Abstract This paper introduces a four-parameter competing risks model called the additive flexible Weibull extension-Lomax distribution. It has a very flexible hazard rate function accommodates different shapes, the most important shapes of them are the bathtub and the modified bathtub shapes. Moreover, it has several new and well-known models as special cases. Some main properties of the additive flexible Weibull extension-Lomax distribution are derived. The model parameters, reliability and hazard rate functions are estimated via the maximum likelihood method based on Type II censored samples. Also, the asymptotic confidence intervals of the parameters, reliability function and the hazard rate function are obtained. A simulation study is carried out to evaluate the performance of the maximum likelihood estimates. The superiority of the proposed distribution over some known distributions is demonstrated through some applications on COVID-19 data in some countries.