We proposed a novel cure rate model in which the number of competing causes follows a Bell–Touchard distribution. We derived its main mathematical properties and implemented Bayesian inference using the Hamiltonian Monte Carlo algorithm. A simulation study was conducted to assess the finite-sample performance of the estimators. The model's applicability was demonstrated using two real datasets: patients with melanoma and patients with cardiovascular disease. In the latter dataset, diabetic patients exhibited higher estimated cure and survival probabilities than non-diabetic individuals, potentially reflecting phenomena such as "reverse epidemiology" or intensified clinical management.