Potential Spreading Dynamics of COVID-19 with Temporary Immunity: A Mathematical Modelling Study

Abstract

Background: The immune response to COVID-19 is currently unknown. Contemporary studies have found that the antibody titre levels in infected patients decrease over time. The recent discoveries of isolated but fully documented reinfection cases from around the world raise the question of what profile the epidemic trajectories may take if immunity were really to be temporary in a significant fraction of the population.Methods: We employ mathematical modelling to answer the above question. We construct a novel delay differential equation model tailored to accommodate different kinds of immune response. We consider two immune responses here : (a) where a recovered case becomes completely susceptible after a given time interval following infection and (b) where a first-time recovered case becomes susceptible to a lower virulence infection after a given interval following recovery, and becomes permanently immunized by a second infection.Findings: Possible solutions to the above model exhibit a large number of waves of disease with the first immune response and two to three waves with the second. These multiple wave solutions are manifest only for some intermediate values of the reproduction number R, which is governed by public health intervention measures. For sufficiently low as well as sufficiently high R, we find conventional single-wave solutions despite the short-lived immunity.Interpretation: Our results cast insight into the potential spreading dynamics of the disease and will also be useful for analysing the spread after a vaccine is invented, and mass vaccination programs initiated.Funding: None to report.Declaration of Interests: The authors have no conflict of interests.