Table 2 Models of the epidemic part ξ_{i, t} with assumptions made on interactions between the viruses with and without the climatic factors

1

λy_{i, t − 1} + τ_{i, k}x_{k, t − 1}

λy _{i, t − 1}

2

\( {\lambda y}_{i,t-1}+\phi \sum \limits_{j\ne i}{w}_{ji}{y}_{j,t-1}+{\tau}_{i,k}{x}_{k,t-1} \)

\( {\lambda y}_{i,t-1}+\phi \sum \limits_{j\ne i}{w}_{ji}{y}_{j,t-1} \)

3

λ_iy_{i, t − 1} + τ_{i, k}x_{k, t − 1}

λ _i y _{i, t − 1}

4

\( {\lambda}_i{y}_{i,t-1}+\sum \limits_{j\ne i}{w}_{ji}{\phi}_i{y}_{j,t-1}+{\tau}_{i,k}{x}_{k,t-1} \)

\( {\lambda}_i{y}_{i,t-1}+\sum \limits_{j\ne i}{w}_{ji}{\phi}_i{y}_{j,t-1} \)

5

λ_{i, t − 1}y_{i, t − 1} + τ_{i, k}x_{k, t − 1}

λ _{i, t − 1} y _{i, t − 1}

6

\( {\lambda}_{i,t-1}{y}_{i,t-1}+\sum \limits_{j\ne i}{w}_{ji}{\phi}_{i,t-1}{y}_{j,t-1}+{\tau}_{i,k}{x}_{k,t-1} \)

\( {\lambda}_{i,t-1}{y}_{i,t-1}+\sum \limits_{j\ne i}{w}_{ji}{\phi}_{i,t-1}{y}_{j,t-1} \)