Since the novel coronavirus (COVID-19) has many kinds of surrounding function proteins,^[17] for the feasibility of calculation, here we choose three kinds of mainly proteins when building the physical model with a reasonably simplify. Similar to other discovered coronavirus such as SARS and MERS, the novel coronavirus (COVID-19) is firstly surrounded by some sparse spike glycoproteins as shown in Fig. 1. Then, under the spike glycoproteins, there is more than one layer of envelope proteins. Although there is still a fraction of hemagglutinin in this area to help fuse viruses to cells,^[18] in our physical model we pick the main envelop proteins as a representative. Inside the novel coronavirus, the nucleocapsid closely attach the RNA, both of them are wandering inside the virus together with a gap space. Considering the complexity of RNA space structure and randomness of RNA movement, hence in our physical model, we can treat them as nucleocapsid surround RNA in a uniform region. Constituent parts including spike glycoproteins, envelope, nucleocapsid and RNA are represented as M1, M2, M3, and M4, respectively. As reported by the Centers for Disease Control and Prevention (CDC), the COVID-19 is a large sized virus whose diameter is approximately 120 nm.^[19] Hence, in this study, the external/inner diameter of M1–M3 are set to be 120/100 nm, 100/80 nm, 60/50 nm, and the RNA(M4) is in the range of 50 nm diameter space.

Fig. 1.

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	Fig. 1. The novel coronavirus (COVID-19) 3D structure and its simplified physical structure model.

For molecular formulas of each constituent parts in the novel coronavirus, we pick and count typical gene sequences of three kinds of proteins and RNA of Wuhan patient from the National Center for Biotechnology Information (NCBI). The sequences of spike glycoproteins (M1) of COVID-19 are picked from Wuhan-Hu-1 (reference sequence: NC_045512.2),^[20] the sequences of envelope (M2), nucleocapsid (M3) and RNA (M4) are picked from Wuhan-Hu-1 (GenBank: MN908947.3).^[21] Table 1 denotes statistical results of 20 amino acid sequences of three kinds of proteins. The average molecular weight of three kinds of proteins (spike proteins (M1), envelope (M2), nucleocapsid (M3)) are 128.89, 131.19, and 124.42, respectively. The average molecular formula of three kinds of proteins (spike proteins (M1), envelope (M2), nucleocapsid (M3)) are , respectively.

Table 1.

Table 1.

Table 1. Statistical data of 20 amino acid sequences of three kinds of proteins from NCBI. . Amino acid Molecular formula Spike protein Envelope protein Nucleocapsid protein Number Proportion Average molecular weight Average molecular formula Number Proportion Average molecular weight Average molecular formula Number Proportion Average molecular weight Average molecular formula Glycine, G C2H5O2N1 82 6.94% 14 6.81% 43 10.64% Alanine, A C3H7O2N 79 6.71% 19 9.06% 37 9.23% Leucine, L C6H13O2N 108 8.98% 35 16.27% 25 6.40% Isoleucine, I C6H13O2N 76 6.47% 20 9.51% 14 3.80% Valine, V C5H11O2N 97 8.12% 12 5.91% 8 2.39% Proline, P C5H9O2N 58 5.06% 5 2.75% 28 7.10% Phenllalanine, F C9H11O2N 77 6.55% 11 5.45% 13 3.57% Methionine, M C5H11O2NS 14 1.60% C(4.9458) 4 2.30% C(5.2297) 7 2.15% C(4.6108) Tryptophan, W C11H12O2N2 12 1.44% H(9.6732) 7 3.65% H(10.203) 5 1.68% H(9.2925) Serine, S C3H7O3N 99 8.28% 128.89 O(2.4870) 15 7.26% 131.19 O(2.3514) 37 9.23% 124.42 O(2.4505) Glutamine, Q C5H10O3N2 62 5.37% N(1.1987) 4 2.30% N(1.2523) 35 8.75% N(1.3042) Threonine, T C4H9O3N 97 8.12% S(0.04242) 13 6.36% S(0.03604) 32 8.05% S(0.01651) Cysteine, C C2H7O2NS 40 3.64% 4 2.30% 0 0% Asparagine, N C4H8O3N 88 7.41% 11 5.45% 22 5.69% Tyrosine, Y C9H11O3N 54 4.74% 9 4.55% 11 3.09% Aspartic acide, D C4H7O4N 62 5.37% 6 3.20% 23 5.92% Glutamic acid, E C5H9O4N 48 4.27% 7 3.65% 12 3.33% Lysine, K C6H14O2N2 61 5.29% 7 3.65% 31 7.81% Arginine, R C6H14O2N3 42 3.80% 14 6.81% 29 7.34% Histidine, H C6H9O2N3 17 1.84% 5 2.75% 4 1.44%

Table 1. Statistical data of 20 amino acid sequences of three kinds of proteins from NCBI. .

