Study of the human infectious safety model under the influence of SARS-CoV-2 on the example of the Perm Krai of the Russian Federation

In the new millennium, humanity is faced with infectious diseases that no one previously knew about. In the end of 2019, an outbreak of a new coronavirus infection occurred in the People’s Republic of China (PRC) with an epicenter in the city of Wuhan (Hubei Province). On February 11, 2020, the International Committee on the Taxonomy of Viruses assigned an official name to the infectious agent - SARS-CoV-2. According to the results of serological and phylogenetic analysis, coronaviruses are divided into four genera: Alphacoronavirus, Betacoronavirus, Gammacoronavirus and Deltacoronavirus. Currently, four seasonal coronaviruses (HCoV-229E, - OC43, -NL63 and -HKU1) are circulating among the world’s population, which are present year-round in the structure of ARI, and, as a rule, cause damage to the upper respiratory tract of mild and moderate severity, as well as two highly pathogenic coronaviruses-Middle East respiratory syndrome virus (MERS) and new coronavirus infection COVID-19. To develop a model of human resistance to the disease caused by the coronavirus family, the elements, links and ways of protecting the Human-Virus-Environment system were identified. The destructive functions of sixteen proteins of the SARS-CoV-2 strain are considered. Deterministic and statistical models of cells infection risk development have been developed. A parameterized system of human protection against coronavirus infection is proposed.


Introduction
One of the most important problems of 2019-2021 is the search for optimal methods for creating human protective functions against coronavirus affect. The use of system analysis methods is one of the promising ways to consider and solve the problems of fighting viral infection in conditions of uncertainty. Currently, about 40 species of viruses are known, united in 4 subfamilies. They have this name because of the structure of their outer shell in the form of a crown. Coronaviruses -viruses with a positive RNA (+RNA) chain, compared to other RNA viruses, have an exceptionally big genome and have a unique replication mechanism. Viral particles of the SARS-CoV-2 strain have a spherical shape with a diameter of 60-120 nm. The height of the protrusions is 9-12 nm.

Development of the Human-Virus-Environment (HVE) system model)
Currently, coronaviruses of acute respiratory syndrome SARS, in particular SARS-CoV-2, are particularly dangerous among viruses. When developing a vaccine against the coronavirus family, it is necessary to have a methodology for studying the characteristics and assessing human life state. To formalize the elements of the HVE system, we introduce the following sets (  The interrelations between system elements are defined by binary relations R (1), which can be understood as functional relations, preferences, sequences, and others that reflect the essence of the relationship of the HVE system elements:

ЕRH E H.
Binary relations can be decomposed into more complex ones with the introduction of an additional variable C, called state. We decompose the binary relations R into two subsets: a healthy (1) and an infected (2) cell. The cell, like any real system, functions under certain physiological conditions determined by the environment. In this case, system (1) is transformed as follows: The security of the HVE system and the state (C) of each element as a whole depend on their properties, changing during the life cycle of the HVE system The state of the HVE system is determined by the properties of the system elements (CV, CE, CH). The nature of changes in these properties during the life cycle of the HVE system, as a rule, worsens due to the aging of the cell and a decrease in protective abilities. Therefore, to build dependencies of real state changes in the HVE system, it is necessary to know some functionality that would determine the safe state of the HVE system and its properties: The state СV of destructive elements of coronaviruses affect the state of the CHVE system: D-, β-, J-, G-CoVs, that have specific chemical and biological properties; on the own state of the CH cell, which depends on the protective functions of the cell, climatogeographic features of human habitation and relations with animals -CE.

Study of the HVE system state assessment model
The state of the HVE system is described by a functionality that characterizes the state of elements arrays (4). Let's examine human safety in more detail. The state of human safety (CH) depends on the safety indicator of its own properties (ΘН); change in the safety indicator from the influence of coronaviruses (ΔΘH(V)); on change in the safety indicator depending on change in environmental parameters (ΔΘH(E)) and is determined by the formula Let's describe in more detail the elements of equation (5).
The intrinsic properties of the cell (ΘН) are determined by the susceptibility to destruction (modification) of nucleic acid elements that provide storage and transmission of genetic information (DNA and RNA) from the effects of coronavirus.
The general destructive functions of the SARS-CoV-2 coronavirus can be described by the function (7). Human safety against the effects of coronaviruses can be estimated by the formula (6).

