If you are an app developer in your free time, then the answer might be yes, but if not, the answer is a resounding no.
It takes marketing efforts to get people to download your app. It takes product management to continuously develop your app to keep your users engaged. It takes a security and operations team to keep you app secured. Then layer on to it that you need to develop the app for iOS (iphones) and Android (all other phones) and it takes a whole lot of resources, which I can tell you aren’t worth the cost, unless you are a massive healthcare organization like “Health Canada” and you want the app to help with self-service and keep the practice running more efficiently and at a lower cost.
All around, it just doesn’t make sense for a doctor or even a small to medium practice to host their own app. Some viable alternatives for patients to utilize are the apps that are operated by electronic health record companies. Through these, patients can use the app to manage their care.
Another alternative, which is included in all of designs, is a mobile optimized website. If you have useful information there that can be easily read on a mobile website, the link and icon can easily be saved to a mobile phone desktop.