Background
Methods: model formulation and description
Parameter | Description |
---|---|
Λ
h
| Recruitment rate of human population |
Λ
v
| Recruitment rate of mosquito population |
μ
h
| Natural death rate of human population |
μ
v
| Natural death rate of mosquito population |
β
| Biting rate of the mosquito to humans |
𝜗
h
| Success rate of transmission of infective filariform larvae from mosquitoes to humans |
𝜗
v
| Success rate of microfilariae transmission from infected-acute and infected-chronic |
humans to susceptible mosquitoes | |
θ
| Accounts for reduced number of adult microfilariae in humans due to treatment and |
quarantine of the infected chronic individuals | |
α
h
| Progression rate of latent individuals to infected-acute individuals |
α
v
| Progression rate from exposed mosquitoes to infected mosquitoes |
κ
| Symptomatic rate of infected-acute individuals progressed to infected-chronic individuals |
n
| Number of screened infected-acute individuals by health personnel |
φ
| Treatment/prevention chemotherapy rate of the infected-acute individuals |
Results
Invariant region
Positivity of the state variables
Existence and stability of steady-state solutions
Local stability of the disease-free equilibrium
Global stability of the disease-free equilibrium
Existence of endemic equilibria
Sensitivity analysis and model simulations
Sensitive indices of \({\mathcal {R}_{0}}\)
Parameter | Value | Source | Parameter | Value | Source |
---|---|---|---|---|---|
μ
h
| 0.000039 |
Λ
h
| 2500 | ||
μ
v
| 0.1429 |
Λ
v
| 1000 | [30] | |
κ
| 10 | Assumed |
β
| 250 | [6] |
φ
| 0.7 | Assumed |
n
| 200 | [6] |
𝜗
h
| 0.01 | [6] |
𝜗
v
| 0.1 | [6] |
α
h
| 0.0238 | Assumed |
α
v
| 0.0555 | Assumed |
θ
| 0.0555 | [30] |
\(\mathcal {R}_{0}\)
| ||
---|---|---|
Parameter |
\(\Upsilon _{p}^{\psi }\)
| Sensitivity index |
Λ
h
|
\(-\frac {1}{2}\)
| -0.5 |
μ
v
|
\(\frac {1}{2} \left (\frac {\alpha _{v}}{\alpha _{v}+\mu _{v}}-3\right)\)
| -1.36013 |
Λ
v
|
\(\frac {1}{2}\)
| 0.5 |
κ
|
\(\frac {1}{2} \kappa \left (\frac {\theta }{\theta \kappa +\mu _{h}}-\frac {1}{\mu _{h}+\kappa +n \varphi }\right)\)
| 0.462806 |
β
| 1 | 1 |
φ
|
\(-\frac {n \varphi }{2 \left (\mu _{h}+\kappa +n \varphi \right)}\)
| -0.466545 |
n
|
\(-\frac {n \varphi }{2 \left (\mu _{h}+\kappa +n \varphi \right)}\)
| -0.466545 |
𝜗
h
|
\(\frac {1}{2}\)
| 0.5 |
𝜗
v
|
\(\frac {1}{2}\)
| 0.5 |
α
h
|
\(\frac {\mu _{h}}{2 \left (\alpha _{h}+\mu _{h}\right)}\)
| 0.0000819193 |
α
v
|
\(\frac {\mu _{v}}{2 \left (\alpha _{v}+\mu _{v}\right)}\)
| 0.360131 |
θ
|
\(\frac {\theta \kappa }{2 \theta \kappa +2 \mu _{h}}\)
| 0.49613 |