Immuno-epidemiological model of two-stage epidemic growth

¹ Department of Mathematics & Statistics, IIT Kanpur, Kanpur 208016, India.
² Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow 117198, Russia.
³ Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France.
⁴ INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France.

^* Corresponding author: malayb@iitk.ac.in

Received: 28 March 2020
Accepted: 6 April 2020

Abstract

Epidemiological data on seasonal influenza show that the growth rate of the number of infected individuals can increase passing from one exponential growth rate to another one with a larger exponent. Such behavior is not described by conventional epidemiological models. In this work an immuno-epidemiological model is proposed in order to describe this two-stage growth. It takes into account that the growth in the number of infected individuals increases the initial viral load and provides a passage from the first stage of epidemic where only people with weak immune response are infected to the second stage where people with strong immune response are also infected. This scenario may be viewed as an increase of the effective number of susceptible increasing the effective growth rate of infected.