A compartmental model of sleeping sickness in central Africa

We present a five-variable compartmental model for the spread of #Trypanosoma brucei gambiense$, the parasite responsible for the transmission (trough tsetse flies) of sleeping sickness in Central Africa. The model's equilibrium points depend on two "summary parameters" : g(r), the proportion removed among human infectives, and R0, the basic reproduction rate. Stability results are obtained for the origin but not for other equilibrium points. A two-variable simplified version of the model is presented and the stability of all its equilibrium points can be investigated analytically. Both models are applied to the Niari focus of Central Africa and used to test the impact of a vector control strategy. The models' results are in agreement with the extinction of the epidemic that was brought about by a fifty percent decrease in vector density. (Résumé d'auteur

AIDS and HIV Surveillance in Europe

As of June 30, 1988, 14,299 European cases of acquired immunodeficiency syndrome (AIDS) had been reported to the World Health Organization; 81 percent of these cases were diagnosed in France, the Federal Republic of Germany, Italy, the United Kingdom and Spain. There were 7,689 homosexual or bisexual cases (54 percent); 3,218 (23 percent) were intravenous (IV) drug abusers; and 1,043 (7 percent) were heterosexuals who had had sexual intercourse with an infected individual. The epidemic started in the early 1980s among homosexuals and resident of African countries who came to Europe for treatment. AIDS started spreading later, in 1983 and 1984, to the IV drug abusing community in which the epidemic is now spreading faster than in any other group. Short term predictions show that by 1989 there may be 56,400 AIDS cases in the European Community alone. The World Health Organization estimates that there are approximately 480,000 persons in Europe infected with the human immunodeficiency virus (HIV), the causative agent of AIDS. The crucial factor concerning the future of the HIV epidemic remains the extent to which the virus will spread beyond the high-risk groups and into the population at large. It is certain however that given the long incubation period of AIDS and the large number of people who are known to be infected, Europe will live through a protracted epidemic that will last at least another decade or two

Projections of the HIV/AIDS Epidemic for Homosexual/Bisexual Men and Intravenous Drug Users in Five European Countries

Projections of the spread of the acquired immunodeficiency syndrome (AIDS) and of its etiologic agent, the human immunodeficiency virus (HIV), are presented for homosexual/bisexual men and intravenous drug users in the five European countries with the largest caseloads. The results suggest that the HIV epidemic for French, German, and British homosexual/bisexual men has peaked around 1985 and declined rapidly thereafter. By the end of the century, and for a median incubation period m of AIDS equal to 8 years, the total numbers infected in these groups are predicted to be about 31,000, 15,000, and 9,000, respectively. (These estimates more than double if m is taken equal to 12 years). The results suggest that the HIV epidemic among Italian and Spanish intravenous drug users (IVDUs) peaked in 1986 and also decreased rapidly thereafter. For an assumed median incubation period m of 8 years, the total number of infected IVDUs by the end of the century is predicted to be about 22,000 and 16,000 in Italy and Spain, respectively. (Again, these estimates more than double if m is taken equal to 12 years.) The projections suggest that in the late 1980s or early 1990s the annual incidence of AIDS cases among IVDUs in Spain and Italy will overtake the incidences of homosexual/bisexual AIDS cases in the Federal Republic of Germany and the United Kingdom. In all cases the annual incidence of AIDS will reach its maximum in the early to mid 1990s. However, the AIDS epidemic will be protracted because of the long incubation period

Faut-il ou non un contrôle des vecteurs dans la lutte contre la maladie du sommeil? : une approche bio-mathématique du problème

La lutte antivectorielle et le dépistage des malades (suivi de leur traitement) sont les deux principaux moyens de lutte contre la maladie du sommeil. Le taux de reproduction de base (taux R de Kermack et McKendrick) d'un modèle à compartiments est utilisé ici pour analyser et comparer ces deux stratégies. Le modèle montre qu'en situation d'endémicité le dépistage est plus efficace que la lutte antivectorielle. Inversement, dans une sitations épidémique, la lutte antivectorielle est relativement plus efficace que le dépistage. Un autre facteur à prendre en considération dans le choix d'une stratégie de lutte est le taux de repas de sang sur homme. Ce taux, indicateur de l'intensité du contact homme-glossine, intervient en effet au carré dans les équations, ce qui corrobore une réalité de terrain perçue le plus souvent de façon intuitive. Au delà d'une certaine valeur, il justifie le contrôle des vecteurs ou le rend même nécessaire. (Résumé d'auteur

