Implication of vaccination against dengue for Zika outbreak

Abstract

Zika virus co-circulates with dengue in tropical and sub-tropical regions. Cases of co-infection by dengue and Zika have been reported, the implication of this co-infection for an integrated intervention program for controlling both dengue and Zika must be addressed urgently. Here, we formulate a mathematical model to describe the transmission dynamics of co-infection of dengue and Zika with particular focus on the effects of Zika outbreak by vaccination against dengue among human hosts. Our analysis determines specific conditions under which vaccination against dengue can significantly increase the Zika outbreak peak, and speed up the Zika outbreak peak timing. Our results call for further study about the co-infection to direct an integrated control to balance the benefits for dengue control and the damages of Zika outbreak.

Figure 1. Transmission diagram.

Figure 2. Sub-flow diagram of Zika infection among humans.

Here, we assume that the susceptible humans (S) are infected by dengue with a ratio of P_d on average and by Zika with a ratio of P_z on average. We further assume that the class I_d will be infected with Zika at a ratio of P_dz while the other part will recover to R_d. Moreover, we assume that the individuals in compartment R_d can be further infected with Zika at a ratio of .

Figure 3

(A) Schematic scenarios which show that vaccination against dengue can increase the total number of Zike infections if the parameters P_z and are located in the red region while it can decrease the total number of Zika infections in the green region; (B) The relationship of the total number of Zika infections to the ratio with or without vaccination against dengue. Here, P_z = 0.3 and P_v = 0.7; (C) The relationship of ΔZ to the effective coverage rate of dengue vaccine P_v while the parameters P_z and are chosen in the red region of (A) with P_z = 0.3; (D) The relationship of ΔZ to the effective coverage rate of dengue vaccine P_v while the parameters P_z and are chosen in the green region of (A) with P_z = 0.3. Other parameters in (A–D) are fixed as P_d = 0.3, P_dz = 0.1, S₀ = 100000.

Figure 4. The value of in time and with respect to the recruitment rate of mosquitos Λ being varied in the interval [10000, 1000000].

The mesh surface represents the solutions without inoculating dengue vaccine to susceptible humans while the other one are the solutions when the susceptible humans are inoculated with dengue vaccine at a ratio of 0.7. Parameters β_dz and β_rz are fixed as 0.18, 0.05, respectively.

Figure 5. Solutions to system S^* with the solid curves being the solutions without vaccination and the dashed curves being the solutions with inoculating the dengue vaccine at the ratio of P_v = 0.7.

Here, β_dz = 0.18, β_rz = 0.05, Λ = 10000.

Figure 6. Solutions of model S^* with the solid lines being the solutions without vaccination and the dashed lines being the solutions after inoculating the dengue vaccine at the ratio of P_v = 0.7.

Here we fixed Λ = 1000000 and all the other parameters as the same as those in Fig. 5.

Figure 7

Solutions of for (A) β_dz = 0.05, β_rz = 0.18, Λ = 10000 and (B) β_dz = 0.05, β_rz = 0.18, Λ = 1000000. The accumulated number of humans infected with Zika for (C) β_dz = 0.18, β_rz = 0.18, Λ = 10000 and (D) β_dz = 0.18, β_rz = 0.05, Λ = 10000.