A comparison of some control strategies for a non-integer order tuberculosis model

Abstract

The aim of this paper is to investigate some optimal control strategies for ageneralized tuberculosis model consisting of four compartments. We constructthe model with the use of Caputo time fractional derivative. Contribution ofdistancing control, latent case finding control, case holding control and theircombinations are discussed and the optimality system is obtained based on theHamiltonian principle. Additionally, we prove that the solution is non-negativeand bounded from above. We present some illustrative examples to determinethe most effective strategy to minimize the number of infected people andmaximize the number of susceptible individuals. Moreover, we discuss thecontribution of the Caputo derivative and the order of the fractional derivativeto efficiency of the control strategies.