Mathematical models are increasingly relied upon as decision-support tools, which estimate risks and generate recommendations to underpin public health policies. However, there are no formal agreements about what constitutes professional competencies or duties in mathematical modelling for public health. In this paper, we propose a framework to evaluate whether mathematical models that assess human and animal disease risks and control strategies meet standards consistent with ethical 'good practice' and are thus 'fit-for-purpose' as evidence in support of policy. This framework is derived from principles of biomedical ethics: independence, transparency (autonomy), beneficence/non-maleficence and justice. We identify ethical risks associated with model development and implementation and consider the extent to which scientists are accountable for the translation and communication of model results to policymakers so that the strengths and weaknesses of the scientific evidence-base and any socio-economic and ethical impacts of biased or uncertain predictions are clearly understood. We propose principles to operationalize a framework for ethically sound model development and risk communication between scientists and policymakers. These include the creation of science-policy partnerships to mutually define policy questions and communicate results; development of harmonised international standards for model development and data stewardship and improvement of the traceability and transparency of models via a searchable archive of policy-relevant models. Finally, we suggest that bespoke ethical advisory groups, with relevant expertise and access to these resources, would be beneficial as a bridge between science and policy, advising modellers of potential ethical risks and providing overview of the translation of modelling advice into policy.