Figure 1.
Model for L. donovani infection, transmission and control.
Compartments represent proportions in humans and vectors, distinguished (vertically) according to their history of infection (defined by diagnostic states). The diagnostics comprised PCR, DAT and LST with combinations shown in the bar on the left margin of the graph. Human hosts are further distinguished (horizontally) by disease and treatment status. μ1 = μH+μK; μ2 = μH+μK+μT1; μ3 = μH+μK+μT2; for further variables and parameters see text, Table 1, Table 2, Table 3 and Table S1 in the Supplement.
Table 1.
Model parameters and variables – sand flies.
Table 2.
Model parameters and variables – humans.
Table 3.
Model parameters and variables – treatment.
Figure 2.
Treatment-related interventions.
Sensitivity analyses of equilibrium solutions to the effects of seven intervention parameters (A) on the prevalence of symptomatic (IHS, IHT1, IHT2, IHL) and asymptomatic infections (IHP, IHD) and (B) on the incidences of KA and PKDL. The ten scenarios refer to ten parameter combinations as shown in Table 4. The default scenario 1 used parameter values as obtained from model calibration. The duration of treatment (parameters τ1, τ2, τ3) varied in scenarios 3 and 4; early case detection (1/γHS) varied in scenarios 5, 6, and 7; and treatment efficacy (fT, p1, p2) varied in scenarios 8, 9 and 10. Scenario 2 represents a best-case scenario, using over-optimistic assumptions for all parameters. The default scenario 1 was compared to more pessimistic intervention parameters in scenarios 5, 6 and 7 and to more optimistic intervention parameters in scenarios 2, 3, 8, 9 and 10. As illustrated by the diagonally proceeding arrow, an optimal intervention would reduce the prevalence and incidence in both dimensions (see Fig. 3 and Table 5 for vector-related interventions).
Table 4.
Parameter combinations of treatment-related interventions.
Figure 3.
Sensitivity analyses into the effects of vector control: (A) on the prevalence of symptomatic and asymptomatic infections and (B) on the incidences of KA and PKDL. The scenarios refer to ten parameter combinations shown in Table 5. The default scenario 1 uses parameter values as obtained from model calibration. Vector population size NF varied in scenarios 2 and 5; the flies' life expectancy 1/μF varied in scenarios 3 and 6; and their feeding cycle duration 1/β varied in scenarios 4 and 7. Scenarios 8, 9 and 10 represent combinations thereof.
Table 5.
Parameter combinations of vector-related interventions.
Figure 4.
Time-dependent effect of reducing the contact rate.
We assumed that the feeding cycle duration of the sand fly was doubled by the intervention from 1/β = 4 days to 8 days (scenario 4 in Fig. 3 and Table 5). The intervention lasted for 5 years (grey box). The solid curve shows the prevalence of KA and the dotted line the prevalence of PKDL.