A model of COVID-19 pandemic with vaccines and mutant viruses

Abstract

This paper proposes a compartment model (SVEIHRM model) based on a system of ordinary differential equations to simulate the pandemic of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2).Emergence of mutant viruses gave rise to multiple peaks in the number of confirmed cases. Vaccine developers and WHO suggest individuals to receive multiple vaccinations (the primary and the secondary vaccinations and booster shots) to mitigate transmission of COVID-19. Taking this into account, we include compartments for multiple vaccinations and mutant viruses of COVID-19 in the model. In particular, our model considers breakthrough infection according to the antibody formation rate following multiple vaccinations. We obtain the effective reproduction numbers of the original virus, the Delta, and the Omicron variants by fitting this model to data in Korea. Additionally, we provide various simulations adjusting the daily vaccination rate and the timing of vaccination to investigate the effects of these two vaccine-related measures on the number of infected individuals. We also show that starting vaccinations early is the key to reduce the number of infected individuals. Delaying the start date requires increasing substantially the rate of vaccination to achieve similar target results. In the sensitivity analysis on the vaccination rate of Korean data, it is shown that a 10% increase (decrease) in vaccination rates can reduce (increase) the number of confirmed cases by 35.22% (82.82%), respectively.

A mathematical model of COVID-19 with multiple variants of the virus under optimal control in Ghana

“…The peak increases from the mild to average level, indicating there would be enough time to prepare before it reaches the peak. In other words, the infection curve flattened [ 39 ]. The effect is to delay the peak of infected individuals and postpone the eradication of the infectious disease.…”

“…COVID-19 has been recorded as one of the deadliest pandemics in human history, infecting more than 690 million people around the world and causing more than 6.9 million deaths [ 45 ]. It is well known from several studies [ 21 , 27 , 28 , 39 ] that implementing strong control strategies with quick decisions in the early stages of an outbreak prevents the explosive increase of the infected individuals. However, excessive control strategies put people into fatigue and limit their outdoor activities.…”

“…In advanced studies on multiple strains, Kim, Choi, and Min. [ 39 ] investigated a multi-strain epidemic model which was based on SEIR model to simulate the COVID-19 pandemic. Their model, the SVEIHRM model, consisted of multiple vaccinations and mutant viruses of COVID-19.…”

Mathematical assessment of the roles of age heterogeneity and vaccination on the dynamics and control of SARS-CoV-2

“…In the absence of vaccination, the effective reproduction number for the homogeneous model (3.1), denoted by , is given by ( Ngonghala, Iboi, Eikenberry, et al., 2020 ; Nishiura & Chowell, 2009 ): where is defined by (3.14) . Similarly, in the presence of vaccination, it follows, from ( Kim et al., 2022 ; Zhao, Musa, et al., 2020 ) and Equations (3.11) , (3.12) , that the effective reproduction number, denoted by , for the homogeneous model (3.1) is given by (where the basic reproduction number, , is given by (3.14) ): …”

Assessing potential surge of COVID-19 cases and the need for booster vaccine amid emerging SARS-CoV-2 variants in Indonesia: A modelling study from West Java

“…Some relied on modified compartmental SIR models to capture the dynamics of COVID-19 spread, later used for modelling-based inference for policymaking [ [10] , [11] , [12] ]. In response to vaccine availability issues, others reported their work in studying the impact of imperfect vaccine efficacy in the vaccine rollout strategy specific to certain regions [ [13] , [14] , [15] ]. Furthermore, some studies also incorporated the effect of vaccines and mutant viruses into the models [ 16 ].…”