<p>Hypersensitivity pneumonitis (HP) is an immune-mediated lung disease caused by inhalation of various environmental antigens. This article primarily focuses on developing a new mathematical model of HP, utilizing several parameters that influence the eight subpopulations. The model comprises eight subpopulations such as susceptible, infected, recovered population, susceptible, infected, recovered human with reduced immunity, and susceptible, infected pigeon population which are influenced by different parameters such as birth rate and death rate of human and pigeon population, interaction rate of infected pigeons with susceptible human population, rate of avoiding exposures, rate of systematic corticosteroids given to infected human and pigeon population, etc. The model is studied using the Legendre wavelet method (LWM) to examine the nature of different subpopulations. Simultaneously, the model is solved using the RK4 method and NDSolve to compare solutions and achieve better accuracy. The convergence analysis of LWM, as well as the uniqueness and existence of solutions, is studied. We have also studied the variation of parameters to show how the nature of differential equations varies. The LWM provides better results when compared to other methods. The HP model offers a better understanding of the disease’s spread.</p>