Optimal strategies for controlling riverine tsetse flies using targets: a modelling study.

BACKGROUND: Tsetse flies occur in much of sub-Saharan Africa where they transmit the trypanosomes that cause the diseases of sleeping sickness in humans and nagana in livestock. One of the most economical and effective methods of tsetse control is the use of insecticide-treated screens, called targets, that simulate hosts. Targets have been ~1 m2, but recently it was shown that those tsetse that occupy riverine situations, and which are the main vectors of sleeping sickness, respond well to targets only ~0.06 m2. The cheapness of these tiny targets suggests the need to reconsider what intensity and duration of target deployments comprise the most cost-effective strategy in various riverine habitats. METHODOLOGY/PRINCIPAL FINDINGS: A deterministic model, written in Excel spreadsheets and managed by Visual Basic for Applications, simulated the births, deaths and movement of tsetse confined to a strip of riverine vegetation composed of segments of habitat in which the tsetse population was either self-sustaining, or not sustainable unless supplemented by immigrants. Results suggested that in many situations the use of tiny targets at high density for just a few months per year would be the most cost-effective strategy for rapidly reducing tsetse densities by the ~90% expected to have a great impact on the incidence of sleeping sickness. Local elimination of tsetse becomes feasible when targets are deployed in isolated situations, or where the only invasion occurs from populations that are not self-sustaining. CONCLUSION/SIGNIFICANCE: Seasonal use of tiny targets deserves field trials. The ability to recognise habitat that contains tsetse populations which are not self-sustaining could improve the planning of all methods of tsetse control, against any species, in riverine, savannah or forest situations. Criteria to assist such recognition are suggested.

Tuberculosis reinfection rate as a proportion of total infection rate correlates with the logarithm of the incidence rate: a mathematical model.

In a significant number of instances, an episode of tuberculosis can be attributed to a reinfection event. Because reinfection is more likely in high incidence regions than in regions of low incidence, more tuberculosis (TB) cases due to reinfection could be expected in high-incidence regions than in low-incidence regions. Empirical data from regions with various incidence rates appear to confirm the conjecture that, in fact, the incidence rate due to reinfection only, as a proportion of all cases, correlates with the logarithm of the incidence rate, rather than with the incidence rate itself. A theoretical model that supports this conjecture is presented. A Markov model was used to obtain a relationship between incidence and reinfection rates. It was assumed in this model that the rate of reinfection is a multiple, rho (the reinfection factor), of the rate of first-time infection, lambda. The results obtained show a relationship between the proportion of cases due to reinfection and the rate of incidence that is approximately logarithmic for a range of values of the incidence rate typical of those observed in communities across the globe. A value of rho is determined such that the relationship between the proportion of cases due to reinfection and the logarithm of the incidence rate closely correlates with empirical data. From a purely theoretical investigation, it is shown that a simple relationship can be expected between the logarithm of the incidence rates and the proportions of cases due to reinfection after a prior episode of TB. This relationship is sustained by a rate of reinfection that is higher than the rate of first-time infection and this latter consideration underscores the great importance of monitoring recovered TB cases for repeat disease episodes, especially in regions where TB incidence is high. Awareness of this may assist in attempts to control the epidemic.