Potential spreading dynamics of COVID-19 with temporary immunity - a mathematical modeling study

Shayak, B.; Sharma, M. M.

COVID-19 is caused by a hitherto nonexistent pathogen, hence the immune response to the disease is currently unknown. Studies conducted over the past few weeks have found that the antibody titre levels in the blood plasma of infected patients decrease over time, as is common for acute viral infections. Fully documented reinfection cases from Hong Kong, India, Belgium and USA, as well as credible to anecdotal evidence of second-time cases from other countries, bring into sharp focus the question of what profile the epidemic trajectories may take if immunity were really to be temporary in a significant fraction of the population. Here we use mathematical modeling to answer this question, constructing a novel delay differential equation model which is 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 time interval following recovery, and becomes permanently immunized by a second infection. We find possible solutions exhibiting large number of waves of disease in the first situation and two to three waves in the second situation. Interestingly however, 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. Our results cast insight into the potential spreading dynamics of the disease and might also be useful for analysing the spread after a vaccine is invented, and mass vaccination programs initiated.