  There are complex interactions between antibody levels and epidemic
propagation, the antibody level of an individual influences the probability of
infection, and the spread of the virus influences the antibody level of each
individual. There exist some viruses that, in their natural state, cause
antibody levels in an infected individual to gradually decay. When these
antibody levels decay to a certain point, the individual can be reinfected,
such as with COVID 19. To describe their interaction, we introduce a novel
mathematical model that incorporates the presence of an antibody retention rate
to investigate the infection patterns of individuals who survive multiple
infections. The model is composed of a system of stochastic differential
equations to derive the equilibrium point and threshold of the model and
presents rich experimental results of numerical simulations to further
elucidate the propagation properties of the model. We find that the antibody
decay rate strongly affects the propagation process, and also that different
network structures have different sensitivities to the antibody decay rate, and
that changes in the antibody decay rate cause stronger changes in the
propagation process in Barabasi Albert networks. Furthermore, we investigate
the stationary distribution of the number of infection states and the final
antibody levels, and find that they both satisfy the normal distribution, but
the standard deviation is small in the Barabasi Albert network. Finally, we
explore the effect of individual antibody differences and decay rates on the
final population antibody levels, and uncover that individual antibody
differences do not affect the final mean antibody levels. The study offers
valuable insights for epidemic prevention and control in practical
applications.
