modelling covid-19 infection dynamics in the presence‎ ‎of‎ ‎interventions‎ ‎and‎ ‎environmental transmission

‎sars-cov-2 (covid-19)‎, ‎a member of the textit{betacoronavirus} family‎, ‎was declared a global pandemic in 2020‎. ‎this study develops a mathematical model to investigate covid-19 transmission in a heterogeneous population in south africa‎, ‎incorporating environmental transmission and non-pharmaceutical interventions (npis) such as mask efficacy‎. ‎we analyze qualitative properties‎, ‎including the stability of disease-free and endemic equilibria relative to the basic reproduction number r0‎. ‎the analysis reveals a transcritical bifurcation at r0 = 1‎, ‎indicating that simply reducing r0 below one is insufficient for disease elimination‎. ‎this underscores the need for complementary measures‎, ‎such as quarantine‎. ‎simulations highlight the roles of symptomatic and asymptomatic infections‎, ‎with reduced mask compliance promoting the persistence of the endemic state‎. ‎the study concludes that quarantine remains a vital intervention for controlling transmission‎.