State variables | Mosquito | Human |
Aquatic | | |
Susceptible | | |
Exposed | | |
Infectious adults | | |
Recovered | | |
Total adults | | |
In order to study the impact of control measures and limited resource on dengue transmission dynamics, we formulate a stage-structured dengue model. The basic investigation of the model, such as the existence of equilibria and their stability, have been proved. It is also shown that this model may undergo backward bifurcation, where the stable disease-free equilibrium co-exists with an endemic equilibrium. The backward bifurcation property can be removed by ignoring the disease-induced death in human population and the global stability of the unique endemic equilibrium has been proved. Sensitivity analysis with respect to $R_0$ has been carried out to explore the impact of model parameters. In addition, numerical analysis manifests that the more intensive control measures in targeting immature and adult mosquitoes are both effective in preventing dengue outbreaks. It is also shown that the earlier the control intervention begins, the less people would be infected and the earlier dengue would be eradicated. Even later epidemic prevention and control can also effectively reduce the severity of pandemic. Moreover, comprehensive control measures are more effective than a single measure.
Citation: |
Figure 2.
The time courses of
Figure 3.
Backward bifurcation diagram. Parameter values used are:
Figure 9.
The cumulative number of infected human hosts according to different control intervention time. Parameter values used when there is no intervention control measures are:
Figure 10.
The prevailing time according to different control intervention time. Parameter values used when there is no intervention control measures are:
Table 1. State variables
State variables | Mosquito | Human |
Aquatic | | |
Susceptible | | |
Exposed | | |
Infectious adults | | |
Recovered | | |
Total adults | | |
Table 2. Parameter definitions and values
Interpretation | Parameter | Range | Reference |
The maximum value of the recruitment | | [1e+10, 5e+10] | Assumed |
rate of viable mosquito eggs | |||
without intervention | |||
Biting rate (the average number of | [0.14, 0.24] | [23] | |
bites per mosquito per day) | |||
The duration of the whole cycle, | | | [24] |
from egg laying to an adult | |||
mosquito eclosion | |||
Mosquito incubation time | [2, 10] days | [23,25] | |
Natural death rate of immature | | [0.2, 0.75] | [15,23] |
mosquitoes | |||
Natural death rate of adult mosquitoes | | [0.02, 0.07] | [15,23] |
Density-dependent mortality rate of | | 0.01 | [15] |
immature mosquitoes | |||
Recruitment rate of human | | 454 | [21] |
Human life span | | 25000 days | [25] |
Human incubation time | 5 days | [25] | |
Human infection duration | 3 days | [25] | |
Human disease-induced death rate | | 0.001, 0.02 | [7,20] |
Transmission probability | | 0.75 | [25] |
(from vectors to human) | |||
Transmission probability | | 0.75 | [25] |
(from human to vectors) | |||
Progression rate from | | 0.01 | Assumed |
Intervention parameter for adult | | [0, 0.04] | Assumed |
mosquito death rate | |||
Intervention parameter for immature | | [0, 0.55] | Assumed |
mosquitoes death rate | |||
Intervention parameter for immature | | [0, | Assumed |
mosquitoes recruitment rate |
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