For starters, the width & height of your image are being specified in the markup. You might be better off removing the width and height attributes and using CSS to define the dimensions of the image. That way you can apply a percentage with & height or similar.
I'm not sure how (or even if) you can handle the map responsively itself because, almost by definition, image maps require browser coordinates - which ties them down to a minimum viewport size. There might be something in HTML5 that you can use (like canvas) but that's not going to be supported by all browsers.
You might be better off dropping the map approach completely and seeing if you can approach this from another angle entirely