Marc Artzrouni

Control strategies for sleeping sickness in Central Africa: a model-based approach

Vector control and the detection (followed by treatment) of infected individuals are the two methods currently available for the control of sleeping sickness. The basic reproduction rate of a compartmental model is used to analyse and compare the two strategies. The efficiency of each strategy will depend on two epidemiologic parameters; the intrinsic contamination rate Q (closely related to the index of new contaminations) that captures the potential spread of the disease, and the intrinsic removal rate from the first stage (intrinsic to the particular trypanosome strain and to the populations susceptibility). The model shows that when the intrinsic removal rate is low (that is, when there is a long first stage characteristic of an endemic situation) the detection of sick individuals is more efficient than vector control. The situation is reversed when the removal rate is high (in an epidemic situation). The conclusions of the analysis are shown to be in general agreement with results obtained in two different sleeping sickness foci of Central Africa.

Persistance et résurgence de la maladie du sommeil à Trypanosoma brucei gambiense dans les foyers historiques. Approche biomathématique d’une énigme épidémiologique

Since the end of the 19th century, historic endemic foci of Trypanosoma brucei gambiense sleeping sickness have proven very persistent. A five-compartment mathematical model with open vector populations was developed in order to study the dynamics of this disease in Central Africa. Of particular interest is the rate at which the disease spreads or goes to extinction at the beginning of an epidemic outbreak. A measure of this rate is the initial halving/doubling time T(o) of the numbers infected; T(o) is a doubling time when the basic reproduction number Ro > 1 and a halving time when Ro < 1. For realistic parameter values, T(o) can be quite large (i.e. several years or even decades) which corresponds to a persistent low-level endemic brought about by an Ro either just above 1 (slow spread) or just below 1 (slow extinction). A resurgence of historical foci can then be caused by a small shift in parameter values that brings Ro well above 1 and decreases T(o). In addition, when Ro is less than 1 (in the absence of vector migrations), simulations show that a very small percentage of infected immigrant flies can bring about high prevalence rates in the human population. The model is validated with field data from historical Congolese, Central and West African foci of the past.

Population dynmaics of sleeping sickness: a microsimulation

A microsimulation model of the spread of Gambian sleeping sickness is described. The model focuses on the randomness of epidemic trajectories brought about merely by the random nature of fly bites on humans. There is a high level of variability in the trajectories, primarily due to the small sizes of the populations involved. There is an inverse relationship between the probability of initial extinction and the size of an epidemic flare-up when the disease takes hold. When a stream of one infected fly enters the focus every 3 days, a low-level endemic can be sustained with less variability. Implications and further subjects of study are briefly discussed.

Estimating tsetse population parameters: application of a mathematical model with density-dependence

Abstract.  A density‐dependent model is used to describe the dynamics of an open population of tsetse flies (Diptera: Glossinidae). Immigration (or emigration) takes place when the total population is below (or above) a biologically determined threshold value. The population is also subjected to birth and death rates, as well as to the risk of being trapped (continuously or intermittently). During trapping the population decreases toward a ‘low’ equilibrium population and when trapping ceases the population starts recovering and increases toward a ‘high’ equilibrium. The model is fitted using data collected on trapped flies in four experiments. The first one was conducted with ‘intermittent trapping’ (i.e. several trapping‐recovery cycles) on Glossina fuscipes fuscipes Newstead in the Central African Republic (Bangui area). In the other experiments, trapping data on Glossina palpalis palpalis (Robineau‐Desvoidy) was collected in ‘aggregate’ form over several days at a time. Two of these were in Congo‐Brazzaville (Bouenza area) and one in the Ivory Coast (Vavoua focus). Estimates are derived for the low and high equilibrium values as well as the trapping rate. The estimated effect of sustained trapping is to reduce the population to low equilibrium values that are 85–87% lower than the levels without trapping. The effects of the natural intrinsic growth and of the migration flows cannot be estimated separately because in the model they are mathematically indistinguishable.