Fourier analysis of 2-point Hermite interpolatory subdivision schemes

Two subdivision schemes with Hermite data on Z are studied. These schemes use 2 or 7 parameters respectively depending on whether Hermite data involve only first derivatives or include second derivatives. For a large region in the parameters space, the schemes are C1 or C2 convergent or at least are convergent on the space of Schwartz distributions. The Fourier transform of any interpolating function can be computed through products of matrices of order 2 or 3. The Fourier transform is related to a specific system of functional equations whose analytic solution is unique except for a multiplicative constant. The main arguments for these results come from Paley-Wiener-Schwartz theorem on the characterization of the Fourier transforms of distributions with compact support and a theorem of Artzrouni about convergent products of matrices

A Multi-Host Agent-Based Model for a Zoonotic, Vector-Borne Disease. A Case Study on Trypanosomiasis in Eastern Province, Zambia

Background: This paper presents a new agent-based model (ABM) for investigating T. b. rhodesiense human African trypanosomiasis (rHAT) disease dynamics, produced to aid a greater understanding of disease transmission, and essential for development of appropriate mitigation strategies. Methods: The ABM was developed to model rHAT incidence at a fine spatial scale along a 75 km transect in the Luangwa Valley, Zambia. The method offers a complementary approach to traditional compartmentalised modelling techniques, permitting incorporation of fine scale demographic data such as ethnicity, age and gender into the simulation. Results: Through identification of possible spatial, demographic and behavioural characteristics which may have differing implications for rHAT risk in the region, the ABM produced output that could not be readily generated by other techniques. On average there were 1.99 (S.E. 0.245) human infections and 1.83 (S.E. 0.183) cattle infections per 6 month period. The model output identified that the approximate incidence rate (per 1000 person-years) was lower amongst cattle owning households (0.079, S.E. 0.017), than those without cattle (0.134, S.E. 0.017). Immigrant tribes (e.g. Bemba I.R. = 0.353, S.E.0.155) and school-age children (e.g. 5–10 year old I.R. = 0.239, S.E. 0.041) were the most at-risk for acquiring infection. These findings have the potential to aid the targeting of future mitigation strategies. Conclusion: ABMs provide an alternative way of thinking about HAT and NTDs more generally, offering a solution to the investigation of local-scale questions, and which generate results that can be easily disseminated to those affected. The ABM can be used as a tool for scenario testing at an appropriate spatial scale to allow the design of logistically feasible mitigation strategies suggested by model output. This is of particular importance where resources are limited and management strategies are often pushed to the local scale. © 2016 Alderton et al

The impact of vector migration on the effectiveness of strategies to control gambiense human African trypanosomiasis

BACKGROUND: Several modeling studies have been undertaken to assess the feasibility of the WHO goal of eliminating gambiense human African trypanosomiasis (g-HAT) by 2030. However, these studies have generally overlooked the effect of vector migration on disease transmission and control. Here, we evaluated the impact of vector migration on the feasibility of interrupting transmission in different g-HAT foci. METHODS: We developed a g-HAT transmission model of a single tsetse population cluster that accounts for migration of tsetse fly into this population. We used a model calibration approach to constrain g-HAT incidence to ranges expected for high, moderate and low transmission settings, respectively. We used the model to evaluate the effectiveness of current intervention measures, including medical intervention through enhanced screening and treatment, and vector control, for interrupting g-HAT transmission in disease foci under each transmission setting. RESULTS: We showed that, in low transmission settings, under enhanced medical intervention alone, at least 70% treatment coverage is needed to interrupt g-HAT transmission within 10 years. In moderate transmission settings, a combination of medical intervention and a vector control measure with a daily tsetse mortality greater than 0.03 is required to achieve interruption of disease transmission within 10 years. In high transmission settings, interruption of disease transmission within 10 years requires a combination of at least 70% medical intervention coverage and at least 0.05 tsetse daily mortality rate from vector control. However, the probability of achieving elimination in high transmission settings decreases with an increased tsetse migration rate. CONCLUSION: Our results suggest that the WHO 2030 goal of G-HAT elimination is, at least in theory, achievable. But the presence of tsetse migration may reduce the probability of interrupting g-HAT transmission in moderate and high transmission foci. Therefore, optimal vector control programs should incorporate monitoring and controlling of vector density in buffer areas around foci of g-HAT control efforts

Chaotic dynamical systems, deceptive computers and new instructional technologies

Chaotic dynamical systems are defined and illustrated with the "doubling function". After less than 60 iterations the orbits become 0. This is due to the binary coding of real numbers in a computer. The simulation dramatically shows that computers may give deceptive (false) results when calculations are done a large number of times. The convergence to 0 does not occur with the "tripling function" but results are equally inaccurate if not visibly so. The presentation illustrates the use of Matlab's "Notebook" in the classroom. Those can be used to present computer simulations "embedded" within a Word 97 document that contains the body of the lecture