Complex dynamic behaviors of a tumor-immune system with two delays in tumor actions

<p style='text-indent:20px;'>The action of a tumor on the immune system includes stimulation and neutralization, which usually have different time delays. In this work we propose tumor-immune to incorporate these two kinds delays due actions. We explore effects model find some phenomena induced by them. When there is only neutralization delay, has uniform upper bound while when varies with delay. The theoretic analysis suggests that, for stability its tumor-present equilibrium may change at most once as delay increases, but increase lead multiple switches Numerical simulations indicate in presence induce switches. Further, equilibria, numerical also demonstrate that present interesting outcomes each increases. These include onset cytokine storm, almost global attractivity tumor-free sufficiently large delays, so on. results show complexity dynamic behaviors delays.</p>