The spread of infectious diseases such as COVID-19 presents many challenges to healthcare systems and infrastructures across the world, exacerbating inequalities and leaving the world's most vulnerable populations most affected. Given their density and available infrastructure, refugee and internally displaced person (IDP) settlements can be particularly susceptible to disease spread. In this paper we present an agent-based modeling approach to simulating the spread of disease in refugee and IDP settlements under various non-pharmaceutical intervention strategies. The model, based on the JUNE open-source framework, is informed by data on geography, demographics, comorbidities, physical infrastructure and other parameters obtained from real-world observations and previous literature. The development and testing of this approach focuses on the Cox's Bazar refugee settlement in Bangladesh, although our model is designed to be generalizable to other informal settings. Our findings suggest the encouraging self-isolation at home of mild to severe symptomatic patients, as opposed to the isolation of all positive cases in purpose-built isolation and treatment centers, does not increase the risk of secondary infection meaning the centers can be used to provide hospital support to the most intense cases of COVID-19. Secondly we find that mask wearing in all indoor communal areas can be effective at dampening viral spread, even with low mask efficacy and compliance rates. Finally, we model the effects of reopening learning centers in the settlement under various mitigation strategies. For example, a combination of mask wearing in the classroom, halving attendance regularity to enable physical distancing, and better ventilation can almost completely mitigate the increased risk of infection which keeping the learning centers open may cause. These modeling efforts are being incorporated into decision making processes to inform future planning, and further exercises should be carried out in similar geographies to help protect those most vulnerable.