The impact of multiple population-wide testing and social distancing on the transmission of an infectious disease

Under the background that asymptomatic virus carriers are contagious and the virus in the infected individuals has mild pathogenicity and enhanced transmissivity for an infectious disease, the phenomenon appears that the majority of infected people do not show any symptoms, but can infect others. Multiple population-wide testing can screen out asymptomatic virus carriers in time. Thus, we develop an infectious disease transmission dynamics model that includes three stages: non-testing period, testing period and testing interval, with multiple population-wide testing and social distancing to study the effects of the first testing time, total testing number, and testing interval time on the transmission of infectious diseases in this paper. The existence, uniqueness, boundedness and positivity of the solution, as well as the formulas of the basic reproduction number and the control reproduction number of the established model are established The numerical results show that the earlier the population-wide testing measure is implemented, the fewer the final size and necessary testing frequency. In the initial stage of the larger-scale spread of infectious disease, the existing virus carriers are not the most. But if population-wide testing measure is implemented during this period, the strongest testing force is required to contain the spread of the epidemic. Besides, population-wide testing combined with restrictive social distancing will significantly reduce the final size, necessary testing frequency, and duration of the epidemic. The testing interval time should be no longer than the incubation period of the virus to prevent and control the epidemic accurately. Therefore, the paper provides a theoretic basis for developing and implementing scientific testing strategies.