How to type prototype-based ES5 class in TypeScript?

I am in the process of converting some of the old ES5 projects to TypeScript. In these projects, there are old-style classes (functions) defined as follows (simplified examples):

function MyClass(arg1) {
  this.arg_prop_1 = arg1;
  this.arg_prop_2 = function() { return this.arg_prop_1; }
}

MyClass.prototype.proto_prop = function() { return this.arg_prop_2() === 42; }

const obj = new MyClass(42);
console.assert(obj.proto_prop());
 

What is the correct / recommended / best way to type this code without actually changing it to ES6 class syntax?

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What I have tried:

To enable TypeScript, I have defined some declarations as follows (not working):

interface MyClassThis {
  arg_prop_1: number;
  arg_prop_2: () => number;
  proto_prop: () => boolean;
}

interface MyClassCtor {
  new (arg1: number): MyClassThis;
}

To begin with, I just followed some code for “Date” type from here. As the above is not working (error: ‘new’ expression, whose target lacks a construct signature, implicitly has an ‘any’ type.(7009)), I’m not completely sure what’s the right way to define types for such old-style class functions.