The Bats-Hosts-Reservoir-People (BHRP) transmission network model
The BHRP transmission network model was posted to bioRxiv on 19 January, 2020 [12]. We assumed that the virus transmitted among the bats, and then transmitted to unknown hosts (probably some wild animals). The hosts were hunted and sent to the seafood market which was defined as the reservoir of the virus. People exposed to the market got the risks of the infection (Fig. 1). The BHRP transmission network model was based on the following assumptions or facts: The bats were divided into four compartments: susceptible bats (SB), exposed bats (EB), infected bats (IB), and removed bats (RB). The birth rate and death rate of bats were defined as nB and mB. In this model, we set ɅB = nB × NB as the number of the newborn bats where NB refer to the total number of bats. The incubation period of bat infection was defined as 1/ωB and the infectious period of bat infection was defined as 1/γB. The SB will be infected through sufficient contact with IB, and the transmission rate was defined as βB.
The hosts were also divided into four compartments: susceptible hosts (SH), exposed hosts (EH), infected hosts (IH), and removed hosts (RH). The birth rate and death rate of hosts were defined as nH and mH. In this model, we set ɅH = nH × NH where NH refer to the total number of hosts. The incubation period of host infection was defined as 1/ωH and the infectious period of host infection was defined as 1/γH. The SH will be infected through sufficient contact with IB and IH, and the transmission rates were defined as βBH and βH, respectively.
The SARS-CoV-2 in reservoir (the seafood market) was denoted as W. We assumed that the retail purchases rate of the hosts in the market was a, and that the prevalence of SARS-CoV-2 in the purchases was IH/NH, therefore, the rate of the SARS-CoV-2 in W imported form the hosts was aWIH/NH where NH was the total number of hosts. We also assumed that symptomatic infected people and asymptomatic infected people could export the virus into W with the rate of μP and μ’P, although this assumption might occur in a low probability. The virus in W will subsequently leave the W compartment at a rate of εW, where 1/ε is the lifetime of the virus.
The people were divided into five compartments: susceptible people (SP), exposed people (EP), symptomatic infected people (IP), asymptomatic infected people (AP), and removed people (RP) including recovered and death people. The birth rate and death rate of people were defined as nP and mP. In this model, we set ɅP = nP × NP where NP refer to the total number of people. The incubation period and latent period of human infection was defined as 1/ωP and 1/ω’P. The infectious period of IP and AP was defined as 1/γP and 1/γ’P. The proportion of asymptomatic infection was defined as δP. The SP will be infected through sufficient contact with W and IP, and the transmission rates were defined as βW and βP, respectively. We also assumed that the transmissibility of AP was κ times that of IP, where 0 ≤ κ ≤ 1.
Fig. 1 Flowchart of the Bats-Hosts-Reservoir-People transmission network model
The parameters of the BHRP model were shown in Table 1.
Table 1 Definition of those parameters in the Bats-Hosts-Reservoir-People (BHRP) model
Parameter Description
nB The birth rate parameter of bats
nH The birth rate parameter of hosts
nP The birth rate parameter of people
mB The death rate of bats
mH The death rate of hosts
mP The death rate of people
1/ωB The incubation period of bats
1/ωH The incubation period of hosts
1/ωP The incubation period of people
1/ω’P The latent period of people
1/γB The infectious period of bats
1/γH The infectious period of hosts
1/γP The infectious period of symptomatic infection of people
1/γ’P The infectious period of asymptomatic infection of people
βB The transmission rate from IB to SB
βBH The transmission rate from IB to SH
βH The transmission rate from IH to SH
βP The transmission rate from IP to SP
βW The transmission rate from W to SP
a The retail purchases rate of the hosts in the market
μP The shedding coefficients from IP to W
μ’P The shedding coefficients from AP to W
1/ε The lifetime of the virus in W
δP The proportion of asymptomatic infection rate of people
κ The multiple of the transmissibility of AP to that of IP.