Executive Summary : | The proposed study aims to model the transmission of this virus and forecast the effect of this pandemic, especially in the Indian context, considering various issues, e.g. variation in population density, age factor, underlying health conditions (especially, malnutrition, tuberculosis (TB), and diabetes) and others factors. |
Outcome/Output: | With the basic SIR model, the importance of basic reproductive number (R0) has been studied. When R0>1, then there will be a disease outbreak. The equation for maximum number of infectives at any given time and number of people end up catching the disease has been deduced. While extending the basic SIR model, time delay in the system has been incorporated. It is noted that the dynamics of the original system remains the same even after incorporating time delay in the system.
The system has been modified with stochastic perturbation in the SIR epidemic model with white noise in the form of Brownian motion or the Weiner process to consider various other factors, for example, climate change, age factor etc. As a result, sufficient conditions for the stochastic stability of disease-free equilibrium are obtained by using a suitable Lyapunov function. For both the system with stochastic differential equation (SDE) and stochastic time-delay system (SDDE), the system is stochastically asymptomatically stable and disease does not occur when ? |