Dynamic of a Two-strain COVID-19 Model with Vaccination

Abstract

COVID-19 is a respiratory illness caused by an RNA virus prone to mutations. In December 2020, variants with different characteristics that could affect transmissibility and death emerged around the world. To address this new dynamic of the disease, we formulate and analyze a mathematical model of a two-strain COVID-19 transmission dynamics with strain 1 vaccination. The model is theoretically analyzed and sufficient conditions for the stability of its equilibria are derived. In addition to the disease-free and endemic equilibria, the model also has single-strain 1 and strain 2 endemic equilibria. Using the center manifold theory, it is shown that the model does not exhibit the phenomenon of backward bifurcation, and global stability of the model equilibria when the basic reproduction number R 0 is either less or greater than unity as the case maybe are proved using various approaches. Simulations to support the model theoretical results are provided. We calculate the basic reproductive number for both strains R_1 and R_2 independently. Results indicate that - both strains will persist when both R 1 > 1 and R 2 > 1 - Stain 2 could establish itself as the dominant strain if R 1 < 1 and R 2 > 1, or when R 2 is at least two times R 1 . However, with the current knowledge of the epidemiology of the COVID-19 pandemic and the availability of treatment and an effective vaccine against strain 1, eventually, strain 2 will likely be eradicated in the population if the threshold parameter R 2 is controlled to remain below unity.

Modelling the transmission dynamics of a multi-strain SARS-CoV-2 epidemic with vaccination for an emerging strain

“…It, however, lacks some key elements like vaccination and waning immunity that have been incorporated in our model. We also included key compartments E 1 ,E 2 ,A 1 and A 2 missing in Sy et al [18] model formulation .…”

“…Vaccination, use of efficient face masks and social distancing are among the most useful non-pharmaceutical and therapeutic measures for controlling spread. Therefore, most of the recently developed models have incorporated these key features [15][16][17][18][19]. However, most SARS-CoV-2 epidemic models developed are single strain and among the few multi-strain models formulated, a number of them miss vaccination which is a major key factor for controlling spread of the virus [14,20,21].…”

“…To b e b est of our knowledge, only a few studies have fo cussed on multi-strain dynamics with vaccination [18]. Moreover, these also lack some major features of virus transmission like latent and asymptomatic infections among others [18].…”

“…To b e b est of our knowledge, only a few studies have fo cussed on multi-strain dynamics with vaccination [18]. Moreover, these also lack some major features of virus transmission like latent and asymptomatic infections among others [18]. Therefore, this study formulated am u l t i -s t r a i nS E I Rm o d e lw i t hv a c c i n a t i o na n di n c o r p o r a t e ds o m eo ft h em o s ti m p o r t a n t key features of SARS-CoV-2 disease transmission using a case study of Uganda.…”

An extended SEIARD model for COVID-19 vaccination in Mexico: analysis and forecast

“…Another model was studied in [14] to compare the outcomes of single-dose and two-dose anti-COVID vaccination regimes. The global stability of a two-strain COVID-19 model with vaccination against one strain was studied in [15]. In [16], the effect of immunity, vaccination, and reinfection with changing parameters was analysed using an SEVIS model, while in [17] an SIQRD model was used to simulate several scenarios of vaccine delivery in Indonesia.…”