Control of Disease Dynamics Under Time Varying Vaccination and Treatment Rates
Keywords:
Infectious diseases, vaccination, treatment, convergence, stability. MSC (2010) 37L45, 37D35, 34D23Abstract
Vaccination and treatment are two major strategies in controlling or eradication of any contagious disease. Usually, both these factors are represented by fixed parameters in most of the studies. In the present work, an SIR (Susceptible-Infectious-Recovered) model of populations is considered with time dependent vaccination and treatment rates and influence of these disease control strategies is studied. Besides establishing the boundedness of solutions, conditions are provided on asymptotic closeness of solutions. Upon further restrictions on vaccination and treatment, it is observed that the populations may be made to approach a pre-specified state affairs which the society could manage. Further study reveals that the system may approach eventually an equilibrium solution of a system with constantrates of vaccination and treatment. Illustrations are provided to understand the technique and its effectiveness.
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