Infectious disease and economic growth: the case of tuberculosis

We consider the links between the health structure of the population and The productive system of an economy which is subject to infectious disease, in particular tuberculosis. Reviewing the models of tuberculosis suggests that a Lotka-Volterra system can capture the dynamics of epidemics. We combine this with a Solow-Swan growth model: output is produced from capital and healthy labour; the demographic parameters of the Lotka-Volterra system are functions of the capital labour ratio. We find three stationary states, two of which are extensions of population equilibria and the third of which has a positive capital labour ratio. there is also a partial balanced growth path in which there is no disease and the healthy population and capital stock grow at a common rate. We find conditions for stability of this path. We analyse the local dynamics and, in the context of global analysis of two examples, find that the economic-epidemiological stationary state is locally stable and an attractor for a wide range of initial conditions. The way in which the net birth rate of susceptibles responds to prosperity determines the level of the stationary state prevalence of the disease. The interaction between the disease and the economy can also decrease the amplitude of epidemic cycles.