Mathematical models are widely used to study the spreading dynamics of infectious diseases. In particular, the “Susceptibles-Infecteds-Recovereds-Deceases”(SIRD) model provides a framework that can be adapted to describe the core spreading dynamics of several human and wildlife infectious diseases. The present work uses a SIRD model using Caputo fractional derivative. In this investigation, the existence and uniqueness of solutions for the model were established. Numerical solutions were obtained using the Adams-Bashforth method. To illustrate the model’s utility, we made forecasts for the spread of the virus SARS-Cov-2 in the region of Tacna in Perú. It is well known that these models can help to forecast the number of infected people, understand the disease dynamics and evaluate potential control strategies.