This paper presents a first model integrating the relation between biodiversity loss and zoonotic pandemic risks in a general equilibrium dynamic economic set-up. The occurrence of pandemics is modeled as Poissonian leaps in economic variables. The planner can intervene in the economic and epidemiological dynamics in two ways: first (prevention), by deciding to conserve a greater quantity of biodiversity to decrease the probability of a pandemic occurring, and second (mitigation), by reducing the death toll through a lockdown policy, with the collateral effect of affecting negatively labor productivity. The policy is evaluated using a social welfare function embodying society's risk aversion, aversion to fluctuations, degree of impatience and altruism towards future generations. The model is explicitly solved and the optimal policy described. The dependence of the optimal policy on natural, productivity and preference parameters is discussed. In particular the optimal lockdown is more severe in societies valuing more human life, and the optimal biodiversity conservation is larger for more ``forward looking'' societies, with a small discount rate and a high degree of altruism towards future generations. Moreover, societies accepting a large welfare loss to mitigate the pandemics are also societies doing a lot of prevention. After calibrating the model with COVID-19 pandemic data we compare the mitigation efforts predicted by the model with those of the recent literature and we study the optimal prevention- mitigation policy mix.