One of the most important problems of supply chain management is distribution management. The fleet composition and size play a significant role in reducing distribution costs. Recently, infectious diseases such as the COVID-19 pandemic have affected human resources, leading to the employment of autonomous vehicles (AVs) getting more attention. This paper proposes a stochastic programming model for the fleet size and mixed vehicle routing problem (FSMVRP), including autonomous and conventional vehicles (CVs) under human resource disruption. An accelerated version of the Progressive Hedging Algorithm (PHA) is applied to solve that. According to numerical results, the obtained value of the stochastic solution (VSS) suggest the model could decrease the fleet cost by about 11 percent on average. Analysis of the expected value of perfect information (EVPI) shows that using the stochastic programming approach for fleet management could minimize the total cost of the fleet by 22%, on average. In addition, the sensitivity analysis shows that using AVs under infectious disease disruption is advisable to improve performance.