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. 2020 Oct 7;7(10):192173.
doi: 10.1098/rsos.192173. eCollection 2020 Oct.

The impact of within-vector parasite development on the extrinsic incubation period

Lauren M Childs  1 , Olivia F Prosper  2
Affiliations

The impact of within-vector parasite development on the extrinsic incubation period

Lauren M Childs et al. R Soc Open Sci. .

Abstract

Mosquito-borne diseases, in particular malaria, have a significant burden worldwide leading to nearly half a million deaths each year. The malaria parasite requires a vertebrate host, such as a human, and a vector host, the Anopheles mosquito, to complete its full life cycle. Here, we focus on the parasite dynamics within the vector to examine the first appearance of sporozoites in the salivary glands, which indicates a first time of infectiousness of mosquitoes. The timing of this period of pathogen development in the mosquito until transmissibility, known as the extrinsic incubation period, remains poorly understood. We develop compartmental models of within-mosquito parasite dynamics fitted with experimental data on oocyst and sporozoite counts. We find that only a fraction of oocysts burst to release sporozoites and bursting must be delayed either via a time-dependent function or a gamma-distributed set of compartments. We use Bayesian inference to estimate distributions of parameters and determine that bursting rate is a key epidemiological parameter. A better understanding of the factors impacting the extrinsic incubation period will aid in the development of interventions to slow or stop the spread of malaria.

Keywords: Bayesian inference; extrinsic incubation period; malaria; mosquito; within-host model.

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Conflict of interest statement

The authors have no competing interests to declare.

Figures

Figure 1.
Figure 1.
Model schematics. Our models consist of ookinetes (E), bursting oocysts (O), non-bursting oocysts (Od) and sporozoites (S) compartments. Ookinetes die at rate μE and transition to oocysts at rate σE with f fraction ultimately bursting. Non-bursting oocysts die at rate μO. (a) Model 1 assumes gamma-distributed bursting with shape parameter N and scale parameter 1/(βN) and N bursting oocyst compartments. (b) Model 2 assumes time-dependent bursting at the rate k/(1 + exp (tb − t)). Upon bursting, m sporozoites burst from each oocyst and reach the salivary gland with probability p.
Figure 2.
Figure 2.
Model selection for multistart parameter fitting. AICc plot for each initial ookinete density E(0) for Model 1 with N oocyst stages, where N ∈ {2, 3, 10, 20, 30, 40, 50, 75, 100}. The AICc for Model 2 is demonstrated by the dashed horizontal line. AICc values are given in electronic supplementary material, table S3.
Figure 3.
Figure 3.
Best fit model solutions and data. Comparison of best fit model and data with oocyst count on the left and sporozoite score on the right. The panels are ordered by initial ookinete number, as indicated by their titles. The median of MCMC posterior draws using Model 2 in dashed blue with the 95% highest density posterior interval shown in shaded grey and best fit multistart, which may be Model 1 or Model 2 (see table 2) in solid red. The black points represent data on oocyst count and sporozoite score, extracted from [14].
Figure 4.
Figure 4.
Summary metrics of oocyst number and sporozoite score. By initial ookinete number, the time of the oocyst peak (top left), the peak number of oocysts (top right), the first time sporozoite score is above 0.01 (bottom left) and the maximum sporozoite score (bottom right).
Figure 5.
Figure 5.
Variation in EIP across different initial ookinete numbers. Distribution of EIP with median (black line) for MCMC simulations. Red stars are the EIP from Model 2 fitted with multistart and blue circles are the EIP from Model 1 with optimized N fitted with multistart. All optimized parameters are found in table 2 with 95% highest density posterior intervals found in electronic supplementary material, table S4.
Figure 6.
Figure 6.
Variation in fitted parameters by initial ookinete number. Distribution of posterior density (shaded pink) with median value (black line) for each parameter from Model 2 fit by the MCMC. The prior distributions for each parameter are found in table 1. Optimal parameters fit by multistart are shown as blue circles for Model 1 and red stars for Model 2. Note that in Model 1, there are not the parameters tb or k so we omit values for Model 1 in the bottom row. The 95% highest density posterior intervals for the MCMC fit parameters are found in electronic supplementary material, table S4.
Figure 7.
Figure 7.
Global sensitivity of extrinsic incubation period. Proportion of variation in EIP with respect to each varied parameter in Model 1 (left) and Model 2 (right) using eFAST. Orange bars indicate individual sensitivity index while blue bars are the total sensitivity index. Increasing colour intensity refers to increasing initial ookinete number. The number of oocyst compartments, N, is not able to be varied in eFAST. For each initial ookinete density, sensitivity is shown for the optimal N: N = 30 for E0 = 100, N = 50 for E0 = 200, N = 50 for E0 = 500, N = 75 for E0 = 800, N = 75 for E0 = 2000, N = 75 for E0 = 4000.
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