usage.js

import React from 'react'
//...

class Slider extends React.Component {
  //...
  render() {
    return (
      <WithSwipe toLeftSwipe={this.next} toRightSwipe={this.prev}>
      //...
      </WithSwipe>
    )
  }
}  

WithSwipe.js

import React from 'react'

export default class WithSwipe extends React.Component {
	xDown = null
	yDown = null

	handleTouchStart = evt => {
		this.xDown = evt.touches[0].clientX
		this.yDown = evt.touches[0].clientY
	}

	handleTouchMove = evt => {
		const xDown = this.xDown
		const yDown = this.yDown

		if (!xDown || !yDown) return

		const xUp = evt.touches[0].clientX
		const yUp = evt.touches[0].clientY

		const xDiff = xDown - xUp
		const yDiff = yDown - yUp

		if (Math.abs(xDiff) > Math.abs(yDiff)) {
			if (xDiff > 0) {
				/* left swipe */
				this.props.toLeftSwipe()
			} else {
				/* right swipe */
				this.props.toRightSwipe()
			}
		}
		/* reset values */
		this.xDown = null
		this.yDown = null
	}

	render() {
		const { children } = this.props
		return (
			<div
				onTouchMove={e => this.handleTouchMove(e)}
				onTouchStart={e => this.handleTouchStart(e)}
			>
				{children}
			</div>
		)
	}
}