Modelling the impact of antibody-dependent enhancement on disease severity of Zika virus and dengue virus sequential and co-infection

Abstract

Human infections with viruses of the genus Flavivirus, including dengue virus (DENV) and Zika virus (ZIKV), are of increasing global importance. Owing to antibody-dependent enhancement (ADE), secondary infection with one Flavivirus following primary infection with another Flavivirus can result in a significantly larger peak viral load with a much higher risk of severe disease. Although several mathematical models have been developed to quantify the virus dynamics in the primary and secondary infections of DENV, little progress has been made regarding secondary infection of DENV after a primary infection of ZIKV, or DENV-ZIKV co-infection. Here, we address this critical gap by developing compartmental models of virus dynamics. We first fitted the models to published data on dengue viral loads of the primary and secondary infections with the observation that the primary infection reaches its peak much more gradually than the secondary infection. We then quantitatively show that ADE is the key factor determining a sharp increase/decrease of viral load near the peak time in the secondary infection. In comparison, our simulations of DENV and ZIKV co-infection (simultaneous rather than sequential) show that ADE has very limited influence on the peak DENV viral load. This indicates pre-existing immunity to ZIKV is the determinant of a high level of ADE effect. Our numerical simulations show that (i) in the absence of ADE effect, a subsequent co-infection is beneficial to the second virus; and (ii) if ADE is feasible, then a subsequent co-infection can induce greater damage to the host with a higher peak viral load and a much earlier peak time for the second virus, and for the second peak for the first virus.

Keywords: DENV; ZIKV; antibody-dependent enhancement; mathematical model; parameter estimation; viral dynamics.

Figure 1.

Schematic diagrams. (a) Schematic diagram for the secondary infection of DENV with a primary infection of ZIKV. (b) Schematic diagram of the co-infection of DENV and ZIKV.

Figure 2.

Shape of the switching function S(A_z). Here, we fix A_min = 50 and A_max = 1600.

Figure 3.

Data information from the existing experimental study [9]. (a) Data of dengue viral loads from macaque infected with DENV only. (b) Data of dengue viral loads from ZIKV convalescence macaque super-infected with DENV. Here, the bars are the mean values of the viral loads on log₁₀-scale while the error bars represent the corresponding standard deviations.

Figure 4.

Results of model fitting. (a) Fitting model (2.1) to the dengue viral loads from macaque infected with DENV only. (b) Fitting model (2.2) to the dengue viral loads from ZIKV convalescence macaque super-infected with DENV. The blue circles represent the mean dengue viral loads on log ₁₀-scale, the error bars are their standard derivations, and the blue curve is the fitting curve.

Figure 5.

The curves of the concentrations of DENV-specific antibody and ZIKV-specific antibody by solving model (2.2). All the parameter values are fixed as the same as those in table 1.

Figure 6.

Solutions of model (2.2) with and without ADN. Red curve: the fitting curve of model (2.2). Blue curves: dengue viral loads by solving model (2.2) while we set S(A_z) = 0 when A_z > A_max in contrast to the red curve. All the parameter values are fixed as the same as those in table 1.

Figure 7.

Sensitivity analysis. (a) PRCCs of the peak dengue viral load and the peak time for the primary DENV-infection (i.e. model (2.1)); (b) PRCCs of peak dengue viral load and the peak time for the secondary DENV-infection with a previous ZIKV-infection (i.e. model (2.2)). ‘*’ denotes PRCCs that are significantly different from zero.

Figure 8.

Solutions of model (2.4) in the case of simultaneous co-infection of DENV and ZIKV with different values of θ_d and θ_z. (a) Dengue viral loads; (b) Zika viral loads. All the other parameter values are chosen from table 1. The small maps on the bottom are the partial enlarged drawing around the peak time.

Figure 9.

Dengue viral loads and Zika viral loads in the case of subsequent co-infection. Here, we set θ_d = θ_z = 0 in (a,b) and θ_d = θ_z = 0.45 in (c,d). The other parameter values are fixed as those in table 1.