A mathematical model for COVID‐19 pandemic—SIIR model: Effects of asymptomatic individuals

Masaki Tomochi, Mitsuo Kono

2020Journal of General and Family Medicine42 citationsDOI Open Access PDF

Abstract

A new mathematical model called SIIR model is constructed to describe the spread of infection by taking account of the characteristics of COVID-19 and is verified by the data from Japan. The following features of COVID-19: (a) there exist presymptomatic individuals who have infectivity even during the incubation period, (b) there exist asymptomatic individuals who can freely move around and play crucial roles in the spread of infection, and (c) the duration of immunity may be finite, are incorporated into the SIIR model. The SIIR model has the advantage of being able to explicitly handle asymptomatic individuals who are delayed in discovery or are extremely difficult to be discovered in the real world. It is shown that the conditions for herd immunity in the SIIR model become more severe than those in the SIR model; that is, the presence of asymptomatic individuals increases herd immunity threshold (HIT).

Topics & Concepts

Herd immunityAsymptomaticCoronavirus disease 2019 (COVID-19)PandemicEpidemic modelMedicineIncubation periodImmunitySevere acute respiratory syndrome coronavirus 2 (SARS-CoV-2)Asymptomatic carrier2019-20 coronavirus outbreakVirologyDemographyImmunologyDiseaseBiologyEnvironmental healthImmune systemInternal medicineVaccinationInfectious disease (medical specialty)IncubationPopulationOutbreakSociologyBiochemistryCOVID-19 epidemiological studiesMathematical and Theoretical Epidemiology and Ecology ModelsSARS-CoV-2 and COVID-19 Research