Modeling and analysis of a two-strain immuno-epidemiological model with reinfection

In this paper, we formulate a two-strain model with reinfection that combines immunological and epidemiological dynamics across scales, using the COVID-19 pandemic as a case study. Firstly, we conduct a qualitative analysis of both within-host and between-host models. For the within-host model, we prove the existence and stability of equilibria, and Hopf bifurcation occurs from the infection equilibrium with immune response. This implies that, under specific immune states, the virus within an infected individual may persist, and its concentration may also oscillate periodically. For the between-host model, the disease-free equilibrium always exists and is locally asymptotically stable when the epidemiological basic reproduction number ${\Re }^0<1$. In addition, the model can have boundary equilibria of strain 1 or strain 2, which are locally asymptotically stable under specific conditions. However, the co-existence equilibrium does not exist. Secondly, to explore the infection and transmission mechanisms of two strain models and obtain reliable parameter values, we utilize statistical data to fit the immuno-epidemiological model. Simultaneously, we conduct an identifiability analysis of the immuno-epidemiological model to ensure the robustness of the fitted parameters. The results demonstrate the reliable estimation of parameter ranges for structurally unidentifiable parameters with minor measurement errors using the affine invariant ensemble Markov Chain Monte Carlo algorithm (GWMCMC). Moreover, simulations illustrate that enhancing treatment of patients infected with BA.2 strains to inhibit the number of viruses released by infected cells can significantly reduce disease spread.