Modeling Microbial Dynamics: Effects on Environmental and Human Health

Abstract: This thesis focuses on formulating and analyzing non linear models for microbial dynamics vis-a-vis human and environmental health. Firstly, we develop and investigate a stoichiometric organic matter decomposition model in a chemostat culture that incorporates the dynamics of grazers. This mechanistic biodegradation model lead to reliable and suggestive ecological insights in the preservation and restoration of our fragile ecosystems. Questions we attempt to answer include: (i) What mechanisms allow microbes and resources to persist uniformly or go extinct? (ii) How do grazing and dead microbial residues affect decomposition? (iii) How can the rate of decomposition be maximized or minimized? Secondly, we designed a greenhouse gas biogenesis model, which may be used to (i) predict the volume of greenhouse gasses emitted at any given time in an oil sands tailing pond and an end pit lake, (ii) calculate the time required to produce a given volume of cumulative greenhouse gases from them and (iii) estimate how long it will take for an oil sands tailing pond and an end pit lake to stop emitting greenhouse gases. Lastly, we formulate and analyze directly and indirectly transmitted infectious disease models. The questions aim to answer include: (i) Why are there irregularities in seasonal patterns of outbreaks amongst different countries? (ii) How can we estimate the transmission function of an infectious disease from a given incidence or prevalence data set? (iii) What is the estimated value of the basic reproduction number in affected regions? (iv) How can we control the period and intensity of pathogenic disease outbreaks?