Table 2 Description of parameters and values used for the multi-serotype dengue model (2.4)–(2.5)

\(\varPi _{{H}} \)

Recruitment rate of human

100 people per day

–

–

\(\varPi _{{V}}\)

Recruitment rate of mosquito

11,690 mosquitoes per day

–

–

\(1/\mu _{{H}}\)

Natural death rate of human

70 years

[50–70]

[29]

\(1/\mu _{{V}} \)

Natural death rate of mosquito

14 days

[8–42]

[53]

\(\delta _{{i}}\)

Disease-induced death rate for infected human with serotype-i

\(\delta _{{1}} = 0.00031\)\(\delta _{{2}} = 0.00063\)

[0.05,0.32]

[59]

\(1/\sigma _{{i}}\)

Rate at which infected human with serotype-i becomes infectious

\(1/\sigma _{{1}}=5.7\) days \(1/\sigma _{{2}}=5.4\) days

[4–10]

[60]

\(1/\gamma _{{i}} \)

Recovery rate from serotype-i

\(1/\gamma _{{1}}=7.9\) days \(1/\gamma _{{2}}=7\) days

[4–12]

[53]

\(1/\sigma _{{Vi}}\)

Rate at which infected mosquito with serotype-i becomes infectious

\(1/\sigma _{{V1}}=10.9\) days \(1/\sigma _{{V2}}=8\) days

[6–12]

[53]

1/λ

Cross immunity between serotypes

3 months

[2–24]

[53, 54]

\(\eta _{{Hi}}\)

Modification parameters with serotype-i

\(\eta _{{H1}}=\eta _{{H2}}=0.0072 \)

[0–1]

[20]

\(\beta _{{i}}\)

Transmission probability rate from infected mosquito with serotype-i to susceptible human

\(\beta _{{1}}=1.320\times 10^{-6}\)\(\beta _{{2}}=1.3080\times 10^{-6}\)

(0,1)

–

\(\beta _{{Vi}}\)

Transmission probability rate from infected human with serotype-i to susceptible mosquito

\(\beta _{{V1}}=9.59\times 10^{-6}\)\(\beta _{{V1}}=9835\times 10^{-6}\)

(0,1)

–

b

Biting rate

0.68 per day

[0.33–1]

[53]

\(\alpha _{H} \)

Inhibitory effect for human

8.648 × 10⁻⁵

(0,1)

[30]

\(\alpha _{V} \)

Inhibitory effect for mosquito

1.3405 × 10⁻⁶

(0,1)

[30]