In this research, an SEIV epidemic model with vaccination, horizontal and vertical transmission, and nonlinear incidence rate is formulated. Local stability and bifurcation analysis in this model is presented in terms of the basic reproduction number R0. This model exhibits a backward bifurcation possibility, that is, the appearance of two endemic equilibria although the basic reproduction number R0 is less than the threshold 1.
                        
                        
                        
                        
                            
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