Nonlinear dynamical behavior of an SEIR mathematical model: Effect of information and saturated treatment.

When a disease spreads in a population, individuals tend to change their behavior due to the presence of information about disease prevalence. Therefore, the infection rate is affected and incidence term in the model should be appropriately modified. In addition, a limitation of medical resources has its impact on the dynamics of the disease. In this work, we propose and analyze an Susceptible-Exposed-Infected-Recovered (SEIR) model, which accounts for the information-induced non-monotonic incidence function and saturated treatment function. The model analysis is carried out, and it is found that when R0 is below one, the disease may or may not die out due to the saturated treatment (i.e., a backward bifurcation may exist and cause multi-stability). Further, we note that in this case, disease eradication is possible if medical resources are available for all. When R0 exceeds one, there is a possibility of the existence of multiple endemic equilibria. These multiple equilibria give rise to rich and complex dynamics by showing various bifurcations and oscillations (via Hopf bifurcation). A global asymptotic stability of a unique endemic equilibrium (when it exists) is established under certain conditions. An impact of information is shown and also a sensitivity analysis of model parameters is performed. Various cases are considered numerically to provide the insight of model behavior mathematically and epidemiologically. We found that the model shows hysteresis. Our study underlines that a limitation of medical resources may cause bi(multi)-stability in the model system. Also, information plays a significant role and gives rise to a rich and complex dynamical behavior of the model.