STUDY OF GLOBAL STABILITY AND OPTIMAL TREATMENT FOR AN INFECTIOUS DISEASE MODEL

摘要

In this paper we considered a nonlinear compartmental SIRS model that accounts for the impact of awareness effect in population. We analyzed and established the global stability of unique infected equilibrium by constructing a suitable Lyapunov function. We found that the basic reproduction number for the model system is independent of awareness parameter and hence eradication of the disease cannot be achieved through awareness only, though it reduces disease prevalence in initial phase. Further, by introducing treatment to infective, we formulate and study corresponding optimal control problem to find optimal treatment policy for providing treatment with minimum cost. With the help of Pontryagin's Maximum Principle the optimal treatment path is obtained analytically. We performed numerical simulations to analyze the results obtained for a representative set of parameters. It is observed that the awareness reduces the infective population during initial phase but is not effective if treatment is not available. While optimal treatment in aware population is very effective in keeping disease load significantly low throughout the period and reducing economical cost. Thus the combined impact of awareness and optimal treatment can bring down disease prevalence in population and also minimize cost incurred.