Using comparison operators in a PHP 'switch' statement

Switches can't do that, but in this particular case you can do something like this:

switch ((int)(($count - 1) / 20)) {
    case 0:
        $priority = 'low';
        break;
    case 1:
        $priority = 'medium';
        break;
    case 2:
        $priority = 'high';
        break;
    case 3:
        $priority = 'severe';
        break;
}

So in (int)(($count - 1) / 20) all values from 0 to 20 will eval to 0, 21 to 40 will eval to 1 and so on, allowing you to use the switch statement for this purpose.

And since we are concatenating values, we can even simplify to an array:

$priorities = ['low', 'medium', 'high', 'severe'];
$priority = $priorities[(int)(($count - 1) / 20)];

A more general case for solving this problem is:

switch (true) {
    case $count <= 20:
        $priority = 'low';
        break;

    case $count <= 40:
        $priority = 'medium';
        break;

    case $count <= 60:
        $priority = 'high';
        break;

    default:
        $priority = 'severe';
        break;
}