The recent coronavirus disease 2019 (COVID-19) outbreak is of high importance in research topics due to its fast spreading
and high rate of infections across the world. In this paper, we test certain optimal models of forecasting daily new cases
of COVID-19 in Oman. It is based on solving a certain nonlinear least-squares optimization problem that determines some
unknown parameters in fitting some mathematical models. We also consider extension to these models to predict the future
number of infection cases in Oman. The modification technique introduces a simple ratio rate of changes in the daily infected
cases. This average ratio is computed by employing the rule of Al-Baali [Numerical experience with a class of self-scaling
quasi-Newton algorithms, JOTA, 96 (1998), pp. 533–553], in a sense to be defined, for measuring the infection changes.