Mathematical modelling of Neglected Tropical Diseases (NTD)

Mathematical modelling of Neglected Tropical Diseases (NTD)


NTD are a group of infectious diseases that have been largely overlooked in terms of public health improvement in recent decades. The NTD Modelling Consortium is about using mathematical frameworks to address questions of relevance to policy makers and program managers.

In SaME, we have been working on two NTD: Leprosy and Visceral Leishmaniasis. Both these diseases rely on early diagnosis of cases and their prompt treatment to prevent onward transmission.


Leprosy is an ancient, iconic disease which epitomises the relationship between disease and stigma – the word “leper” survives where the disease has long gone. Leprosy has greatly reduced over the past three decades, but the annual incidence appears to have plateaued at about 250,000 per year. The epidemiology of leprosy is complicated by a long and variable incubation period: the time between infection and disease is many years, so that the cases we see in 2016 will have been infected (on average) in 2006. Once diagnosed, leprosy is easily treated.

We have been working on a statistical methodology to estimate the number of people who are in the non-clinical incubating phase. This means that we can predict the future numbers of cases, which depends on how much effort is put into finding cases (so that they can be treated and transmission reduced).

This method, back-calculation, was developed initially to model the HIV/AIDS epidemic. Our aim is to develop it so that it takes into account socio-economic and cultural variables as the risk of infection and disease is not spread uniformly. Our aim is to create a tool that can be used by program managers to target case-finding more efficiently.

Visceral Leishmaniasis

VL is a vector-borne infection transmitted by sandflies. SaME’s efforts have been directed at the disease in India, Nepal and Bangladesh. The current definition of clinical disease means that individuals have to have been transmitting for at least 14 days before they are eligible for treatment.

SaME’s involvement has been to develop a simple transmission dynamic framework that highlights the needs for future diagnostics. Our results suggest that diagnostics need to be highly specific (i.e. that people who test positive are highly likely to be true positives), but that sensitivity need not be high (i.e. that some people who are truly positive will test negative, but will be diagnosed later by the current system). Such a diagnostic could have a big influence on reducing the incidence of infection.

As with leprosy, VL is largely confined to the poorest in the affected communities. Why this is the case is largely unexplored and unknown.

Further information: What makes a tropical disease neglected?

Almost all NTD have at least one of a selection of features that make them hard to control:

  • Poor diagnosis
    • Resulting in a large proportion of infections which are clinically indistinct (high asymptomatic prevalence)
    • Poor immunological markers (mirroring the relative ineffectiveness of host immunity)
  • Ineffective vaccination
    • Mirroring the relative ineffectiveness of host immunity
  • Long incubation period and / or low apparent pathogenicity (i.e. chronic disease rather than acute death)
    • Low political profile and interacts with diagnostic problems.
  • Transmitted via ubiquitous behaviour
    • Typically the risk behaviours are essentials (e.g. washing, sleeping, eating)
  • Typically diseases of poor, marginal, populations with low political profile
    • This is circular and self-reinforcing in that these people are compromised by the burden of disease that they bear.

It is only relatively recently (1993) that it was recognised that NTD are likely to play a key role in maintenance of poverty. It is now generally accepted that controlling NTDs will facilitate economic development.

More information

  • Partners & References: Leprosy
    • The modelling work is being supported by the Novartis Foundation via the NTD Modelling Consortium.
    • We are collaborating with Ron Crump and Diana Lockwood.
    • The leprosy work is in development. We have one publication that demonstrates the feasibility of the approach.
  • Partners: VL


  • Graham Medley,

Image: Prediction and reported annual numbers of new leprosy cases, multibacillary cases and cases with grade 2 disability from 2010 to 2014 in Thailand. Posterior probability distributions for predicted values came from running the back-calculation model excluding the observed values for 2010–2014. Reproduced from Back-calculating the incidence of infection of leprosy in a Bayesian framework.

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