# Conservation laws for a mathematical model of HIV transmission

## TL;DR

This paper applies Ibragimov's theorem to identify conservation laws in a nonlinear differential equation model of HIV transmission, enhancing understanding of the model's invariant properties.

## Contribution

It demonstrates how to use Ibragimov's theorem to derive conservation laws for a specific HIV transmission model, linking symmetries to invariants.

## Key findings

- Derived conservation laws for the HIV model
- Identified symmetries related to the model
- Enhanced understanding of the model's invariants

## Abstract

A theorem due to Nail H. Ibragimov (2007) provides a connection between symmetries and conservation laws for arbitrary differential equations. The theorem is valid for any system of differential equations provided that the number of equations is equal to the number of dependent variables. In this paper we use the theorem to determine conservation laws for a nonlinear system of differential equations that represents a mathematical model for HIV transmission.