Mathematical modeling analysis reveals critical spreading speed thresholds in populations with asymptomatic transmission, highlighting key drivers of epidemic expansion.
Many infectious diseases have the characteristics that recovered individuals may still be reinfected, asymptomatic carriers are infectious, and the infection rate is a nonlinear function. In this paper, we introduce a susceptible-asymptomatic-infectedrecovered- susceptible (SAIRS) model with nonlinear incidence to clarify the spreading dynamics of such infectious diseases. By ingeniously constructing an operator and its invariant region, we determine the threshold parameter R 0 (referred to as the basic reproduction number) and the critical spreading speed c * (referred to as the minimum wave speed) of a traveling wave solution. From this, we obtain the conditions expressed by system parameters for the spread from an initial disease-free state to an epidemic. It has been theoretically proved that the spreading speed is a key factor for an infectious disease to become an epidemic.
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Tang et al. (2026) studied this question.
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