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Over the past two decades, epidemic spreading on complex network has been a vibrant and highly successful research avenue. The dynamics of epidemic spreading on signed networks has nonetheless received fairly little attention. Signed networks contain edges that are labeled as either positive or negative, in relation to their propensity to either accelerate or mitigate epidemic spreading. To that effect, we here propose a modified signed-susceptible-infectious-susceptible epidemiological model, which incorporates positive and negative transmission rates based on structural balance theory. We also consider dynamical transmission rates to determine the influence of structural balance on the dynamics of epidemic spreading. We use Erdős-Rényi random networks and Barabási-Albert scale-free networks, together with the Monte Carlo method, to determine the peak fraction of infected nodes and the epidemic …