Scientific publication is immensely important to the scientific endeavour. There is, however, concern that rewarding scientists chiefly on publication creates a perverse incentive, allowing careless and fraudulent conduct to thrive, compounded by the predisposition of top-tier journals towards novel, positive findings rather than investigations confirming null hypothesis. This potentially compounds a reproducibility crisis in several fields, and risks undermining science and public trust in scientific findings. To date, there has been comparatively little modelling on factors that influence science trustworthiness, despite (...) the importance of quantifying the problem. We present a simple phenomenological model with cohorts of diligent, careless and unethical scientists, with funding allocated by published outputs. This analysis suggests that trustworthiness of published science in a given field is influenced by false positive rate, and pressures for positive results. We find decreasing available funding has negative consequences for resulting trustworthiness, and examine strategies to combat propagation of irreproducible science. (shrink)