Table 2.

Table 2.

Table 2. Statistical data of 4 nucleobase sequences of an original RNA from NCBI. . RNA Nucleobase Adenine Uracil Cytosine Guanine Molecular structure Molecular formula C5H5N5 C4H4O2N2 C4H5ON3 C5H5ON5 Number 8954 9594 5492 5863 Proportion 29.94% 32.08% 18.37% 19.61% Average molecular weight 126.46 Average molecular formula C4.50H4.68O1.02N3.67

Table 2. Statistical data of 4 nucleobase sequences of an original RNA from NCBI. .

When an incident electron irradiates inside COVID-19, a series of collision process between energetic electrons and the virus structure molecule will occur. Based on the energy loss situation, the collision process can be divided into elastic scattering process without energy loss and inelastic scattering process with energy loss.^[22] In this study, we calculate the elastic scattering process with Rutherford mode, and handle the inelastic scattering process with the fast secondary electron (FSE) mode. We should track each electron (including incident electron and generated secondary electron) until its energy depleted or outgoing from the virus surface with a Monte Carlo numerical simulation.

For elastic scattering process, it is necessary for us to obtain scattering angle during the collision between electron and atoms. Here we use the Rutherford mode to calculate the elastic scattering cross section

For the inelastic scattering process, we should consider not only the change of angle but also the transfer of energy.^[23] Based on the FSE mode, the inelastic scattering cross section when considered quantum spinning mechanism can be expressed as follows:

Apart from variation of direction, the energy of electron will transform during the inelastic scattering.^[24,25] Here we can use the continuous slowing down approximation (CSDA) method to calculate the energy loss in each step. The energy loss can be calculated by Bethe mode,

When electron incident virus, a series of Monte Carlo methods will judge what kind of scattering will occur in each collision based on random numbers and scattering feature.

Figure 2 shows the ionization situations in the COVID-19 sphere under two kinds of incident conditions, point irradiation and uniform irradiation. For better demonstrating the ionization feature, the default irradiated electron number is set to be 20000. The default incident electron primary energy is set to be 10 keV. Since the incident electrons and generated inner secondary electrons will occur in a series of inelastic ionization processes, the final ionization amount is much larger than the incident electron numbers. Form the point irradiation shown in Fig. 2(a), we can find that after suffering a string of collision processes, the intensity of ionization comes to be more divergency, while this tendency is equalized in the situation of uniform irradiation Fig. 2(b). In the broadside, the ionization intensity appears to be fewer because the electrons are easier to escape and thus lots of cascade collisions release.

Fig. 2.

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	Fig. 2. Atom-ionization 3D distribution in the COVID-19 sphere under point and uniform E-beam irradiation: (a) point irradiation, (b) uniform irradiation.

Each of inelastic scattering caused ionization will excite a pair of free electron and hole. Figure 3 denotes the excitation distribution in both irradiation direction z and virus sphere radial direction R. The E-beam incident condition is in default uniform irradiation. For Fig. 3(a), the irradiation point is at z = 60 nm, and the tendency of decrease in both ends can be explained by variation of valid cross-sectional volume.

Fig. 3.

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	Fig. 3. Excitation number distribution in irradiation direction z (a) and radial direction R (b).

As shown in radial direction in Fig. 3(b), we can intuitively obtain the ionization situation in every four areas. Since spike proteins sparsely distribute around the outermost shell, the ionization it suffered is not high as denoted in the M1 area. The major excitation occurs in M2 as denoted, which means the envelope layer suffers the most irradiation ionization. After skipping over a gap space, the nucleocapsid (M3) still suffers a high E-beam irradiation ionization, while the ionization of RNA (M4) rapid recedes with R in the central of virus COVID-19.

When the energetic electron exhibits inelastic scattering with an atom, a part of electron energy loss results in excitation of free-electron pairs, while another part of electron energy loss may transform to phonon which may lead to geometry structural damage. Hence, for accurately evaluating the influence of E-beam irradiation on virus, we should also investigate the characteristics of electron energy loss.

Figure 4(a) is the normalized electron energy loss spectrum in the whole COVID-19. Although the incident primary electron energy is as high as 10 keV, the mainly electron energy loss focused on 10 eV to 87 eV reaches as much as 78.4%. Hence, if a 10 keV incident electron depletes its energy within one virus, it needs about hundreds of inelastic scattering, which is scarcely possible for a ∼100-nm-diameter COVID-19. Since each electron energy loss does always comes from excitation of free electron and hole, the times of electron energy loss are much larger than the excitation number, as shown in Fig. 4(b). The overall tendency of distribution of energy loss times in radial direction is similar to the excitation number distribution, owing to high randomness and denseness, the curve of energy loss distribution is more smoothness.

