Two-strain mathematical virus model with delay for Covid-19 with immune response

Abstract

In this manuscript, we analyze a new virus model of SARS-CoV-2 infection with immune response. The initial model was proposed by Mochan et al. [23] to describe an experiment made on Macaques. We consider the latent period of newly infected cells by introducing a delay in the model. We fully analyze the quality properties of the model and investigate strategies to reduce secondary infections. Moreover, we investigate the impact of the latent period on the spread of the infection. We observe due to the delay, the possibility to reach an infection-free state when R0>1. This observation is not possible when the delay is not considered. We also demonstrate the occurrence of a Hopf bifurcation when R0>1. We further introduce two control parameters to prevent new infections and inhibit viral production, and we formulate an optimal control problem aiming to minimize infections, virus proliferation and the cost of treatment. We establish the existence of the optimal solution and illustrate the theoretical results numerically. In contrast to Mochan et al. [23] results, our simulations show that increased suppression of viral production can change a lethal or chronic infection to a survivable scenario or acute infection. We also observe that the latency period can cause several states of chronic infection before the host recovers totally. Moreover, the density of viruses increases as the latent period is long. The reason being that the immune system is alerted with a delay (after the latent period), which is an advantage for the replication of viruses.

Keywords

• Virus model
• Hopf bifurcation
• Delay differential equations
• Optimal control
• Basic reproduction number
• Stability analysis