A comparison of two mathematical models of the impact of mass drug administration on the transmission and control of schistosomiasis.

The predictions of two mathematical models describing the transmission dynamics of schistosome infection and the impact of mass drug administration are compared. The models differ in their description of the dynamics of the parasites within the host population and in their representation of the stages of the parasite lifecycle outside of the host. Key parameters are estimated from data collected in northern Mozambique from 2011 to 2015. This type of data set is valuable for model validation as treatment prior to the study was minimal. Predictions from both models are compared with each other and with epidemiological observations. Both models have difficulty matching both the intensity and prevalence of disease in the datasets and are only partially successful at predicting the impact of treatment. The models also differ from each other in their predictions, both quantitatively and qualitatively, of the long-term impact of 10 years' school-based mass drug administration. We trace the dynamical differences back to basic assumptions about worm aggregation, force of infection and the dynamics of the parasite in the snail population in the two models and suggest data which could discriminate between them. We also discuss limitations with the datasets used and ways in which data collection could be improved.

Soil-Transmitted Helminths: Mathematical Models of Transmission, the Impact of Mass Drug Administration and Transmission Elimination Criteria.

Infections caused by soil-transmitted helminthias (STHs) affect over a billion people worldwide, causing anaemia and having a large social and economic impact through poor educational outcomes. They are identified in the World Health Organization (WHO) 2020 goals for neglected tropical diseases as a target for renewed effort to ameliorate their global public health burden through mass drug administration (MDA) and water and hygiene improvement. In this chapter, we review the underlying biology and epidemiology of the three causative intestinal nematode species that are mostly considered under the STH umbrella term. We review efforts to model the transmission cycle of these helminths in populations and the effects of preventative chemotherapy on their control and elimination. Recent modelling shows that the different epidemiological characteristics of the parasitic nematode species that make up the STH group can lead to quite distinct responses to any given form of MDA. When connected with models of treatment cost-effectiveness, these models are potentially a powerful tool for informing public policy. A number of shortcomings are identified; lack of critical types of data and poor understanding of diagnostic sensitivities hamper efforts to test and hence improve models.

Studies of the Transmission Dynamics, Mathematical Model Development and the Control of Schistosome Parasites by Mass Drug Administration in Human Communities.

Schistosomiasis is global in extent within developing countries, but more than 90% of the at-risk population lives in sub-Saharan Africa. In total, 261 million people are estimated to require preventive treatment. However, with increasing drug availability through donation, the World Health Organization has set a goal of increasing coverage to 75% of at-risk children in endemic countries and elimination in some regions. In this chapter, we discuss key biological and epidemiological processes involved in the schistosome transmission cycle and review the history of modelling schistosomiasis and the impact of mass drug administration, including both deterministic and stochastic approaches. In particular, we look at the potential impact of the WHO 2020 schistosomiasis treatment goals.

What is required in terms of mass drug administration to interrupt the transmission of schistosome parasites in regions of endemic infection?

BACKGROUND: Schistosomiasis is endemic in 54 countries, but has one of the lowest coverages by mass drug administration of all helminth diseases. However, with increasing drug availability through donation, the World Health Organisation has set a goal of increasing coverage to 75 % of at-risk children in endemic countries and elimination in some regions. In this paper, we assess the impact on schistosomiasis of the WHO goals in terms of control and elimination. METHODS: We use an age-structured deterministic model of schistosome transmission in a human community and the effect of mass drug administration. The model is fitted to baseline data from a longitudinal re-infection study in Kenya and validated against the subsequent re-infection data. We examine the impact on host worm burden of the current treatment trend, extrapolated to meet the WHO goals, and its sensitivity to uncertainty in important parameters. We assess the feasibility of achieving elimination. RESULTS: Model results show that the current treatment trend, extrapolated to the WHO goals, is able to greatly reduce host worm burdens. If coverage is continued at the same level beyond 2020, elimination is possible for low to moderate transmission settings, where transmission intensity is defined by the basic reproduction number, R0. Low levels of adult coverage have a significant impact on worm burden in all settings. Model validation against the re-infection survey demonstrates that the age-structured model is able to match post-treatment data well in terms of egg output, but that some details of re-infection among school children and young adults are not currently well represented. CONCLUSIONS: Our work suggests that the current WHO treatment goals should be successful in bringing about a major reduction in schistosome infection in treated communities. If continued over a 15 year period, they are likely to result in elimination, at least in areas with lower transmission.

What impact will the achievement of the current World Health Organisation targets for anthelmintic treatment coverage in children have on the intensity of soil transmitted helminth infections?

BACKGROUND: It is the aim of the World Health Organisation to eliminate soil-transmitted helminths (STH) as a health problem in children. To this end, the goal is to increase anthelmintic treatment coverage for soil transmitted helminths to reach 75 % in pre-school aged and school aged children by 2020 in endemic countries. In this paper, we use mathematical models to investigate the impact of achieving this goal on the burdens of Ascaris lumbricoides, Trichuris trichuria and hookworm. METHODS: We employ a deterministic fully age-structured model of STH transmission and mass drug administration to examine the changes in worm burden in response to the known and projected coverage trends in children up to 2020 and beyond. Parameters are estimated from worm expulsion data and age intensity profiles before treatment using maximum likelihood methods. Model validation is performed using reinfection studies for Ascaris and analyses are conducted to assess the sensitivity of the predicted outcomes to variation in parameter estimates including transmission intensity (R0), children's contributions to the pool of infective stages and drug coverage levels. RESULTS: The impact of the required increase in coverage trends are quite different across the three species. Ascaris burdens are reduced dramatically by 2020 with elimination predicted within studied the setting a further 10 years. For Trichuris and hookworm, however, impact is more limited, due to issues of drug efficacy (Trichuris) and distribution of worms in the population (hookworm). Sensitivity analysis indicates that results are largely robust. However, validation against Ascaris data indicates that assumptions concerning re-infection among children may have to be revised. CONCLUSIONS: The 2020 coverage target is predicted to have a major impact on Ascaris levels by 2020. However, there is evidence from model validation that Ascaris in children is more resilient to treatment than currently assumed in the model. Broader coverage across all age classes is required to break transmission for hookworm and alternative dual drug treatment approaches are needed for Trichuris.