Fig. 4.

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	Fig. 4. Normalized energy loss spectrum (a) and energy loss distribution in radial direction R (b).

Because of differences in molecular formula and space structure in the four areas, the energy loss spectrum and the total energy loss will appear to be different. Figure 5(a) is the normalized electron energy loss spectrum in M1, M2, M3 and M4 presented with black, red, blue and green dotted lines. From the energy loss spectrum curve of M2 in Fig. 5(a), we can find that its peak energy loss is larger than other three areas, which results in the double-peak curve in Fig. 4(a). A larger peak energy loss of M2 means that electron may lose more energy when across a unit length in envelope compared with others. After integrating all of loss energies in each area, the total energy loss in M1–M4 is shown in Fig. 5(b). Values of total energy loss in M1–M4 are . The envelope protein M2 suffers the most electron energy loss damage, while protects the RNA M4 suffer the least electron energy loss damage.

Fig. 5.

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	Fig. 5. Normalized energy loss spectrum (a) and the total energy loss (b) in the four areas.

Considering electrons with different energies may occur diverse collision processes, E-beam irradiation with different primary energy also has different impact on virus COVID-19. Figure 6 shows the atom ionization 3D distribution and the excitation number distribution under four different incident conditions: 1 keV, 5 keV, 10 keV, and 20 keV. Incident electron numbers of the four conditions are also set to be default 20000. We can find that when the incident energy is as low as 1 keV, the incident electrons can not reach all virus area, only the upper area appears to be of ionization. Most of the electron-hole excitation occurs in M2, and the electron irradiation damage can be resisted by envelope protein. When the incident energy rises to 5 keV, incident electrons can reach all of the virus area. As the incident energy keeps enhancing, the ionization number decreases and distribution shifts toward inner.

Fig. 6.

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	Fig. 6. Atom ionization 3D distribution and excitation number distribution in radial direction under different incident primary energies: (a) 1 keV, (b) 5 keV, (c) 10 keV, (d) 20 keV.

After integrating the energy loss in each area under different incident energies, in the major resistance area M2, the energy loss decreases with incident energy because a larger energy electron can more easily across the envelope layer, which also results in the total energy loss decreasing with incident energy when the incident energy is larger than 2 keV. As a core of virus, because under protects of multilayer, the energy loss of RNA M4 appears to be very weak when the incident energy is 1 keV. With the increase of incident energy, the energy loss in RNA M4 first enhances and then decreases. This is mainly because, on the one hand, a larger energy electron has more possibility to reach the RNA M4 area, on the other hand, a larger energy also has a longer mean free path that corresponds to less collision times. For COVID-19, when the incident electron energy is 2 keV, the damage resulted by collision energy loss reaches the maximum. We define the damage efficiency to be the ratio of the total loss energy in virus to the total incident energy, as shown in Fig. 7(b) with blue percentage. The damage efficiency when incident energy is 2 keV can still reach 55%.

Fig. 7.

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	Fig. 7. Energy loss in areas (a) and variation of total energy loss with irradiation energy (b).

Considering the exhausted COVID-19 always appears in the form of surrounding aerosol environment, we should analyze the resistance effects of surrounding environment on electron beam irradiation penetration. The surrounding aerosol is a suspension of fine airborne solid or liquid particles in gas whose typical layer thickness is less than several micrometers. Here we pick the liquid as the main component of surrounding environment.

Figure 8(a) shows the irradiated electron energy loss when across the surrounding layer in three different thickness situations: 100 nm, 500 nm and 1000 nm. Because of a longer layer thickness comes from a more collision process, the primary electron energy can be continuous dissipation, and the penetration loss spectrum appears to be flatter, such as 1000 nm situation. For the situation of a thinner surrounding layer, there are still a small amount of low energy penetration electrons, which are mainly exited secondary electrons near the edge. When the primary electron energy is 10 keV, the average penetration losses for the 100 nm, 500 nm and 1000 nm thick layers are 0.3983 keV, 1.8773 keV, and 3.9472 keV, respectively. Average penetration loss proportion defined as ratio of loss energy in primary energy linearly increases with layer thickness. Although a thicker layer results in a larger energy loss, the penetration electron number does not monotonously decreases with layer thickness for the generation of excited secondary electrons. As shown in Fig. 8(b), the penetration proportion reaches 1.008 in the case of layer thickness 100 nm, which means that the penetration electron number is larger than the incident electron number. When the layer thickness is larger than 1000 nm, the penetration proportion rapidly decreases. In industry, if the virus is pre-placed in a dry environment for evaporating the surrounding layer, the protection of surrounding layer on virus will be effectively suppressed.

Fig. 8.

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	Fig. 8. Electron penetration loss in COVID-19 surrounding environment: (a) penetration loss spectrum, (b) different surrounding layer thickness situations.