Visceral leishmaniasis in the Indian subcontinent: modelling epidemiology and control

Abstract

Background: In the Indian subcontinent, about 200 million people are at risk of developing visceral leishmaniasis (VL). In 2005, the governments of India, Nepal and Bangladesh started the first regional VL elimination program with the aim to reduce the annual incidence to less than 1 per 10,000 by 2015. A mathematical model was developed to support this elimination program with basic quantifications of transmission, disease and intervention parameters. This model was used to predict the effects of different intervention strategies.

Methods and findings: Parameters on the natural history of Leishmania infection were estimated based on a literature review and expert opinion or drawn from a community intervention trial (the KALANET project). The transmission dynamic of Leishmania donovani is rather slow, mainly due to its long incubation period and the potentially long persistence of parasites in infected humans. Cellular immunity as measured by the Leishmanin skin test (LST) lasts on average for roughly one year, and re-infection occurs in intervals of about two years, with variation not specified. The model suggests that transmission of L. donovani is predominantly maintained by asymptomatically infected hosts. Only patients with symptomatic disease were eligible for treatment; thus, in contrast to vector control, the treatment of cases had almost no effect on the overall intensity of transmission.

Conclusions: Treatment of Kala-azar is necessary on the level of the individual patient but may have little effect on transmission of parasites. In contrast, vector control or exposure prophylaxis has the potential to efficiently reduce transmission of parasites. Based on these findings, control of VL should pay more attention to vector-related interventions. Cases of PKDL may appear after years and may initiate a new outbreak of disease; interventions should therefore be long enough, combined with an active case detection and include effective treatment.

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 = μ_H+μ_K; μ₂ = μ_H+μ_K+μ_T1; μ₃ = μ_H+μ_K+μ_T2; for further variables and parameters see text, Table 1, Table 2, Table 3 and Table S1 in the Supplement.

Figure 2. Treatment-related interventions.

Sensitivity analyses of equilibrium solutions to the effects of seven intervention parameters (A) on the prevalence of symptomatic (I_HS, I_HT1, I_HT2, I_HL) and asymptomatic infections (I_HP, I_HD) 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/γ_HS) varied in scenarios 5, 6, and 7; and treatment efficacy (f_T, 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).

Figure 3. Vector-related interventions.

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 N_F varied in scenarios 2 and 5; the flies' life expectancy 1/μ_F 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.

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.