1Università di Milano-Bicocca Dipartimento di Matematica e Applicazioni, Via Cozzi 53, 20125 Milano, Italy email@example.com.
2Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.
3Division of Infectious Diseases Department of Internal Medicine, 'San Gerardo' Hospital, Università di Milano-Bicocca, 20900 Monza, Italy.
Sequential monotherapy is the most widely used therapeutic approach in the treatment of hepatitis B virus (HBV) chronic infection. Unfortunately, under therapy, in some patients the hepatitis virus mutates and gives rise to variants which are drug resistant. We wonder whether those patients would have benefited from the choice of combination therapy instead of sequential monotherapy. To study the action of these two therapeutic approaches and to explain the emergence of drug resistance, we propose a stochastic model for the infection within a patient who is treated with two drugs, either sequentially or contemporaneously, and who, under the first kind of therapy develops a strain of the virus which is resistant to both drugs. Our stochastic model has a deterministic approximation which is a slight modification of a classic three-strain model. We discuss why stochastic simulations are more suitable than the study of the deterministic approximation, when modelling the rise of mutations (this is mainly due to the amplitude of the stochastic fluctuations). We run stochastic simulations with suitable parameters and compare the time when, under the two therapeutic approaches, the resistant strain first reaches detectability in the serum viral load. Our results show that the best choice is to start an early combination therapy, which allows one to stay drug resistance free for a longer time and in many cases leads to viral eradication.