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We formulate a general age-of-infection epidemic model with two pathways: thesymptomatic infections and the asymptomatic infections. We then calculate thebasic reproduction number $\mathcal{R}_0$ and establish the final sizerelation. It is shown that the ratio of accumulated counts of symptomaticpatients and asymptomatic patients is determined by the symptomatic ratio $f$which is defined as the probability of eventually becoming symptomatic afterbeing infected. We also formulate and study a general age-of-infection modelwith disease deaths and with two infection pathways. The final size relation isinvestigated, and the upper and lower bounds for final epidemic size are given.Several numerical simulations are performed to verify the analytical results.

An age-of-infection model with both symptomatic and asymptomatic infections