Dynamical behavior of SIRS epidemic model with media awareness as control strategy

Background: In the modern era, the spread of disease is very fast with the transportation allowing more than a million people a day to cross international borders. To control this spreading of disease, the health officials may have various pharmaceutical and non-pharmaceutical (wearing masks, closing schools, isolation, staying at home etc.) options. Media plays a very important role to communicate awareness in public for use of non-pharmaceutical interventions (NPIs) to control the epidemics. Methods & Materials: Determine the basic reproduction number by using a next generation matrix operator. Discuss stability criterion of the equilibrium points of the model with bifurcation theory. Carry out parameter sensitivity analysis by using the normalized forward sensitivity index. Perform the numerical simulation of the model to verify the results of qualitative analysis using MATLAB. Results: Result 1. The disease free equilibrium (DFE) is locally asymptotically stable, if R0<1 and unstable, if R0>1. Result 2. The endemic equilibrium (EE) is locally asymptotically stable for R0>1, but close to 1. Result 3. The coefficient of media awareness m does not effect R0. Result 4. The level of endemic equilibrium is significantly affected by media coefficient m. Conclusion: In this paper, we proposed a SIRS epidemic model incorporating media awareness as control strategy and investigated the asymptotic stability of the model in both disease-free equilibrium and endemic equilibrium states. The disease free equilibrium is locally asymptotically stable for basic reproduction number R0 < 1, a transcritical bifurcation occurs at R0 = 1 and a unique locally asymptotically stable endemic equilibrium exists for R0 > 1. We observed that the coefficient of media awareness m does not effect R0 and hence the qualitative features of the model remain unaltered, but the level of endemic equilibrium is significantly affected by media coefficient. We calculate normalized forward sensitivity indices for the basic reproduction number and state variables at endemic equilibrium with respect to various parameters and identified respective sensitive parameters. Numerical simulations of the system justify the analytic findings and we also observed that the level of endemic equilibrium is significantly affected by media coefficient m.