The demise of the native app, both on the desktop and mobile has been forecast since the development of HTML5. These two articles give a clear insight into the current state-of-play.
First, a view from product marketing: https://moz.com/blog/mobile-web-mobile-apps-invest-marketing-whiteboard-friday
Second, a high-level technology comparison for product management: http://waracle.net/html5-vs-hybrid-vs-native-app-development/
And if you want to get started right now: https://developers.google.com/web/progressive-web-apps?hl=en