According to the World Health Organization (https://covid19.who.int/), more than 764 million people have been confirmed with COVID-19 infection, and at least 6.9 million of them have died as of April 30, 2023. COVID-19 has spread to almost every country in the world because of air travel. Cases of COVID-19 virus transmission from an index patient who was the individual affected with the first known case of COVID-19 in the flight to fellow passengers in commercial airplanes have been widely reported. This investigation first used computational fluid dynamics (CFD) to simulate airflow in airliner cabins. Based on the CFD results, a deterministic model and a probabilistic model were used to evaluate COVID-19 virus (SARS-CoV-2) transport in an airline cabin. The deterministic model used CFD with Lagrangian method to calculate droplet distribution in a cabin and the number of viral copies inhaled by a fellow passenger. The probabilistic model used CFD to determine the quantum concentration and the Wells-Riley equation to calculate the probability if a fellow passenger may be infected. This study first validated the airflow, air temperature, and virus concentration simulated by a tracer-gas with the corresponding experimental data measured in a seven-row, single-aisle cabin mockup. The results show that the CFD results were in reasonable agreement with the experimental data. Then the deterministic and probabilistic models were used to predict COVID-19 infection in the business-class cabin of a Boeing 787-9 flight. The flight was VN54 from London to Hanoi on March 2, 2020, where the index patient infected at least 12 fellow passengers with a total of 20 passengers in the business-class cabin. The two models gave the same prediction accuracy of 84.2%, although the infection distributions differed slightly. The deterministic model was physically meaningful but demanded a high computing resource and long computing time, compared with the probability model. The quantum number and viral copies generated by the index patient were crucial for the accuracy of the results. Both models can be used to predict infection distribution in airliner cabins.