Modelling fractional-order dynamics of covid-19 with environmental transmission and vaccination: A case study of Indonesia

SARS-CoV-2 is the newly emerged infectious disease that started in Wuhan, China, in early December 2019 and has spread the world over very quickly, causing severe infections and death. Recently, vaccines have been used to curtail the severity of the disease without a permanent cure. The fractional-order models are beneficial for understanding disease epidemics as they tend to capture the memory and non-locality effects for mathematical models. In the present study, we analyze a deterministic and fractional epidemic model of COVID-19 for Indonesia, incorporating vaccination and environmental transmission of the pathogen. Further, the model is fitted to Indonesia’s active cases data from 1 June 2021 to 20 July 2021, which helped determine the model parameters’ value for our numerical simulation. Mathematical analyses such as boundedness, existence and uniqueness, reproduction number, and bifurcation were presented. Numerical simulations of the integer and fractional-order model were also carried out. The results obtained from the numerical simulations show that an increase in the contact rate of the virus transmission from the environment leads to an increase in the spread of SARS-CoV-2. In contrast, an increase in the vaccination rate negatively impacts on our model basic reproduction number. These results envisage here are essential for the control and possibly eradicate COVID-19 in Indonesia.