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An analysis of tuberculosis model with exponential decay law operator. (English) Zbl 1485.92116

Summary: In this paper, we explore the dynamics of tuberculosis (TB) epidemic model that includes the recruitment rate in both susceptible and infected population. Stability and sensitivity analysis of the classical TB model is carried out. Caputo-Fabrizio (CF) operator is then used to explain the dynamics of the TB model. The concept of fixed point theory is employed to obtain the existence and uniqueness of the solution of the TB model in the light of CF operator. Numerical simulations based on homotopy analysis transform method (HATM) and Padé approximations are performed to obtain qualitative information on the model. Numerical solutions depict that the order of the fractional derivative has great dynamics of the TB model.

MSC:

92D30 Epidemiology
26A33 Fractional derivatives and integrals
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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