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.

A new approach to modelling schistosomiasis transmission based on stratified worm burden.

BACKGROUND/OBJECTIVE: Multiple factors affect schistosomiasis transmission in distributed meta-population systems including age, behaviour, and environment. The traditional approach to modelling macroparasite transmission often exploits the 'mean worm burden' (MWB) formulation for human hosts. However, typical worm distribution in humans is overdispersed, and classic models either ignore this characteristic or make ad hoc assumptions about its pattern (e.g., by assuming a negative binomial distribution). Such oversimplifications can give wrong predictions for the impact of control interventions. METHODS: We propose a new modelling approach to macro-parasite transmission by stratifying human populations according to worm burden, and replacing MWB dynamics with that of 'population strata'. We developed proper calibration procedures for such multi-component systems, based on typical epidemiological and demographic field data, and implemented them using Wolfram Mathematica. RESULTS: Model programming and calibration proved to be straightforward. Our calibrated system provided good agreement with the individual level field data from the Msambweni region of eastern Kenya. CONCLUSION: The Stratified Worm Burden (SWB) approach offers many advantages, in that it accounts naturally for overdispersion and accommodates other important factors and measures of human infection and demographics. Future work will apply this model and methodology to evaluate innovative control intervention strategies, including expanded drug treatment programmes proposed by the World Health Organization and its partners.

Dynamic regulation of single- and mixed-species malaria infection: insights to specific and non-specific mechanisms of control.

Our increasing appreciation of the high prevalence of mixed-species Plasmodium infection in malaria-endemic regions has resulted in controversy regarding the likely mechanism(s) of regulation for mixed parasite burden within an individual human host. In the present study, we examined dynamic models of Plasmodium spp. regulation by fever and by non-specific (NS) and species-specific (SS) immunity (including the influence of their variable time-delays, duration, and efficacy) in order to assess the likely role of these factors in regulating detectable parasitemia and clinical disease. Our models suggest that in order to observe the irregular waves of fever and parasitemia that are often found in multiply infected subjects, there must be a differential SS immune effect (beyond the regulatory effects of the species-transcendent density-dependent factors previously posited to control mixed-species parasitemia), and time-dependent variation in immunity to the dominant species. By implementation of individual SS immune controls of non-permanent duration, the resulting multi-dimensional model can be viewed as multiple single-species oscillators coupled via a NS species-transcendent controller. This extended model exhibits the essential patterns of long-term mixed infections. Although this 'circuit-immunity' model gives only a qualitative estimate of the complex web of participating agents and reaction pathways, it provides a starting point for future studies of the specific and NS within-host mechanisms that regulate mixed-species malaria infection.

Heterogeneous model of schistosomiasis transmission and long-term control: the combined influence of spatial variation and age-dependent factors on optimal allocation of drug therapy.

Prior field studies and modelling analyses have individually highlighted the importance of age-specific and spatial heterogeneities on the risk for schistosomiasis in human populations. As long-term, large-scale drug treatment programs for schistosomiasis are initiated in subSaharan Africa and elsewhere, optimal strategies for timing and distribution of therapy have yet to be fully defined on the working, district-level scale, where strong heterogeneities are often observed among sublocations. Based on transmission estimates from recent field studies, we develop an extended model of heterogeneous schistosome transmission for distributed human and snail population clusters and age-dependent behaviour, based on a 'mean worm burden + snail infection prevalence' formulation. We analyse its equilibria and basic reproduction patterns and their dependence on the underlying transmission parameters. Our model allows the exploration of chemotherapy-based control strategies targeted at high-risk behavioural groups and localities, and the approach to an optimal design in terms of cost. Efficacy of the approach is demonstrated for a model environment having linked, but spatially-distributed, populations and transmission sites.

Forced two-dimensional turbulence in spectral and physical space.

Two-dimensional (2D) turbulence in the energy range exhibits nonuniversal features, manifested in the departure (at low k) from the k(-5/3) energy spectrum law, variable energy flux, and irregular, nonlocal transfers. To unravel the underlying mechanism we conducted a detailed study of the 2D turbulence in spectral and physical space. It revealed complex multiscale organization of vorticity field and dynamic processes, ranging from large-scale meandering jets to strong localized vortices. The latter bear prime responsibility for the nonuniversal behavior of 2D turbulence, and we examined their statistical features and the growth mechanism. Our results are based on the numeric simulation of 2D turbulence on the 512 grid under different forcing-dissipation conditions.

Nonuniversal features of forced two-dimensional turbulence in the energy range.

We examine energy spectra, fluxes, and transfers of two-dimensional forced incompressible turbulence with linear drag in the energy range, and find marked departures from 5/3 law and the idea of locality. Any attempt to bring the system into the "ideal cascade state" would result either in spectral (bulge) or flux distortion. We corroborate this observation by DNS (spectral code) and eddy-damped quasinormal Markovian simulations. We examine the energy peak wave number k(p), in terms of drag coefficient lambda, and energy dissipation rate epsilon, and find a relation k(p) approximately C(lambda(3)/epsilon)(1/2) to hold with C approximately 50, but only within a limited range of parameters.