puerta-Yepes, Understanding epidemics from mathematical models: Details of the 2010 dengue epidemic in Bello (Antioquia, Colombia), Appl. Math. Model. 43 (2017), pp. 566–578. doi: 10.1016/j.apm.2016.11.022

 Google Scholar