Dynamical analysis of mathematical model for Bovine Tuberculosis among human and cattle population

Dipo Aldila; Siti Leah Latifa; Putri A. Dumbela

doi:10.5614/cbms.2019.2.1.6

Authors

Dipo Aldila Department of Mathematics, Universitas Indonesia, Indonesia, Depok 16424
Siti Leah Latifa Department of Mathematics, Universitas Indonesia, Indonesia, Depok 16424
Putri A. Dumbela Department of Mathematics, Universitas Indonesia, Indonesia, Depok 16424

DOI:

https://doi.org/10.5614/cbms.2019.2.1.6

Keywords:

Basic Reproduction Number, Bovine Tuberculosis, Reinfection

Abstract

Bovine Tuberculosis (BTB) is a disease that can attack humans through cattle.The process of transmission can occur through the air and cattle products that are not treated properly. When humans are infected with BTB, reinfection, and relapse may occur. This phenomenon is modeled as an eleven-dimension dynamical system. Our aim is to gain insight into the effect of separation of human activity area into the transmission dynamics of BTB. The model incorporates (among many others features) the dynamics of BTB among human and cattle population, density-dependent infection rate, and reinfection, are rigorously analyzed and simulated. The trivial disease-free equilibrium of the model is shown to be locally asymptotically stable when the two associated basic reproduction number are less than unity. Although the non-trivial equilibrium cannot be shown explicitly, for a special case, this equilibrium is still possible to show and discuss further. Our results suggest that controlling BTB in cattle population may indirectly control the spread of BTB in human. An example of controlling the infected population of infected cattle can be done with the annihilation of infected cattle.

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