Under the background that asymptomatic virus carriers have infectivity for an infectious disease, we establish a difference equations model with vaccination and virus testing in this paper. Assuming that the vaccine is 100% effective for susceptible people but cannot stop the infectivity of asymptomatic virus carriers, we study how to combine vaccination and virus testing at the beginning of an epidemic to effectively block the spread of infectious disease in different population sizes. By considering the daily processing capacity of the vaccine and daily proportion of testing, the corresponding numerical simulation results are obtained. It is shown that when vaccine availability and virus testing capacity are insufficient, a reasonable combination of the above two measures can slow down or even block the spread of infectious disease. Single virus testing or vaccination can also block the spread of infectious disease, but this requires a lot of manpower, material and financial resources. When the daily proportion of virus testing is fixed, the ratio of the minimum daily processing capacity of vaccines used to block the spread of infectious disease to the corresponding population size is rather stable. It demonstrates that effective protective measures of the same infectious disease in countries and regions with different population sizes can be used as a reference. These results also provide a certain reference for decision makers on how to coordinate vaccines and virus testing resources to curb the spread of such an infectious disease in a certain population size.
Keywords: difference equations model; population size; synergistic effects; vaccination; virus testing.