On the use of mechanistic and data-driven models in population dynamics: the case of tuberculosis in the US over that past two centuries

JUAN P. APARICIO & CARLOS CASTILLO-CHAVEZ

BIOMAT 2010. International Symposium on Mathematical and Computational Biology

WORLD SCIENTIFIC

Año: 2011; p. 73 - 95

Population dynamics theory most often addresses biological questions through its use of simple mechanistic deterministic or stochastic models. In the context of specific applications, however, the use of models tailored to fit the case under study is essential. Most frequently the use of statistical models of the data are the preferred approach regularly bypassing the advantages provided by mechanistic dynamical models parameterized with population-relevant parameters. In this manuscript we show how data may be used to parameterize what is often referred as a hybrid model. That is, a mechanistic data-driven, parameter-scarce, dynamical systems model is fitted to data with time-dependent population-level parameters. The case of the tuberculosis epidemic in United States over long-time scales is used to illustrate this approach. Specifically, a model is built and used to explore the effects of variations in transmission and/or progression on the decline of tuberculosis rates during the twentieth century. This study also makes use of available data generated over two significantly distinct spatial scales: one (global) involving the United States and the second (local) utilizing the tuberculosis data generated by the state of Massachusetts. The assumption that no changes in progression rates from latent to active tuberculosis have taken place leads to conclusion that the maximum rate of variation of tuberculosis transmission must have taken place before any major medical intervention were implemented (including the use of antibiotics). Next, under the assumption of constant transmission rates, it is shown that the maximum rate of variation in tuberculosis progression rates must have occurred around the beginning of the twentieth century, that is, when the maximum variation was recorded for the mortality rates. These results, among others discussed in this manuscript, support the view that improved living conditions must have been the main force driving the tuberculosis decline over the past two centuries in the United Stated