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 introduce 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 cases depending on the environmental impact of production: (1) a low impact implies two steady states with high and low biodiversity respectively; (2) a large impact rules out any steady state. Conversely, when the dilution effect becomes high, a (unique) steady state always exists: a strong dilution effect works as a buffer and prevents the human pressure from being lethal for biodiversity in the long run. 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, we show that a limit cycle can arise around the high biodiversity steady state when the dilution effect is low. Surprisingly, the limit cycle is preserved under a high dilution effect. In other words, even if a strong dilution effect preserves the biodiversity in the long run and prevents the economy from the green paradox, it does not shelter the economy from the occurrence of biodiversity fluctuations.

生物学家指出，生物多样性的丧失有助于促进疾病的传播。在流行病学中，这种现象称为稀释效应。我们的论文旨在将这种效应引入考虑了传染病传播的经济模型中。更准确地说，我们将SIS模型嵌入到Ramsey模型（1928年）中，其中来自生产的污染外部性影响生物多样性的演变。生物多样性被吸收为可再生资源，并影响疾病的传染性（稀释作用）。根据平衡的预算规则，对企业的生产征收绿色税以资助污染。从长远来看，无病和地方病是可能的。我们仅关注第二种情况，我们发现稀释效应的大小决定了稳态数。当稀释效应仍然很低时，有两种情况取决于生产的环境影响：（1）低影响意味着分别具有高生物多样性和低生物多样性的两个稳态；（2）较大的影响会排除任何稳态。相反，当稀释效果变高时，始终存在（唯一）稳态：强烈的稀释作用起到缓冲作用，从长远来看，可防止人为生物多样性造成致命压力。此外，在低稀释效应下，较高的绿色税率总是在低稳态下损害生物多样性，而在高稀释效应下这种绿色悖论就结束了。在短期内，我们表明，当稀释效应较低时，在高生物多样性稳定状态附近可能会出现极限循环。出人意料的是，极限循环在高稀释效果下得以保留。换句话说，即使长期以来强烈的稀释效应可以保护生物多样性并防止经济脱离绿色悖论，也无法使经济免受生物多样性波动的影响。