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Theory and Modern Applications

Table 1 Description of parameters of co-infection model (1)

From: A co-infection model of dengue and leptospirosis diseases

Parameter

Description

Π

Human recruitment rate

Ω

Dengue vector recruitment rate

Λ

Leptospirosis vector recruitment rate

\(\beta _{1}\)

Rate of transmissibility of leptospirosis b/n dengue infected human and leptospirosis vector contact

\(\alpha _{1}\)

Transmission rate from leptospirosis only infected to the susceptible human population

\(\alpha _{2}\)

Transmission rate from leptospirosis vector to susceptible human population

\(\delta _{1}\)

Disease induced death rate of human due to leptospirosis only

\(\delta _{2}\)

Disease induced death rate of animal due to leptospirosis only

\(\sigma _{1}\)

Dengue disease waning immunity

\(\sigma _{2}\)

Leptospirosis disease waning immunity

\(\sigma _{3}\)

Dengue–leptospirosis disease waning immunity

μ

Natural death rate of human population

\(\mu _{vd}\)

Natural death rate of dengue vector

\(\mu _{vl}\)

Natural death rate of leptospirosis vector

\(\rho _{1}\)

Transmission rate from dengue only infected human to susceptible dengue vector population

\(\rho _{2}\)

Transmission rate from leptospirosis only infected human to susceptible leptospirosis vector population

\(\gamma _{1}\)

Rate of recovery from dengue disease

\(\gamma _{2}\)

Rate of recovery from dengue disease

ε

Rate of recovery from dengue–leptospirosis co-infection diseases

ϱ

Mortality rate related to leptospirosis vector due to the disease