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Effect of awareness programs in controlling the prevalence of an epidemic with time delay. (English) Zbl 1228.92067

Summary: A nonlinear mathematical model with delay to capture the dynamics of the effect of awareness programs on the prevalence of any epidemic is proposed and analyzed. It is assumed that pathogens are transmitted via direct contact between susceptibles and infectives. It is assumed further that the cumulative density of awareness programs increases at a rate proportional to the number of infectives. It is considered that awareness programs are capable of inducing behavioral changes in susceptibles, which result in the isolation of aware populations. The model is analyzed using the stability theory of differential equations and numerical simulations. The model analysis shows that, though awareness programs cannot eradicate infection, they help in controlling the prevalence of disease. It is also found that time delays in execution of awareness programs destabilizes the system and periodic solutions may arise through Hopf-bifurcations.

MSC:

92D30 Epidemiology
34K60 Qualitative investigation and simulation of models involving functional-differential equations
91D99 Mathematical sociology (including anthropology)
92C60 Medical epidemiology
37N25 Dynamical systems in biology
65C20 Probabilistic models, generic numerical methods in probability and statistics
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