Modeling the effect of time delay in budget allocation to control an epidemic through awareness

Abstract

The emergence of any new infectious disease poses much stress on the government to control the spread of such disease. The easy, fast and less expensive way to slow down the spread of disease is to make the population be aware of its spread and possible control mechanisms. For this purpose, government allocates some funds to make public aware through mass media, print media, pamphlets, etc. Keeping this in view, in this paper, a nonlinear mathematical model is proposed and analyzed to assess the effect of time delay in providing funds by the government to warn people. It is assumed that susceptible individuals contract infection through the direct contact with infected individuals; however the rate of contracting infection is a decreasing function of funds availability. The proposed model is analyzed using stability theory of delay differential equations and numerical simulations. The model analysis shows that the increase in funds to warn people reduces the number of infected individuals but delay in providing the funds destabilizes the interior equilibrium and may cause stability switches.