ReduxNavigation.js

import React from "react"
import * as ReactNavigation from "react-navigation"
import { connect } from "react-redux"
import AppNavigation, { isDrawerOpen } from "./AppNavigation"
import { BackHandler } from "react-native"
import PropTypes from "prop-types"

class ReduxNavigation extends React.Component {

    static propTypes = {
        dispatch: PropTypes.func.isRequired,
        nav: PropTypes.object.isRequired,
    }

    _shouldCloseApp = () => this.props.nav.index === 0

    _goBack = () => this.props.dispatch(ReactNavigation.NavigationActions.back())

    _closeDrawer = () => this.props.dispatch(ReactNavigation.NavigationActions.navigate({
        routeName: "DrawerClose"
    }))

    _handleBackPress = () => {
        if (isDrawerOpen(this.props.nav)) {
            this._closeDrawer()
            return true
        }
        if (this._shouldCloseApp()) {
            return false
        }
        this._goBack()
        return true
    }

    componentWillMount() {
        BackHandler.addEventListener("hardwareBackPress", this._handleBackPress)
    }

    componentWillUnmount() {
        BackHandler.removeEventListener("hardwareBackPress", this._handleBackPress)
    }

    render() {
        const { dispatch, nav } = this.props
        const navigation = ReactNavigation.addNavigationHelpers({
            dispatch,
            state: nav
        })

        return <AppNavigation navigation={navigation} />
    }
}


const mapStateToProps = state => ({ nav: state.nav })
export default connect(mapStateToProps)(ReduxNavigation)

BTW isDrawerOpen is a simple function, which extracts info from nav and returns a boolean:
const isDrawerOpen = (nav) => nav.routes[0].index === 1

Note that the path might be different for you, based on the way you hooked up your navigators.