Conceived and designed the experiments: HPD RRS MB JCD. Performed the experiments: AS RRS. Analyzed the data: AS HPD. Contributed reagents/materials/analysis tools: AP BO SS SR. Wrote the paper: AS RRS.
The authors have declared that no competing interests exist.
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.
Parameters on the natural history of
Treatment of Kalaazar 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 vectorrelated 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.
Visceral Leishmaniasis is a neglected, lifethreatening disease affecting the poorest of the poor. It has received more attention in light of the regional VL elimination program. A deterministic compartmental model was developed to estimate parameters for
Leishmaniasis is a vectorborne disease, which is caused by protozoan flagellates and is transmitted by phlebotomine sand flies. Clinical manifestations of leishmaniasis include cutaneous leishmaniasis (CL), mucocutaneous leishmaniasis (MCL), visceral leishmaniasis (VL) and postkalaazar dermal leishmaniasis (PKDL). The only lifethreatening form is VL, which is strongly linked with poor housing
VL, also called Kalaazar (KA), causes more than 50,000 deaths each year worldwide
PKDL, first described by Brahmachari in 1922
Cases with VL and HIV coinfection have been reported from 35 countries. Both cellular and humoral responses to
The classical confirmatory test for VL used to be the microscopic detection of amastigote parasites from aspirates of lymph nodes, bone marrow or spleen
When taking a bloodmeal on an infected host, female sand flies ingest the amastigote form of the parasites. In the sand fly gut, the parasites develop into procyclic promastigote flagellar forms, which divide and later on differentiate into metacyclic promastigotes. These forms migrate to the pharyngeal valve and can then be transmitted at subsequent blood meals. In the human host, parasites change back to amastigotes and multiply in cells of the mononuclear phagocyte system, impeding the immune defence mechanisms of macrophages
In 2005, the governments of India, Nepal and Bangladesh started the first regional VL elimination program, aiming to reduce the annual incidence of VL to less than 1 per 10,000 by 2015. The program focuses on treatmentrelated control strategies, such as early diagnosis and complete treatment, and vectorrelated control strategies, including indoor residual insecticide spraying.
Currently, four drugs for VL treatment are available. 1) Pentavalent antimonials have been the firstline treatment for over 70 years. This treatment is long (20 to 30 days), is toxic (3–5% deaths due to treatment) and is accompanied by increasing failure rates; for instance in foci of the Bihar state, India, with up to 60% treatment failures, a phenomenon that is assumed to be caused by drug resistance
Vector control is an effective tool for controlling VL, as demonstrated in the 1950s in India by malaria control with DDT. Indoor spraying, in particular, reduces sand fly densities, also longlasting insecticidetreated bed nets and to a minor extent environmental management
The first mathematical study of the dynamics of KA employed a deterministic model to explain the observed interepidemic periods between 1875 and 1950 in Assam, India
Our model focuses on the transmission dynamics of
The transmission dynamics of
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.
Description  Value  Reference  

No. of vectors per 
527  Estimated, 95% CI (347 to 990) 

Equilibrium prevalence of infectious sand flies  0.5%  
1/ 
Life expectancy of sand flies  14 days 

1/ 
Sojourn time 
5 days 

1/ 
Feeding cycle duration  4 days 


Probability that a human becomes infected when an infectedfly takes a blood meal on a susceptible person  1  Assumed (correlated with 
Durations regardless of mortality, i.e., conditional on surviving (e.g. the sojourn time of flies in the latent stage
Description  Value  Reference  

No. of humans  100  Scaling factor (in relation to 

Prevalence 
76%  KalaNet data 

Prevalence 
10%  KalaNet data 

Prevalence 
2%  KalaNet data 

Prevalence 
12%  KalaNet data 

Prevalence 
0.015%  KalaNet data 

Prevalence 
0.005%  Model result basedon a fraction of treatment failure 

Prevalence 
50%  
1/ 
Baseline life expectancy ofhumans  40 years  Assumed 

Excess mortality rate causedby KA  1/(5 months)  Assumed 

Probability that a susceptible fly becomes infected when feedingon a human host of type 
0.0125  = 

Probability that a susceptible fly becomes infected when feedingon a human host of type 
0.025  Estimated, 95%CI (0.012 to 0.038) 

Probability that a susceptible fly becomes infected when feedingon a human host of type 
1  Assumed 

Probability that a susceptible fly becomes infected when feedingon a human host of type 
1  Assumed 

Fraction of asymptomatically infected hosts ( 
0.33%  Estimated, 95% CI (0.22% to 0.49%) 