Necessary and sufficient conditions for human infection with coronavirus
A necessary condition of transition from one state of HVE system to another is the presence of the coronavirus (CoV), and sufficient -given distance (x) to the hazard (coronavirus), the speed of epidemic spread (w) and time effects (W) (table 1).
Dangerous state of effect on the human immune system (the necessary is present (c), but there are no sufficient conditions)1 State of infectious process in the body (presence of the necessary (c) and sufficient conditions ( State of cell death (destruction of the nucleus, cell organelles and cell membrane) (presence of the necessary (c) and sufficient conditions (x,W, w)1  The interrelations between probabilistic states of the HVE system are presented in figure 3, which shows that the HVE system can go from a safe state (1) to dangerous state (2), infection state (3) and vice versa, while increasing the body's immune system, the cell prevents the penetration and reproduction of coronavirus. The transition from the infectious state to the state of cell death (4) is final, since the cell is destroyed and dies at this moment. The system of differential equations for the probability graph of states pi and transition coefficients Oij of the HVE system is shown in Figure 3.
The system of coefficients Oij describing the dynamics of SARS-CoV-2 influence in accordance with the Kolmogorov system of equations (Figure 3 The probability matrix of the human condition P is described by an array:  Fig. 3. Graph of the probability of states pi and transition coefficients Oij of the HVE system: safe (1), dangerous (2), infectious (3) and cell death (destruction) (4).
The formalization of the space of hazard parameters i of the CoV virus allows to assess the degree of safety of human infection: Thus, the total indicator for multiple virus sources is calculated as an arithmetic mean or equal to zero if at least one of the virus sources is dangerous:°°® Based on the sanitary and epidemiological norms in force on the territory of the Russian Federation, the minimum permissible distance between people x d =1.5 m is determined, the permissible exposure time W d is set by the employer based on the epidemiological situation in the region.
Using equations (10) and (11),it is possible to calculate the epidemiological level of safety in the studied region (province).

Statistical model of cell infection
Coronaviruses have some unique features in RNA transcription, protein composition, and assembly mechanisms. They penetrate into the cell by adsorptive endocytosis. After that, genomic RNA is attached to ribosomes, which leads to the synthesis of viral RNA- With the known laws of a random variable distribution, using the system of equations (14), it is possible to determine the probability of cell infection in order to take timely measures to prevent the protection of the population. To further simplify the calculations, we take as the defining equation the function of coronavirus presence c(t) and the argument of the equation Oc, which we take as the corresponding coefficients Oij of the transition matrix (8).

Influence of SARS-CoV-2 viral infection on the development of human disease
SARS-CoV-2 refers to the viruses of pulmonary pneumonia. Figure 4 shows reticular (fibrous) changes in the human lungs. Indirectly, SARS-CoV-2 affects other vital organs, cardiovascular pathology, myocardial infarction, renal failure can develop. At the next stage of research, we will select the coefficients of the matrix (8) taking into account the full-scale data on pandemic development on the example of the Perm Krai of the Russian Federation. Let's consider the dynamics of the pandemic development in the period from November 15 to December 15, 2020 on the example of the Perm Krai of the Russian Federation ( Figure 5). The number of deaths (state p4) is marked with a red line, the number of tests with a positive reaction (state p3) is marked with a blue line, the number of people cured (state p1) is marked with a green line. The article [11] shows approaches to the development of an express analyzer for the presence of SARS-CoV-2 antibodies using a solid-phase immunochromatographic method, which can also increase the detection of infected people in the Russian Federation.   Protection L should ensure that exposure to coronavirus hazards does not exceed the permissible values (Figures 8a, 8b, 8c). The safety of the HVE system according to the parameters of the source of coronaviruses danger will be ensured if the inequalities are met: The safety assessment of the HVE system for the i-th source of coronavirus danger, taking into account the protection coefficients, will be determined by the expression (13), taking into account the fulfillment of inequalities (14) of 2020 was calculated. A method for assessing the safety of the HVE system, taking into account the protection coefficients, has been developed. The use of the developed models in practice will reduce the risk of human disease, taking into account vaccination and other organizational and technical means of protection.