This study modeled the spread of an influenza epidemic in the population of Oran, Algeria. We investigated the mathematical epidemic model, SEIR (Susceptible-Exposed-Infected-Removed), through extensive simulations of the effects of social network on epidemic spread in a Small World (SW) network, to understand how an influenza epidemic spreads through a human population. A combined SEIR-SW model was built, to help understand the dynamics of infectious disease in a community, and to identify the main characteristics of epidemic transmission and its evolution over time. The model was also used to examine social network effects to better understand the topological structure of social contact and the impact of its properties. Experiments were conducted to evaluate the combined SEIR-SW model. Simulation results were analyzed to explore how network evolution influences the spread of desease, and statistical tests were applied to validate the model. The model accurately replicated the dynamic behavior of the real influenza epidemic data, confirming that the susceptible size and topological structure of social networks in a human population significantly influence the spread of infectious diseases. Our model can provide health policy decision makers with a better understanding of epidemic spread, allowing them to implement control measures. It also provides an early warning of the emergence of influenza epidemics.

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