Italian Journal of Pure and Applied Mathematics (Ital. J. Pure Appl. Math.) (20170101), No.~37, 139-156. ISSN: 1126-8042 (print).eISSN: 2239-0227.
Subject
34 Ordinary differential equations -- 34K Functional-differential and differential-difference equations 34K18 Bifurcation theory 34K20 Stability theory 34K60 Qualitative investigation and simulation of models
37 Dynamical systems and ergodic theory -- 37N Applications 37N25 Dynamical systems in biology
Dengue fever and dengue hemorrhagic fever are acute mosquito borne infectious diseases that have spread rapidly around the globe. The infected individuals usually have a complex immune response within 7 days of the onset of the fever. \par In this paper the authors divide the time delay into four cases and study the stability and Hopf bifurcation of the model in three of the cases. They present the results of their simulations (in which they use Matlab) which imply the numerical condition for periodic solutions and Hopf bifurcation.