Population biology of malaria within the mosquito: density-dependent processes and potential implications for transmission-blocking interventions

Abstract

Background: The combined effects of multiple density-dependent, regulatory processes may have an important impact on the growth and stability of a population. In a malaria model system, it has been shown that the progression of Plasmodium berghei through Anopheles stephensi and the survival of the mosquito both depend non-linearly on parasite density. These processes regulating the development of the malaria parasite within the mosquito may influence the success of transmission-blocking interventions (TBIs) currently under development.

Methods: An individual-based stochastic mathematical model is used to investigate the combined impact of these multiple regulatory processes and examine how TBIs, which target different parasite life-stages within the mosquito, may influence overall parasite transmission.

Results: The best parasite molecular targets will vary between different epidemiological settings. Interventions that reduce ookinete density beneath a threshold level are likely to have auxiliary benefits, as transmission would be further reduced by density-dependent processes that restrict sporogonic development at low parasite densities. TBIs which reduce parasite density but fail to clear the parasite could cause a modest increase in transmission by increasing the number of infectious bites made by a mosquito during its lifetime whilst failing to sufficiently reduce its infectivity. Interventions with a higher variance in efficacy will therefore tend to cause a greater reduction in overall transmission than a TBI with a more uniform effectiveness. Care should be taken when interpreting these results as parasite intensity values in natural parasite-vector combinations of human malaria are likely to be significantly lower than those in this model system.

Conclusions: A greater understanding of the development of the malaria parasite within the mosquito is required to fully evaluate the impact of TBIs. If parasite-induced vector mortality influenced the population dynamics of Plasmodium species infecting humans in malaria endemic regions, it would be important to quantify the variability and duration of TBI efficacy to ensure that community benefits of control measures are not overestimated.

Figure 1

Graphical description of the mathematical model describing sporogonic development within the mosquito prior to the introduction of an intervention. The model charts the number of macrogametocytes, $L_i^1$, ookinetes, $L_i^2$, oocysts, $L_i^3$, and salivary gland sporozoites, $L_i^4$, within mosquito i. For a full list of notation see Additional file 1. The graphs under each arrow indicate the density-dependent processes describing the number of parasites which develop into the subsequent life-stage. Shaded areas indicate the 95% confidence intervals for the best-fit model fitted in [2].

Figure 2

The impact of transmission-blocking interventions which target different parasite life-stages on the prevalence and density of salivary gland sporozoites. The Figure shows the relationship between the number of macrogametocytes ingested and the mean prevalence of infectious mosquitoes (dashed lines, A and B) or the mean number of salivary gland sporozoites per mosquito (solid lines, D and E). The model (described in Protocol S1) was run with either no intervention (black line) or representing an intervention which reduced the production of a Plasmodium life-stage by 60%: macrogametocytes (yellow line); ookinetes (blue line); oocysts (green line); salivary gland sporozoites (red line). The grey dotted-dashed line in panel B and panel E (where it lies on top of the red line) indicates an overall reduction in sporozoite density/prevalence of 60% as a benchmark for comparison. The shaded areas of panels A and D depict the 95% confidence intervals for the best-fit model. Panel D illustrates the importance of using an individual-based model (with which to account for parasite aggregation), as simply combining the three density-dependent functions within a mean-based, deterministic model (thin dotted-dashed line) underestimates the severity of the non-linear relationship. Panels C and F show which is the best life-stage to target to reduce transmission for a range of gametocyte densities and intervention efficacies: macrogametocytes (yellow surface); ookinetes (blue surface); sporozoites (red surface).

Figure 3

The impact on transmission of interventions which target different parasite life-stages. The Figure shows the relationship between the number of macrogametocytes ingested and transmission according to whether the latter is dependent on the presence (dashed lines, panels A, B, C and D) or density (solid lines, panels E, F, G and H) of salivary gland sporozoites. The mean number of infectious bites per mosquito and the lifetime mean number of salivary gland sporozoites available to be injected per mosquito are both estimated assuming the mosquito is infected at its first bloodmeal. Parasite-induced vector mortality is dependent on the number of oocysts at day 10 (A, B, E and F) or salivary gland sporozoites on day 21 (C, D, G and H). In panels A, C, E and G the model was run with either no intervention (black line) or representing an intervention which reduced the production of a life-stage by 60%: gametocytes (yellow line); ookinetes (blue line); oocysts (green line); salivary gland sporozoites (red line). Note that the black and red lines overrun each other in panel A. The thin grey dotted-dashed line indicates an overall efficacy of 60% for comparison. The contour plots (panels B, D, F and H) show the relationship between gametocytaemia, the efficacy of an intervention which targeting oocysts and the overall reduction in transmission that this intervention causes.

Figure 4

The relationship between gametocytaemia and transmission for three different theoretical transmission blocking vaccines which have the same mean efficacy but differ in their variance. The two panels show the impact of the interventions which reduce the production of ookinetes by an average of 60% if malaria transmission is dependent on the presence (dashed line, panel A) or density (solid line, pane B) of salivary gland sporozoites. Predictions are shown for no intervention (black line) or for a TBV which generates a range of antibody responses in the vaccinated population corresponding to a ratio of the 97.5% percentile to the 2.5% percentile of 9 fold (low variance, light green), 68 fold (medium variance, dark green) or 6664 fold (high variance, purple) [31].