Abstract
In the present paper, based on the conditions that asymptomatic virus carriers are contagious and all symptomatic infected individuals wear masks, we study the impact of wearing masks in the susceptible and the asymptomatic virus carriers on the spread of infectious diseases by developing a differential equation model. At first, we give the existence, uniqueness, boundedness, and positivity of the solution as well as the basic reproduction number R_{0} for the established model. Then, for two cases of wearing masks in the susceptible and the asymptomatic virus carriers where the proportion of wearing masks is fixed and the proportion of wearing masks changes with time, the results of the numerical simulation are shown in a series of pictures, and quantitative description of effects of the proportion of the population wearing masks, the protective effect of masks, and the time when they start wearing masks on the epidemic is given. Our results show that under the situation that the proportion of wearing masks is positively related to the confirmed new cases and new deaths, though the proportion will be close to 1 during the high incidence of patients, the effect on controlling the spread of such infectious diseases is far worse than the case of always maintaining a relatively higher proportion (≥0.66) of wearing masks.
Highlights
Emerging infectious diseases (EID) generally happen suddenly, spread rapidly, and have another characteristic of the high incidence of susceptibility crowd
Exported people of COVID-19 are contagious in the incubation period, which motivates us to study the effect of wearing masks in the susceptible and exported populations on the epidemic of this infectious disease
The numerical simulation results are shown which imply that when all the symptomatic infected individuals wear masks, and wearing masks could not reduce the probability of infection of the susceptible population if the proportion of wearing masks in the susceptible and exported populations is constant, as long as the masks are effective, the final number of the infected population and the death toll could be effectively reduced
Summary
Emerging infectious diseases (EID) generally happen suddenly, spread rapidly, and have another characteristic of the high incidence of susceptibility crowd. EID have become a key concern in the global public health field [1]. The infectious disease COVID-19 caused by a novel coronavirus which broke out at the end of 2019 in Wuhan, China, is different from the previous cases. It is contagious in the latent period, and its transmission speed is faster than that of other infectious diseases. Shao et al [3] and Lauer et al [4] point out the importance of asymptomatic virus carriers during the transmission of COVID-19. Backer et al [5] estimate the mean incubation period of COVID-19 virus by investigating the travel history and symp-
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