Environmental pollutant continues to pose a great threat to public health, leading to development of chronic diseases. In this study, a nonlinear mathematical model is formulated and analysed to study the effect of genetic risk, environmental pollutant, public health education/awareness on asthma development. Conditions for the existence of the unique positive steady state and permanence of the system are assessed. Using Lyapunov function analysis, the unique positive steady state is locally and globally asymptotically stable. Results reveal that genetic risk, pollutant emission rate, effective exposure rate of population to polluted environment and recurrence rate contribute to asthma prevalence. However, sufficiently effective pollutant reduction strategies, improvement in compliance to public health education/awareness together with human dependent environmental pollutant depletion lead to a marked reduction in disease prevalence.