Table 1.
Parameter values for the underlying within-vector model.
All values, apart from G0 and d, were obtained from Teboh-Ewungkem et al. [15]. G0 was varied. d was obtained from Teboh-Ewungkem et al. [16].
Table 2.
CTMC transition probabilities for the stochastic within-vector model.
*Note that probabilities are denoted in the standard form used by [40]. For calculation, the term as written is divided by the sum of all transitions. See SI File for details.
Fig 1.
Dynamics of the within-vector model.
The temporal dynamics of the deterministic model (black line) and the average dynamics across 1000 stochastic simulations (blue curve) overlays 100 simulations of the single-parasite population CTMC model (gray lines) with initial gametocyte number G0 = 300 for zygotes (A), ookinetes (B), oocysts (C) and sporozoites (D). Observe that not all simulations produce a positive number of sporozoites. In fact, out of 10,000 simulations, 2.58% produce no sporozoites.
Fig 2.
Comparison of life cycle model with published data.
(A) Experimental data (blue circles) extracted (using Plot Digitizer) from Figure 1A in [46] along with the mean number of oocysts per mosquito calculated from our simulation data. The experimental data is scaled to be in units of gametocytes per five μL rather than gametocytes per one μL. A regression line to the log-log experimental data (dashed green) and to a subset of the experimental data over the range of initial gametocyte densities used to parameterize the model (solid green) is shown along with our model simulations (red stars). (B) Experimental data (black circles) from Figure 1 in [47] of oocyst intensity and prevalence (reproduced with permission) compared to results of the simulation starting from 150 (red shading), 300 (green shading) and 450 (blue shading) gametocytes. The colored areas represent the range of oocyst intensity and prevalence observed from simulations.
Fig 3.
Comparison of stochastic and deterministic dynamics of oocysts and sporozoites.
(A) Each of the first four rows illustrate the dynamics of the oocyst (left column) and sporozoite (right column) populations from individual simulations of the CTMC model using 50% fitness bias and G0 = 300. (B) The dynamics of the deterministic model for oocysts (left) and sporozoites (right). Observe the variation in dynamics possible with the CTMC model.
Fig 4.
Cumulative and ruptured oocysts.
The mean cumulative number (on day 21) of oocysts formed (A) and the total number of ruptured oocysts (B) resulting from the 10,000 simulations of the two-parasite population CTMC model (dots) and deterministic model (crosses) is illustrated for initial gametocyte number G0. Here, the CTMC model utilizes a more biologically realistic continuous rupture function for oocyst bursting, compared to the step function used in the deterministic model. (See S4 Fig for the comparison of models both using a step bursting function.) Left to right the columns illustrate the results for 0%, 10% and 50% fitness biases, respectively.
Fig 5.
Oocyst intensity and prevalence.
The scatter plots show mean oocyst intensity (x-axis) versus mean oocyst prevalence (y-axis), calculated 1000 times. Oocyst prevalence is defined as the proportion of mosquitoes harboring oocysts (i.e. simulations producing at least one oocyst). Oocyst intensity is defined as the number of oocysts per mosquito (i.e. per simulation). To produce each point, we randomly drew ten mosquitoes (that is, ten stochastic realizations) from our 10,000 simulations of the stochastic model and computed the oocyst prevalence and intensity for these ten mosquitoes on day seven. The histograms show the density of points in the scatter plot for different values of oocyst intensity (horizontal graph) and oocyst prevalence (vertical graph). In the left and right columns, the initial gametocyte number is G0 = 150 and G0 = 450, respectively. Top to bottom the rows illustrate the results for 0%, 10% and 50% fitness biases, respectively. Observe that as G0 increases, the differences in distribution of the genetically distinct parasite populations becomes more pronounced.
Fig 6.
Number of unique barcode sequences.
(A) The number of unique barcode sequences from two genetically distinct parasite populations as a function of the number of barcode positions that initially differ. (B) Distribution of the unique barcode sequences when looking at 15 differences between the two initial parasite populations. Colors indicate the number of starting gametocytes with darker colors representing lower initial gametocyte numbers. Left to right the columns illustrate the results for 0%, 10% and 50% fitness biases, respectively. Gray bars in (A) show the similarity in parasite populations for the distributions in (B).
Fig 7.
Nucleotide diversity of ruptured oocysts.
Nucleotide diversity, π, by differing number of starting positions between genetically distinct parasite populations. Left to right the columns illustrate the results for 0%, 10% and 50% fitness biases, respectively. Colors refer to the initial gametocyte number with darker colors representing lower gametocyte numbers.
Fig 8.
Frequency that multiple genetically distinct parasites are passed in an infectious bite.
The fraction of infectious bites that harbor one (black), two (brown) or multiple (beige) parasites with distinct barcode sequences. When the mosquito is infected with a small number of gametocytes, 34% of infectious bites are composed of a single sequence. At larger initial gametocyte numbers the proportion of infectious bites passing only a single genetically distinct parasite population falls to nearly 0. Ten sporozoites were assumed to be present in a single infectious bite.