I think the advantages are very clear in terms of costs and resources. Since it was given that the hospital does not has an existing system architecture of servers nor the IT staff with expertise, it would have to spend an unimaginable amount of budget to buy all the new servers to host the app and also to hire a big IT team with expertise to maintain it. By using cloud servers instead of physical ones, we are essentially delegating the costs of purchasing physical servers and hiring expert staff to the cloud service provider, which could save a lot of money. Cloud servers also tend to be scalable, so it charges the hospital based on how much traffic/capacity/computing power was used. This also helps to save costs. If there is only a small number of users for the app, we do not have to pay much for the servers. If we buy physical servers, we are forced to pay a large amount of fixed costs no matter the number of users.
I think the PaaS model would be the most appropriate in this case. SaaS is not appropriate since it is given that we are trying to develop our own web app for patients instead of using an existing software product by another company, so SaaS is not applicable. PaaS offers just the right amount of flexibility. We only need a platform to deploy our app, but we want everything else to be handled by the provider (hardware, OS, database) to save our hassle. PaaS fits this purpose. IaaS offers even more customization for the user, allowing to set up the OS and virtual machines on their own preferences, but this would mean too many things to be set up manually. Therefore, PaaS offers just the right amount of what we need, and allows us to focus on the app development instead of worrying about other things.