Mathematics Projects 2009

Linear and Affine Transformation

Faculty Mentor - Charles Lam

This mathematic experience is specifically designed for high school students and will be based on discrete mathematics. A study of topics in number theory through basic computer programming with the software Maple will be conducted.

Connections between Coccidioidomycosis incidence and climatic fluctuations

Faculty Mentor - Jorge Talamantes

Coccidioidomycosis (valley fever) is a fungal infection found in the southwestern US, northern Mexico, and some places in Central and South America. The fungi which cause it (Coccidioides immitis and Coccidioides posadasii) are normally soil-dwelling but, if disturbed, become air-borne and infect the host when their spores are inhaled. It is thus natural to surmise that weather conditions which foster the growth and dispersal of Coccidioides must have an effect on the rate of infection of humans in the endemic areas. Our work so far1 has attempted to quantify this relationship in Kern County, California (where C. immitis is endemic). We have examined the effect on incidence fluctuations (about a seasonally-varying background) resulting from the following weather parameters: precipitation, surface temperature, and wind speed. We have performed several studies by means of a simple linear correlation analysis, and by a generalized auto regressive moving average model. Our first analysis suggested that linear correlations between climatic parameters and incidence are weak; our second analysis indicated that incidence can be predicted largely by considering only the previous history of incidence in the county - the inclusion of climate- or weather-related time sequences improves the model only to a relatively minor extent. We then performed preliminary analyses in which we compared the response (to weather) of Cociodioides spp. in Kern County to the response in Pima County, Arizona. Our work showed that the fungi behave differently in those two locations.

Our REVS-UP group last summer computed correlations between valley fever incidence in Tulare County, and concentrations of particular matter of size 10 micrometers or less (PM₁₀). (The rationale behind using PM₁₀ concentrations is that Coccidioides spores are roughly 5 micrometers in size - thus, the measured PM₁₀ concentration should have a proportional concentration of fungal spores.) We found that those correlations are not statistically significant. The work we will do this summer entails extending our Tulare County analysis to include precipitation and satellite image-derived soil moisture to see whether these parameters can help in predicting disease outbreaks, either by themselves, or in conjunction with PM₁₀ data. (The rationale for using precipitation and soil moisture data is that moist soil conditions should increase fungal growth, and thus enhance disease transmission.) We will then compare these results with Kern and Pima results to continue our investigation of the universality of Cocciodioides spp. response to changes in environmental conditions.

¹ see, e.g., Talamantes J, S Behseta and CS Zender (2007) Fluctuations in Climate and Incidence of Coccidioidomycosis in Kern County, California: a review, in Annals of the New York Academy of Sciences 1111, 73 (2007), doi: 10.1196/annals.1406.028