Study on the virulence evolution of SARS-CoV-2 and the trend of the epidemics of COVID-19

Abstract

This is the first attempt to investigate the effects of the factors related to non-pharmaceutical interventions (NPIs) and the physical condition of the public on virulence evolution of SARS-CoV-2 and the trend of the epidemics of COVID-19 under an adaptive dynamics framework. Qualitative agreement of the prediction on the epidemics of COVID-19 with the actual situations convinced the rationality of the present model. The study showed that enhancing both NPIs (including public vigilance, quarantine measures, and hospitalization) and the physical condition of the public (including susceptibility and recovery speed) contributed to decreasing the prevalence of COVID-19 but only increasing public vigilance and decreasing the susceptibility of the public could also reduce the virulence of SARS-CoV-2. Therefore, controlling the contact rate and infection rate was the key to control not only the epidemic scale of COVID-19 but also the extent of its harm. On the other hand, the best way to control the epidemics was to increase the public vigilance and physical condition because both of them could reduce the prevalence and case fatality rate (CFR) of COVID-19. In addition, the enhancement of quarantine measures and hospitalization could bring the (slight) increase in the CFR of COVID-19.

Keywords: COVID‐19; adaptive dynamics; compartment model; non‐pharmaceutical intervention; physical condition; virulence evolution.

FIGURE 1

Transmission diagram of COVID‐19 under NPIs

FIGURE 2

The effects of the factors related to NPIs on the virulence evolution of SARS‐CoV‐2: variation of evolutionary singularity with (A) contact rate‐related parameter $c_{\kappa }$; (B) quarantine rate q; and (C) hospitalization rate h as well as (D) the contour plot of evolutionary singularity varying with both h and $c_{\kappa }$. Parameters in (A) $c=30e^{-c_{\kappa }\alpha },q=0.9,h=0.9,{\beta }_I=\alpha /\left(14\alpha +0.218\right),{\beta }_E=\alpha /\left(70\alpha +0.218\right),{\gamma }_{I_f}=1/\left(5245\alpha +1.3\right),{\gamma }_{I_q}=1/\left(1049\alpha +1.3\right)$; (B) $c=30e^{-2\alpha }$, and others are the same as those in (A); (C) $c=30e^{-2\alpha }$, and others are the same as those in (A); and (D) $q=0.9$, and others are the same as those in (A) [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 3

The effects of the factors related to NPIs on the prevalence (the line in black) and CFR (dotted line in red) of COVID‐19: (A) contact rate‐related parameter $c_{\kappa }$; (B) quarantine rate q; and (C) hospitalization rate h. Parameters in (A) are the same as those in Figure 2A; (B) $c=30e^{-2\alpha },$ $h=0.9,{\beta }_I=\alpha /\left(40\alpha +0.218\right),{\beta }_E=\alpha /\left(200\alpha +0.218\right),{\gamma }_{I_f}=1/\left(5245\alpha +10\right),{\gamma }_{I_q}=1/\left(1049\alpha +10\right)$; (C) $q=0.9$, and others are the same as those in (B) [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 4

The effects of the factors related to the physical condition of the public on the virulence evolution of SARS‐CoV‐2: the contour plot of evolutionary singularity varying with (A) infection rate‐ and recovery rate‐related parameters $c_{{\beta }_I}$ and ${\kappa }_{\gamma }$; (B) the relative infection rate regulated by the physical condition of the public $c_{{\beta }_E}/c_{{\beta }_I}$ and $c_{{\beta }_I}$; and (C) the relative recovery rate $c_{{\gamma }_{I_f}}/c_{{\gamma }_{I_q}}$ regulated by medicine and ${\kappa }_{\gamma }$. Parameters in (A) $c=30e^{-2\alpha },q=0.4,h=0.4,{\beta }_I=\alpha /\left(c_{{\beta }_I}\alpha +0.218\right),{\beta }_E=\alpha /\left(c_{{\beta }_E}\alpha +0.218\right),{\gamma }_{I_f}=1/\left(c_{{\gamma }_{I_f}}\alpha +{\kappa }_{\gamma }\right),{\gamma }_{I_q}=1/\left(c_{{\gamma }_{I_q}}\alpha +{\kappa }_{\gamma }\right),c_{{\beta }_E}/c_{{\beta }_I}$ = 5, $c_{{\gamma }_{I_f}}/c_{{\gamma }_{I_q}}$ = 5, $c_{{\gamma }_{I_q}}$ = 1049; (B) ${\kappa }_{\gamma }=1.3$; and (C) $c_{{\beta }_I}=14,c_{{\beta }_E}=70$, and other parameters in (B) and (C) are the same as those in (A) [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 5

The effects of thefactors related to the physical condition of the public on the prevalence (solid line in black) and CFR (dotted line in red) of COVID‐19: (A) recovery rate‐related parameter ${\kappa }_{\gamma }$; (B) infection rate‐related parameter $c_{{\beta }_I}$. Parameters in (A) ${\beta }_I=\alpha /\left(250\alpha +0.218\right),{\beta }_E=\alpha /\left(1250\alpha +0.218\right)$, and other parameters are the same as those in Figure 4A; (B) ${\gamma }_{I_f}=1/\left(5245\alpha +10\right),{\gamma }_{I_q}=1/\left(1049\alpha +10\right)$, and other parameters are the same as those in Figure 4A [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE C1

Transmission diagram of COVID‐19 when considering the asymptomatic patients (orange parts) and the loss of immunity (magenta parts) [Colour figure can be viewed at wileyonlinelibrary.com]