Effects of masks on the transmission of infectious diseases

• Published in: Advances in difference equations Vol. 2021; no. 1; p. 169
• Main Authors: Han, Lili, Pan, Qiuhui, Kang, Baolin, He, Mingfeng
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 18-03-2021; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Asymptomatic; Asymptomatic virus carriers; Basic reproduction number; Difference and Functional Equations; Differential equation model; Differential equations; Disease control; Duration of the epidemic; Functional Analysis; Infectious diseases; Masks; Mathematical models; Mathematical Models of Infectious Diseases; Mathematics; Mathematics and Statistics; Numerical results; Ordinary Differential Equations; Partial Differential Equations; Viruses; Basic reproduction number; Duration of the epidemic; Differential equation model; Asymptomatic virus carriers; Numerical results
• ISSN: 1687-1839; 1687-1847; 1687-1847
• DOI: 10.1186/s13662-021-03321-z

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.