Mathematical models and the fight against diseases in Africa

n this age of molecular biology, The healthcare industry, politicians and the community at large are trying to find ‘magic bullet’ drugs and vaccines to conquer disease. Although smallpox has been eradicated and polio may soon be a scourge of the past, many pathogens replicate rapidly and mutate prodigiously, enabling them to evolve ways to circumvent our immune systems, as well as our drugs and vaccines. To fight and win the war against new emerging infections such as HIV/AIDS, TB and now SARS (severe acute respiratory syndrome), it is important to understand the temporal and spatial dynamics of the pathogens in human and, in some cases, animal reservoirs or vector populations. It is also necessary to understand the complex web of socio-economic factors pertinent to controlling the spread of disease, so that feasible, affordable and, most importantly, effective public-health policies can be devised and implemented

Martingale representation and hedging policies

The integrand, when a martingale under an equivalent measure is represented as a stochastic integral, is determined by elementary methods in the Markov situation. Applications to hedging portfolios in finance are described.martingale representation Girsanov's theorem stochastic flow diffusion hedging portfolio

Time variability and heterogeneity in the coma of 67P/Churyumov-Gerasimenko

International audienceComets contain the best-preserved material from the very beginning of our planetary system. Their nuclei and comae composition reveal clues about physical and chemical conditions during the early Solar system when comets formed. ROSINA/DFMS (Rosetta Orbiter Spectrometer for Ion and Neutral Analysis / Double Focusing Mass Spectrometer) onboard the Rosetta spacecraft has measured the coma composition of comet 67P/Churyumov-Gerasimenko (67P) with excellent time resolution and compositional detail. Measurements were made over many comet rotation periods and a wide range of latitudes. These measurements show large fluctuations in composition in a heterogeneous coma that has diurnal and possibly seasonal variations in the major outgassing species: H2O, CO, and CO2. These results indicate a complex coma-nucleus relationship where seasonal variations may be driven by temperature differences near the comet surface