STUDIES ON THE INTERACTION MECHANISM BETWEEN THE MRNA VACCINE AGAINST SARS-COV-2 AND THE IMMUNE SYSTEM

Vaccines are an effective tool in the fight against infectious diseases. However, mathematical models of SARS-CoV-2 focus on the macroscopic situation, while articles on vaccines focus on effectiveness and safety. We develop four mathematical models to investigate the immune system and the microdynamics of antigens and viruses in individuals injected with mRNA vaccines. We first theoretically analyze the optimal model, calculate all equilibria, and prove that the disease-free equilibrium is globally asymptotically stable while the others are unstable. This suggests that after a certain period after vaccination, the infected cells and antigens will no longer exist in vivo and will be eliminated by the immune system over time or will die naturally. This theoretically proves the safety of the mRNA vaccines. Then, we use the differential algebra to analyze the structural identifiability of the models. We find that two of them are globally identifiable while the other two are unidentifiable, but once a certain parameter is fixed, then they are identifiable as well. To select the optimal model among four models, we use the Affine Invariant Ensemble Markov Chain Monte Carlo algorithm for data fitting and parameter estimation. We find that the roles of memory cells in killing infected cells and promoting immune cells and neutralizing antibodies in the process of mRNA vaccination are not significant and can be ignored in the modeling. On the other hand, the innate immunity of the human body plays an important role in this process. In addition, we also analyze the practical identifiability of the parameters of the optimal model. The results show that even if the structure of the system is globally identifiable, it does not ensure that all the parameters are practically identifiable. After random sampling and simulating the four unidentifiable parameters, we find that only two variables, infected cells Ⅱ and antibodies, are sensitive to these unidentifiable parameters, but the results are still within acceptable ranges. This suggests that our fitting results are generally reliable. Finally, we simulate multiple booster injections and find that booster injections are indeed effective in maintaining antibody levels in vivo, which could otherwise gradually die off over time. Therefore, booster injections are beneficial to help the human body increase and maintain immunity.