Administration of Defective Virus Inhibits Dengue Transmission into Mosquitoes

Abstract

The host-vector shuttle and the bottleneck in dengue transmission is a significant aspect with regard to the study of dengue outbreaks. As mosquitoes require 100-1000 times more virus to become infected than human, the transmission of dengue virus from human to mosquito is a vulnerability that can be targeted to improve disease control. In order to capture the heterogeneity in the infectiousness of an infected patient population towards the mosquito population, we calibrate a population of host-to-vector virus transmission models based on an experimentally quantified infected fraction of a mosquito population. Once the population of models is well-calibrated, we deploy a population of controls that helps to inhibit the human-to-mosquito transmission of the dengue virus indirectly by reducing the viral load in the patient body fluid. We use an optimal bang-bang control on the administration of the defective virus (transmissible interfering particles (TIPs)) to symptomatic patients in the course of their febrile period and observe the dynamics in successful reduction of dengue spread into mosquitoes.

Keywords: defective particles; dengue transmission; dengue virus; mosquito infectious dose; population of models.

Figure 1

Dengue virus host-to-vector transmission model: The virus ($V\left(t\right)$) and the defective interfering (DI) particles ($D\left(t\right)$) are transmitted from infected hosts to mosquitoes. The susceptible mosquitoes (S) can be infected by virus or DI particles to generate the two types of infected mosquitoes, $I_V$ and $I_D$. Further, a dually-infected population ($I_{VD}$) is generated from co-infection by $D\left(t\right)$ and $V\left(t\right)$, simultaneously. The model has been considered in two-compartments. The $D\left(t\right)$ and $V\left(t\right)$ are generated in the within-host compartment and infect the mosquito population in the other compartment. For each within-host model (shown in left box), multiple plausible transmission models has been calibrated (shown by multiple lines). The shaded domain indicates the days of high fever.

Figure 2

Population of models for infected mosquitoes: The dengue virus infected mosquito data for 408 exposure experiments with 208 hospitalised dengue patients reported in Nguyen et al. [33] are calibrated to construct serotype-specific population of models (POMs). The black scattered points in the top panel represent the fraction of viral infected mosquitoes (${\tilde{I}}_V$) observed in the exposure experiment. The group of lines in different colours (in the top, middle and bottom panels) are the calibrated POMs outputs for different patient models in the population.

Figure 3

Variability in accepted model parameters: The parameters accepted in the POMs are shown in box plots for the four serotypes. The density of the parameters (A, $\mu$, $\varphi$) are shown in the scatter plots in the background of the box plots.

Figure 4

Mosquito infectious dose: The infected mosquitoes by virus (${\tilde{I}}_V$) and DI particles (${\tilde{I}}_D$) are shown in scattered plots with respect to the ${\mathrm{Log}}_{10}$ values of corresponding within-host virus ($V\left(t\right)$) and DI particles ($D\left(t\right)$) levels. Different colours represent different patient models. These scatter plots represent the phase portrait of the data shown in Figure 2 versus the viraemia data reported in our previous model [32] and is a way to estimate the ranges of different mosquito infectious doses ($MID$s), say $MI{D}_{50}$.

Figure 5

Controlled population of transmission models: Each serotype-specific POMs (from Figure 2) are considered after applying optimal bang-bang control to construct the controlled POMs (cPOMs). The infected mosquitoes by virus only (${\tilde{I}}_{VC}$), by DI only (${\tilde{I}}_{DC}$) and by both (${\tilde{I}}_{VDC}$), are computed by using the controlled within-host plasma viraemias in the populations for four dengue serotypes.

Figure 6

Controlled MIDs: Scatter plots show the controlled infected fractions ($I_{VC}$ and $I_{DC}$) of the mosquito population versus the controlled patient viraemias ($V\left(t\right)$ and $D\left(t\right)$). The transmission of DI particles with respect to the ${\mathrm{Log}}_{10}$ values of the plasma DI particles ($D\left(t\right)$) has notable rise after applying the control (see Figure 4).

Figure 7

Control efficiency: The reduction in the human-to-mosquito virus transmission was evaluated by Jensen-Shannon (J-S) divergence ($\mathcal{D}$), calculated between the distributions of the virus infected mosquitoes before (${\tilde{I}}_V$) and after (${\tilde{I}}_{VC}$) applying the optimal control. The box plot for each serotype explains the variation in the J-S divergence on each day of the febrile period (in the insets). The main scatter plot compares the efficiency of the applied optimal controls for different serotypes, in terms of J-S divergence versus normalised control expense (C) (red: DENV-1, blue: DENV-2, green: DENV-3, cyan: DENV-4). The control expense was computed by the area under the control curve [32].