Biodiversity, infectious diseases and the dilution effect

Biologists point out that biodiversity loss contributes to promote the transmission of diseases. In epidemiology, this phenomenon is known as dilution effect. Our paper aims to model this effect in an economic model where the spread of an infectious disease is considered. More precisely, we embed a SIS model into a Ramsey model (1928) where a pollution externality coming from production affects the evolution of biodiversity. Biodiversity is assimilated to a renewable resource and affects the infectivity of the disease (dilution effect). A green tax is levied on production at the firm level to finance depollution according to a balanced budget rule. In the long run, a disease-free and an endemic regime are possible. We focus only on the second case and we find that the magnitude of the dilution effect determines the number of steady states. When the dilution effect remains low, there are two steady states with high and low biodiversity respectively. Conversely, when the dilution effect becomes high, the steady state is always unique. Moreover, under a low dilution effect, a higher green-tax rate always impairs biodiversity at the low steady state, while this green paradox is over under a high dilution effect. In the short run, limit cycles can arise in both the cases even if only a low dilution effect can lead to the occurrence of Bogdanov-Takens and generalized Hopf bifurcations.