This paper develops an analytical solution describing propagation of two viral waves in an axon and applies the obtained analytical solution to investigating the dynamics of merging of these two waves as they move retrogradely toward the neuron body. The viral diffusivity and viral degradation are accounted for in the model. Computational results are presented for two situations: when all dynein motors move with the same velocity and when dynein motor velocity distribution is characterized by a probability density function (pdf). The effect of various model parameters on the time it takes for the waves to merge is discussed. It is proposed that observing the dynamics of wave merging can be used for determining parameters characterizing viral transport, such as the viral diffusivity. This may contribute toward better understanding of viral transport properties and potentially help in developing novel viral detection techniques.