React Native - React Native Architecture

react native is only view, but you can try to build your MVC Architecture. here is my model you can use it as a model for your mvc Architecture.

react-native-model

Best way to do it is, by using Redux or Relay Architecture

Yes. React Native is just the "V" in those software design patterns you're mentioning. If you consider other libraries around React, like Flux, then maybe my answer isn't 100% accurate. I recommend reading this:

https://medium.com/javascript-inside/what-if-react-was-really-only-the-v-in-mvc-5854fd6f601c

Here's a more complete answer, considering the App not being just React Native but also the backend and the data models involved:

https://medium.com/of-all-things-tech-progress/understanding-mvc-architecture-with-react-6cd38e91fefd

Hope it helps.