Chapter Two - Mathematical Modelling of Leprosy and Its Control
Introduction
Leprosy or Hansen's disease is an infectious disease caused by the bacterium Mycobacterium leprae. Most people are able to clear the bacterium before disease occurs, or are resistant against infection (Fine, 1982). For those developing disease, leprosy affects the skin, the peripheral nerves, the mucosa of the upper respiratory tract and the eyes. The different clinical signs of leprosy depend on the response of the immune system of the patient. When the cellular immune response is strong enough to keep the infection localized, the tuberculoid form will develop. If the cellular response is insufficient or not present, the bacterium can spread systemically and cause lepromatous leprosy. Lepromatous leprosy has many more bacilli in lesions than the tuberculoid form. For treatment purposes, cases are classified into paucibacillary (PB) and multibacillary (MB) leprosy, based on the extent of the disease in terms of bacterial load and number of skin patches (WHO, 1998).
The infection can cause nerve function impairments, leading to secondary complications, such as infection of untreated wounds and ulcers on palms and soles. Nerve function impairment can develop gradually, or during periods of inflammation, called reactions. Chronic disability and social stigma cause substantial suffering to those affected by leprosy. The median incubation time is 3.5 years for PB leprosy and 10.0 years for MB leprosy (Fine, 1982, Meima et al., 2004). The fact that very young children are found with symptomatic leprosy, and that some veterans develop leprosy over 20 years after returning from endemic areas (Noordeen, 1985) shows the wide variation in the incubation period.
Although M. leprae can remain viable for some time outside the human body (Desikan, 1977), it is commonly accepted that the main route of infection is through direct transmission from an infectious to a susceptible person. Patients can shed many bacilli through their nose, and nasal carriage of healthy persons indicates that direct respiratory transmission through aerosols is the most likely route of transmission (Hatta et al., 1995), although skin-to-skin transmission is also considered to be possible (Noordeen, 1985). Both routes require close and direct contact. Due to their higher number of bacilli and poorer immune response, patients with MB leprosy are thought to be the only infectious individuals, or at least the most infectious individuals (Fine, 1982). The detection of leprosy is based on clinical signs: skin lesions, loss of sensitivity of skin lesions and thickened nerves, thus established after physical examination. The basis for leprosy control is treatment with multidrug therapy (MDT), a combination of two or three antibiotics, including rifampicin, according to the type of leprosy, PB or MB (WHO, 1994).
In 1991, the 44th World Health Assembly adopted the objective of eliminating leprosy globally as a public health problem by the year 2000 (WHO, 1991). Leprosy elimination was thereby defined as reducing the prevalence rate to less than 1 case per 10,000 population. Although this was achieved at the global level by the end of 2000, in many countries a sizable leprosy problem still persists. The current leprosy control strategy is formulated by the World Health Organization (WHO) as the ‘Enhanced global strategy for further reducing the disease burden due to leprosy 2011–2015’ (WHO, 2009). The strategy aims to reduce the global rate of new cases with grade-2 (i.e. visible) disabilities per 100,000 population by at least 35% by the end of 2015, compared with the baseline at the end of 2010. The approach underlines the importance of early detection and quality of care in an integrated service setting. The WHO expects this strategy to reduce the transmission of the disease in the community and thus lower the occurrence of new cases. Recently, WHO has formulated ‘roadmap targets’ to overcome the global impact of 17 neglected tropical diseases, including leprosy. These targets are set for the period 2015–2020 and for leprosy are defined as (1) global interruption of transmission by 2020 and (2) reduction of grade-2 disabilities in newly detected cases to below 1/million population at global level by 2020 (WHO, 2012).
Section snippets
The Current Epidemiological Situation and Challenges
In the year 2012 a total of 232,857 new leprosy cases were registered in the world and less than 20 countries reported >1,000 new cases, indicating that leprosy is gradually becoming limited to a few countries (WHO, 2013). Three endemic countries (India, Brazil and Indonesia) account for nearly 80% of all new cases in the world. This global annual number of newly detected leprosy cases has been fairly stable over the past 7 years, indicating that transmission of M. leprae is ongoing (Figure 1).
Heterogeneity in Leprosy
Heterogeneity is due to differences between individuals in exposure to infection with M. leprae and in developing leprosy after exposure. Relevant forms of heterogeneity in the population are contact heterogeneity, heterogeneity in susceptibility and spatial heterogeneity. These forms of heterogeneity are not mutually exclusive.
Infection with a directly-transmitted bacterial infection, such as M. leprae, needs contact between an infectious host and a susceptible host. By heterogeneity in the
Leprosy Models
Three mathematical models for leprosy transmission and control have been described. Two of the three models are compartmental models (Lechat et al., 1985, Meima et al., 1999) and one is a microsimulation or individual-based model (Fischer et al., 2010). Another model in the literature combines a simple leprosy model with a tuberculosis model (Lietman et al., 1997). The purpose of the latter model was to explore whether immunity acquired from tuberculosis infection could have contributed to the
Future Challenges
Many uncertainties remain with respect to leprosy. A variety of host immunogenic factors influences both an individual's susceptibility to infection with M. leprae and the pathologic course of the disease; research in this area is ongoing (Adams et al., 2012, Alter et al., 2011). In particular, questions remain regarding mechanisms of natural immunity and susceptibility to the MB and PB forms of leprosy, which show marked variation in distribution in different parts of the world. SIMCOLEP has
Conclusion
Although three different mathematical models have been developed for leprosy, mathematical models in leprosy have not been applied extensively. This is in part due to the limited size of the leprosy problem in terms of numbers and health burden compared to many other infectious diseases such as HIV/AIDS, tuberculosis and malaria. Even within the group of neglected tropical diseases, the contribution of leprosy is modest. Few scientists have taken lasting interest in leprosy and funding for
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