Impact of reproduction number on the multiwave spreading dynamics of COVID-19 with temporary immunity: A mathematical model

Abstract

Objectives: The recent discoveries of phylogenetically confirmed COVID-19 reinfection cases worldwide, together with studies suggesting that antibody titres decrease over time, raise the question of what course the epidemic trajectories may take if immunity were really to be temporary in a significant fraction of the population. The objective of this study is to obtain an answer for this important question. Methods: We construct a ground-up delay differential equation model tailored to incorporate different types of immune response. We considered two immune responses: (a) short-lived immunity of all types, and (b) short-lived sterilizing immunity with durable severity-reducing immunity. Results: Multiple wave solutions to the model are manifest for intermediate values of the reproduction number R; interestingly, for sufficiently low as well as sufficiently high R, we find conventional single-wave solutions despite temporary immunity. Conclusions: The versatility of our model, and its very modest demands on computational resources, ensure that a set of disease trajectories can be computed virtually on the same day that a new and relevant immune response study is released. Our work can also be used to analyse the disease dynamics after a vaccine is certified for use and information regarding its immune response becomes available.

Keywords

• COVID-19 reinfection
• SEIRS-type delay model
• Simple and complex immune response
• Multiple wave solutions