Twenty years of Leishmaniasis dynamics in northwest Argentina: Time-series analysis and mathematical modeling

MARCELO BALLESTEROS, JOS\'E F. GIL, JUAN CARLOS ROSALES AND JUAN PABLO APARICIO

santiago

Simposio; BIOMAT 2011: International Symposium on Mathematical and Computational Biology; 2011

BIOMAT consortium

Leishmaniasis is a vector-borne disease transmitted by sandflies. Humans are incidental host unable to transmit the disease. Persistence in the wild is due to a cycle involving sandfly transmission to several species of rodents (reservoir hosts). In this work we analyzed and used 20-year data on cases of leishmaniasis and rainfall from San Ramon de la Nueva Oran, in Salta Province, Argentina. Time series of human cases shown a non-stationary trend and correlate with the rainfall series.  Records of human cases were used as a surrogate measure of the disease dynamics in the wild. We developed several individual-based models for the host-vector system assuming random mixing among contacts between spatially local host and vector populations. Using extensive numerical simulations we computed several parameters describing disease dynamics as the Basic Reproductive Number or epidemic size.   Results were used to select simple stochastic and deterministic population models. We show that classical models using incidence rate proportional to the ratio vector to host populations are the most adequate to describe the transmission process. We also show that for populations sizes compatible with the random mixing assumption stochastic effects dominates the dynamics, and therefore, larger population dynamics should be described by metapopulation type models. We feed the model?s parameters using the observed rainfall values. We also considered the observed demographic growth.  Human cases were simulated assuming a constant exposure to the risk area. Model solutions show both qualitative and quantitative agreement with reported cases.