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The Philadelphia chromosome-negative myeloproliferative neoplasms (MPNs) are a group of haematological malignancies triggered by a driver mutation, most commonly the JAK2 V617F mutation, which is acquired in a haematopoietic stem cell. The diseases are characterised by an overproduction of myeloid cells and may result in severe complications such as thrombosis, myelofibrotic transition, and potentially progression to acute myeloid leukaemia. Treatment with interferon-α (IFN-α) can potentially deplete the disease-driving malignant stem cell population, thereby leading to long-term remission. We extend a mechanistic compartmental differential equation model of MPN progression to account for the effects of IFN-α treatment. In agreement with experimental mouse studies, we assume that IFN-α acts through effects on malignant stem cell differentiation and malignant progenitor and precursor cell apoptosis. We use a hierarchical Bayesian inference procedure to infer the drug response parameters of the model based on measurements of the JAK2 V617F variant allele frequency (VAF) for N=56 patients from the Danish DALIAH study, both on the individual and the population level, with 14 patients left out for subsequent testing. The model estimates are found to agree with data. The drug response parameters are found to act synergistically on the reduction of JAK2 VAF, with the model being able to capture qualitatively different types of treatment responses. Using the inferred information about the population distribution of drug response parameters is found to improve predictions compared to predictions without prior knowledge on a testing cohort. Such predictions may aid clinical decision-making regarding IFN-α treatment in patients with MPNs.