Modeling and analysis of the transmission dynamics of tuberculosis without and with seasonality

A deterministic model of tuberculosis without and with seasonality is designed and analyzed into its transmission dynamics. We first present and analyze a tuberculosis model without seasonality, which incorporates the essential biological and epidemiological features of the disease. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium coexists with one or more stable endemic equilibria when the associated basic reproduction number is less than unity. The statistical data of tuberculosis (TB) cases show seasonal fluctuations in many countries. Then, the extension of our TB model by incorporating seasonality is developed and the basic reproduction ratio is defined. Parameter values of the model are estimated according to Samuel Bowong is also with UMI 209 IRD/UPMC UMMISCO, Bondy, Projet MASAIE INRIA Grand Est, France and LIRIMA, Projet GRIMCAPE, Cameroon. S. Bowong ( ) Laboratory of Applied Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, P.O. Box 24157 Douala, Cameroon e-mail: [email protected] S. Bowong · J. Kurths Postdam Institute for Climate Impact Research (PIK), Telegraphenberg A 31, 14412 Potsdam, Germany J. Kurths Department of Physics, Humboldt Universitat zu Berlin, 12489 Berlin, Germany demographic and epidemiological data in Cameroon. The simulation results are in good accordance with the seasonal variation of the reported cases of active TB in Cameroon.