Fraction of asymptomatically infected hosts ( 
0.01%  

Fraction of asymptomaticallyinfected hosts ( 
99.77%  = 1−( 
1/ 
Sojourn time^{§} in the early asymptomatic stage 
60 days  
1/ 
Sojourn time^{§} in the late asymptomatic stage 
12 days  Estimated, 95%CI (9 to 15) 
1/ 
Duration between diagnosisof KA and onset of treatment  1 day  Conditions in the KalaNet trial 
1/ 
Period^{§} of DATpositivityin state 
74 days  Estimated, 95%CI (65 to 84) 
1/ 
Period^{§} of DATpositivityin state 
74 days  = 1/ 
1/ 
Period^{§} of LSTpositivityin state 
307 days  Estimated, 95% CI (260 to 356) 
Description  Value  Reference  
1/ 
Duration of firstline KAtreatment  30 days 

1/ 
Duration of secondline KA treatment  30 days 

1/ 
Duration of PKDL treatment  180 days 


Fraction of treatment fatality  5%  Personal communication, MB 

Excess mortality rate caused byfirstline KA treatment  0.00167  = 

Excess mortality rate caused by secondline KA treatment  0.00167  = 

Fraction of KA patients not responding to KA firstlinetreatment (conditional onsurviving treatment, 1− 
5% (100% = 


Fraction of KA patients whoappear to recover under KAfirstline treatment but willdevelop PKDL (conditional on surviving treatment, 1− 
3% (100% = 
Personal communication, MB 

Fraction of KA patientsrecovering during KAfirstline treatment (conditionalon surviving treatment, 1− 
92% (100% = 
= 1−( 

Fraction of KA patients whoappear to recover under KAsecondline treatment but will develop PKDL (conditional on surviving treatment, 1− 
3% (100% = 
= 

Fraction of KA patientsrecovering during KAsecondline treatment(conditional on survivingtreatment, 1− 
97% (100% = 
= 1− 
1/ 
Duration until relapse to PKDL  21 months 
The basic SusceptibleInfectedRecovered (SIR) type model was modified with respect to the history of infection, considering five stages in the natural history of infection. These stages were described based on different combinations of three diagnostic markers to categorise people living in endemic areas: PCR (index P, earliest marker for
Humans are born as susceptibles (
After infection, humans enter the early asymptomatic stage
The fraction
Secondline treatment (in state
Excess mortality 1) affects KA patients whose mortality rate increases the baseline mortality rate
We considered sand flies in the susceptible (
We assumed that each blood meal of a susceptible sand fly leads to a sand fly infection if taken from a symptomatically infected human (
The probability that a fly becomes infected when feeding on asymptomatically infected hosts of type
The model was fitted to data from the KalaNet project (KALANET, ClinicalTrials.gov NCT00318721), a community intervention trial in India and Nepal to investigate the effectiveness of insecticidetreated bed nets. The KalaNet trial was conducted between 2006 and 2008. Around 35,000 cases of VL have been reported during this period by the Government of India, Ministry of Health and Family Welfare; thus, the prevalence of VL during the KalaNet trial was lying almost in between the official numbers of 10,000 and 75,000 cases, respectively, after 1970
Interventions in the KalaNet trial did not show an effect on VL incidence and seroconversion; thus, we included data from interventions and control clusters in our analyses. The KalaNet data showed a prevalence of 12% PCRpositive (from 1,923 measurements on 909 individuals in total) and 14% DATpositive individuals (from 43,171 measurements on 17,662 individuals in total). An intersection of 2% was positive for both markers (from 1,899 measurements on 893 individuals in total). Hence, 76% of the population was negative for PCR and DAT. Confidence intervals for these prevalences were not computed, as the large sample size would suggest an unrealistically high precision. No LST data were available in the KalaNet study. The average incidence of symptomatic VL was 0.27% per year, with an estimated prevalence of 0.015% (15 cases per 100,000). Definition for symptomatic infection was adopted from the KalaNet project: People with fever lasting for two weeks or more were examined by a physician and tested with a rapid diagnostic test for VL
The beforementioned proportion of 76% of humans who are negative for PCR and DAT includes 1) humans who either have never been infected (susceptible newborns:
There was no active detection for PKDL cases in the KalaNet trial. The proportion of treatment failures among KA patients under first and secondline treatments who will develop PKDL via a putatively recovered stage (
First and secondline treatment lasts about 1 month for KA patients and about 6 months for PKDL patients. For KA patients surviving treatment, a fraction of treatment failure of 5% is assumed
Model solutions were numerically computed using the software Matlab Version 7.120635 (R2011a) by a RungeKutta algorithm with variable step size (procedure ode15s). Parameters were estimated by fitting the model to observations from the KalaNet project (DAT and PCRpositivity, symptomatic VL and sand fly infection) and information from the literature (LSTpositivity, prevalence of HIV and prevalence of HIVinfected among symptomatic VL).
We used the model to estimate the following eight parameters:
1/
1/
1/
The parameter vector
The likelihood was maximized by minimizing the negative logLikelihood −ln(L), using Matlab procedure fminsearch. Confidence intervals were computed by the profile likelihood
The parameter estimates (
Humans remained on average 1/(
Taken these durations together, humans with an asymptomatic course were infected on average every 596 days ( = 150 days
Given a 0.5% prevalence of infected sand flies
We investigated interventions recommended by the VL elimination program, including treatmentrelated control strategies, such as early case detection or treatment optimisation. We also considered vectorrelated control strategies, such as breeding site control, indoor spraying or use of bed nets, to explore possibilities and constraints in VL control.
We used the model to predict how different treatment regimens and early case detection affect VL prevalence and incidence. Early case detection, e.g., due to improved diagnosis, reduces the period of symptomatic KA before the start of treatment. The existing drugs vary in their treatment durations (from 30 days for antimonials and conventional Amphotericin B to 5 days for Ambisome) and in their recovery rates (from 99% for conventional Amphotericin B to 91% for Ambisome). We used seven model parameters to study the effects of the different treatmentrelated interventions, including the following: duration of firstline, secondline and PKDL treatments (
Sensitivity analyses of equilibrium solutions to the effects of seven intervention parameters (A) on the prevalence of symptomatic (
Scenario  
Parameter  Default 1  2  3  4  5  6  7  8  9  10 
Duration firstline treatment 1/ 




