The breakdown of trusted sources of information is probably one of the most serious problems today, since in the absence of a common ground, it will be impossible to address the problems that trouble our contemporary world. The Covid-19 pandemic is just a recent situation where the lack of agreed stances has led to failure and hopelessness. In fact, disinformation surrounding the Covid-19 has been a distinctive feature of this pandemic since its very beginning and has hampered what is perhaps the most important initiative to prevent the spread of the coronavirus, viz., an effective communication between scientifically-minded health authorities and the general public. To investigate how disinformation threatens epistemic security, here we propose and solve analytically a model where the individuals must accurately estimate some property of their hazardous environment. They can either explore the environment or copy the estimate from another individual, who may display a distorted version of its estimate. The parameters of the model are the hazardousness of the environment σ 2 , the copying probability w, which is a proxy for the credulity of the individuals, their degree of deceitfulness γ, and the cost of copying corrupted information η. We focus on the copying strategy that maximizes the survival chances of the individuals and find that the pure strategy w = 0 is optimal for small σ 2 and large γ and η. Since culture requires copying (and hence some degree of credulity), this is a doomsday scenario where culture is lost. However, when the individuals are likely to behave honestly, the other pure strategy w = 1 becomes optimal. Otherwise, the mixed strategy 0 < w < 1 is optimal. We find a rich phase-diagram where these optimal strategies are separated by continuous and discontinuous transition lines that join smoothly at a tricritical point.