Research on nonlinear infectious disease models influenced by media factors and optimal control

In this article, a mathematical model was developed to describe disease control by media factors. The Lambert W function was used to convert the system definition by implicit functions into explicit functions. We analyzed the dynamics of the defined piecewise smooth system and verified the correctness of the theoretical analysis through numerical simulation. Research revealed that media factors can delay the peak of an epidemic and reduce the scale of the epidemic. It is worth noting that adopting different control measures has a certain impact on the scale of the epidemic; the analysis results indicate that implementing dual-control is the most effective way to limit the spread of diseases and this strategy may provide clues for disease control.