Transmission dynamics and mechanisms of endemicity of scrapie in the UK sheep population.

SUMMARYScrapie is a fatal neurological disease of sheep which is endemic in the United Kingdom. It is one of the family of transmissible spongiform encephalopathies (TSEs) that includes BSE. In this paper, we developed a micro-simulation model for scrapie in the UK sheep population, incorporating the genetic and structural diversity of the population and infectious contact between flocks through trading. The simulation was fitted to epidemiological data from a range of sources. We found a detection/reporting probability of 16% (95% CI 12-17) for animals dying of scrapie. Prevalence of infected animals in the population was about 0.15%. Infected individuals were found in 9% of flocks overall, rising to 60% in Shetland and 75% in Swaledale flocks. Mean values of R0 for flocks varied with breed from 2.43 (Shetland) to 0.21 (Suffolk). We also examined the possible long-term persistence of scrapie in the UK flock in the absence of any intervention.

Control of scrapie in the UK sheep population.

Scrapie is a fatal transmissible spongiform encephalopathy (TSE) of sheep, endemic in the UK for centuries. Interest in the disease has been heightened over the last decade by the possibility of the related BSE being transmissible to and between sheep and a range of control interventions has been proposed and implemented. In this paper, we examined the effect of these policies and their components on observed case rate, susceptible allele frequency and R0 within the framework of a large simulation model of the British sheep population and its breeding and trading structure. We compared interventions with the natural fade-out of scrapie in the population through loss of susceptible genotypes in the absence of control. We compare the results of interventions with the natural course of the scrapie epidemic. Our model suggested that scrapie will persist in the national flock for 300-400 years with the impact on gene frequencies confined largely to high case-rate breeds, such as Shetland and Swaledale. We found the National Scrapie Plan (NSP) to be the most effective in terms of the removal of both susceptible genotypes and scrapie from the population. Complete eradication of scrapie can be achieved within 32 years (95% CI 23-43 years). The Compulsory Scrapie Flock Scheme (CSFS) is as effective as the NSP in reducing the observed case rate but has a limited impact on the frequencies of susceptible genotypes in the population overall. In combination with the NSP, eradication of scrapie is achieved >10 years faster. Of the components of the CSFS, the breeding and culling aspects are each almost as effective as the full policy, with trading restrictions contributing little. We have speculated on the impact of control measures on the possibility BSE infection within the national flock by examining their effect on flock R0 for BSE across different breeds.

Response of a deterministic epidemiological system to a stochastically varying environment.

Fluctuations in the natural environment introduce variability into the biological systems that exist within them. In this paper, we develop a model for the influence of random fluctuations in the environment on a simple epidemiological system. The model describes the infection of a dynamic host population by an environmentally sensitive pathogen and is based on the infection of sugar beet plants by the endoparasitic slime-mold vector Polymyxa betae. The infection process is switched on only when the temperature is above a critical value. We discuss some of the problems inherent in modeling such a system and analyze the resulting model by using asymptotic techniques to generate closed-form solutions for the mean and variance of the net amount of new inoculum produced within a season. In this way, the variance of temperature profile can be linked with that of the inoculum produced in a season and hence the risk of disease. We also examine the connection between the model developed in this paper and discrete Markov-chain models for weather.

The effect of cultivation on the size, shape, and persistence of disease patches in fields.

Epidemics of soil-borne plant disease are characterized by patchiness because of restricted dispersal of inoculum. The density of inoculum within disease patches depends on a sequence comprising local amplification during the parasitic phase followed by dispersal of inoculum by cultivation during the intercrop period. The mechanisms that control size, shape, and persistence have received very little rigorous attention in epidemiological theory. Here we derive a model for dispersal of inoculum in soil by cultivation that takes account into the discrete stochastic nature of the system in time and space. Two parameters, probability of movement and mean dispersal distance, characterize lateral dispersal of inoculum by cultivation. The dispersal parameters are used in combination with the characteristic area and dimensions of host plants to identify criteria that control the shape and size of disease patches. We derive a critical value for the probability of movement for the formation of cross-shaped patches and show that this is independent of the amount of inoculum. We examine the interaction between local amplification of inoculum by parasitic activity and subsequent dilution by dispersal and identify criteria whereby asymptomatic patches may persist as inoculum falls below a threshold necessary for symptoms to appear in the subsequent crop. The model is motivated by the spread of rhizomania, an economically important soil-borne disease of sugar beet. However, the results have broad applicability to a very wide range of diseases that survive as discrete units of inoculum. The application of the model to patch dynamics of weed seeds and local introductions of genetically modified seeds is also discussed.

Quantitative analysis and model simplification of an epidemic model with primary and secondary infection.

Models of particular epidemiological systems can rapidly become complicated by biological detail which can obscure their essential features and behaviour. In general, we wish to retain only those components and processes that contribute to the dynamics of the system. In this paper, we apply asymptotic techniques to an SEI-type model with primary and secondary infection in order to reduce it to a much simpler form. This allows the identification of parameter groupings discriminating between regions of contrasting dynamics and leads to simple approximations for the model's transient behaviour. These can be used to follow the evolution of the developing infection process. The techniques examined in this paper will be applicable to a large number of similar models.