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This paper deals with the problem of modeling and parameter estimation of a deterministic model of tuberculosis (abbreviated as TB for tubercle bacillus). We first propose and analyze a tuberculosis model without seasonality that 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 new TB cases show seasonal fluctuations in many countries. Then, we extend the proposed TB model by incorporating seasonality. We propose a numerical study to estimate unknown parameters according to demographic and epidemiological data in Cameroon. Simulation results are in good accordance with the seasonal variation of the reported new cases of active TB in Cameroon. [ABSTRACT FROM AUTHOR]