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Mathematical modelling based on the compartmental Susceptible – Exposed – Infected - Recovered (SEIR) model is proposed in this paper to study the pandemic outbreak. In addition, simulations from both the deterministic approach as well as the stochastic approach are implemented to validate the present study. Among each state, the transitions between different categories are simulated by using various graph models including the complete graph, the steady Erdos-Renyi graph, as well as the varying Erdos-Renyi graph. The related parameters for the SEIR model are chosen from available literature and the effect of some other factors such as the inflow or outflow of travellers in a city as well as the impact of vaccination rate is explored. Furthermore, the difference between the simulation results coming from the deterministic SEIR model and the stochastic SEIR one is examined to check the availability of the present simulation. It is found that, the stochastic simulation based on the complete graph is more consistent with the deterministic SEIR model.