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The COVID-19 pandemic is one of the contagious diseases involving all the world in 2019–2020. Also, all people are concerned about the future of this catastrophe and how the continuous outbreak can be prevented. Some countries are not successful in controlling the outbreak; therefore, the incidence is observed in several peaks. In this paper, firstly single-peak SIR models are used for historical data. Regarding the SIR model, the termination time of the outbreak should have been in early June 2020. However, several peaks invalidate the results of single-peak models. Therefore, we should present a model to support pandemics with several extrema. In this paper, we presented the generalized logistic growth model (GLM) to estimate sub-epidemic waves of the COVID-19 outbreak in Iran. Therefore, the presented model simulated scenarios of two, three, and four waves in the observed incidence. In the second part of the paper, we assessed travel-related risk in inter-provincial travels in Iran. Moreover, the results of travel-related risk show that typical travel between Tehran and other sites exposed Isfahan, Gilan, Mazandaran, and West Azerbaijan in the higher risk of infection greater than 100 people per day. Therefore, controlling this movement can prevent great numbers of infection, remarkably. [ABSTRACT FROM AUTHOR]