30  30  30  30  30  30 
Duration secondline treatment 1/ 




30  30  30  30  30  30 
Duration PKDL treatment 1/ 




180  180  180  180  180  180 
Early case detection 1/ 


1  1 



1  1  1 
Treatment fatality 


5  5  5  5  5 

5  5 
Treated fraction leading to retention of KA 


5  5  5  5  5  5 

5 
Treated fraction leading to relapse into PKDL 


3  3  3  3  3  3  3 

These results suggest that transmission of KA is predominantly driven by asymptomatically infected hosts who are not eligible for treatment. Treatment can reduce the prevalence of symptomatic disease, but the incidence of KA still remains on comparable levels. For a given treatment efficacy, shorter treatment durations reduced the patients' treatment burden but had little effect on the overall intensity of transmission.
We selected three model parameters to study the effects of breeding site control, indoor spraying and use of bed nets, the effects of which were interpreted in terms of the model as follows. Breeding site control was assumed to reduce the vector population size
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
Scenario  
Parameter  Default 1  2  3  4  5  6  7  8  9  10 
No. of vectors ( 


527  527 

527  527 


527 
Life expectancy of sand flies 1/ 

14 

14  14 

14 

14 

Feeding cycle duration 1/ 

4  4 

4  4 

4 


The equilibrium solutions shown in
We assumed that the feeding cycle duration of the sand fly was doubled by the intervention from 1/
Visceral Leishmaniasis is a neglected, lifethreatening disease affecting the poorest of the poor, as this vectorborne disease is strongly linked to poor housing
The transmission dynamics of
For analysing the process of human recovery, published studies involving the LST were used to estimate the duration of the cellular immune response based on LSTpositivity. Previous studies reported prevalences of positive LST results among recovered KA patients (who are expected to be LSTpositive) ranging from 30% to 80%
Apart from problems with the antigen (see above), there are in principle two possibilities to explain a proportion of only 50% LSTpositive individuals (cf. before: >90% LSTpositive individuals would be expected under the assumption of lifelong LSTpositivity). These two explanations depend on how infection spreads, as follows: 1) If infection is clustered (e.g., withinhousehold transmission predominates due to a low rate of transmission between households) then lifelong LSTpositivity may exist on the level of the individual, and a low, ‘average’ LSTprevalence in the population must result from the demographic process, i.e., it must result from deaths of LSTpositive individuals and the births of individuals who are LSTnegative. 2) If infection is not clustered, but spreads homogeneously within the human population, then a low LSTprevalence in the population must involve loss of the ‘individual’ LSTpositivity (as opposed to option 1 where the ‘average’ LSTpositivity gets lost). As the birth rate is not sufficient to explain a prevalence of 50% LSTpositive individuals (see above), we proceeded with the assumption of loss of LSTpositivity. Under this assumption, humans in active
A considerable loss of LST positivity has been reported from an endemic VL focus in Ethiopia
A short and effective treatment regimen or early case detection can reduce the prevalence of KA but has almost no effect on the incidence of the disease (
The current vectorrelated interventions comprise irregular indoor spraying and exposure prophylaxis, such as untreated bed nets. As summarised by
Whereby treatmentrelated interventions only reduce symptomatic infection, vector control is also efficient against asymptomatic infection (
As found during the KalaNet study, the use of treated bed nets may not provide this efficacy. Indoor density of
Despite the fact that vector control has the potential to effectively reduce
To determine the role of LSTpositive individuals (
The effects of different prevalences of infected sand flies were also analysed, as the prevalence of infected sand flies may vary regionally. The default assumption of
We assumed that the period of DATpositivity is the same for symptomatic and for asymptomatic cases (1/
A full factorial sensitivity analysis is provided in
Our simulation results show that transmission of
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We thank Martin Eichner for helpful discussions while developing this model, and Helmut Pitters for assistance in programming with Matlab.