Pre-exposure prophylaxis and antiretroviral treatment interventions with drug resistance

•Introduction of a mathematical model for the spread of HIV incorporating both PrEP use for HIV prevention and ARV use for HIV treatment.•Either PrEP or ARV use as a single intervention strategy was found to be inadequate in sustainably reducing the spread of HIV.•A combination of both interventions, at high levels, offers the best potential for significant reduction of new HIV infections.•The PrEP efficacy level was found to be a key control factor for effective reduction of HIV incidence.•PrEP drug resistance could be one of the key drivers of HIV spread. We introduce a model for HIV/AIDS which can be utilized to assess the impact of combining pre-exposure prophylaxis (PrEP) and antiretroviral drugs (ARVs) use interventions (incorporating drug resistance). Mathematical and numerical analyses are carried out to investigate the effects of the combined controls in the presence of PrEP drug resistance. Our results predict a significant decrease in the number of new HIV infections when PrEP and ARVs are concurrently implemented at high levels. The results also reveal that PrEP drug resistance has the potential to slow down or reverse the effects of PrEP, especially at low efficacy levels.