| Citation: |
Mugen Huang, Linchao Hu, Bo Zheng. COMPARING THE EFFICIENCY OF WOLBACHIA DRIVEN AEDES MOSQUITO SUPPRESSION STRATEGIES[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 211-230. doi: 10.11948/2019.211
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COMPARING THE EFFICIENCY OF WOLBACHIA DRIVEN AEDES MOSQUITO SUPPRESSION STRATEGIES
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Abstract
Wolbachia is an endosymbiotic bacterium which manipulates host reproduction by cytoplasmic incompatibility, and restrains the transmission of dengue virus in Aedes mosquitoes. A novel strategy for dengue control involves releasing Wolbachia infected males into nature to suppress wild Aedes mosquito population. We develop a model of delay differential equations, integrating larval density-dependent competition and diapausing eggs, to compare the efficiency of different suppression strategies. The global asymptotical stability of the complete suppression state identifies the releasing amount threshold ascertaining suppression. Based on the experimental data for Aedes albopictus population in Guangzhou, our simulations show that the mosquito density in the highest peak season can be reduced by more than $ 95\% $ when the number of released males is above the releasing threshold. The best time to initiate the suppression is in early March, lasting until the end of June, followed by the parallel releasing policy from July to November. However, the egg bank has neglectable effects on the control of dengue vector in Guangzhou. -
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References
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Mugen Huang, Linchao Hu, Bo Zheng. COMPARING THE EFFICIENCY OF WOLBACHIA DRIVEN AEDES MOSQUITO SUPPRESSION STRATEGIES[J]. Journal of Applied Analysis & Computation, 2019, 9(1): 211-230. doi: 10.11948/2019.211
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Figure 1.
$ E_0 $ is globally asymptotically stable for (1.4) when$ \bar{R}\ge\bar{\alpha}(\sqrt{\bar{\alpha}b}-1)^2 $ . Take$ R = 8200 $ ,$ \phi(t) = 5000 $ and$ \psi(t) = 100 $ for$ t\in [-30, 0] $ , and all other parameters as in (3.2). -
Figure 2. Monthly changes of natural Aedes albopictus larvae and adults in Guangzhou. The two curves are simulated numerically by Equations (1.2) with
$ R = 0 $ ,$ K_L = 500 $ , the initial data$ \phi(t) = 5000 $ and$ \psi(t) = 100 $ for$ t\in [-35, 0] $ , and all the other parameters as in Table 2. -
Figure 3. Wolbachia can suppress wild Aedes albopictus population successfully with different released number vectors. With the same initial data and parameter values as in Fig. 2, the suppression rate
$ \gamma=10.49\% $ for$ \Re=(8200, 1200, 9500, 100, 150) $ ,$ \gamma=4.83\% $ for$ \Re=(12000, 1600, 14000, 100, 0) $ ,$ \gamma=4.92\% $ for$ \Re=(9800, 2500, 10000, 100, 0) $ , and$ \gamma=4.90\% $ for$ \Re=(5800, 5800, 5800, 0, 0) $ . -
Figure 4. Comparison of different suppression strategies with similar suppression efficiency. With the same initial data and parameter values as in Fig. 2, the suppression rate
$ \gamma = 4.90\% $ for$ \Re = (5800, 5800, 5800, 0, 0) $ , and$ \gamma = 4.95\% $ for$ \Re = (4000, 6500, 6800, 100, 0) $ for fixed releasing policy, and$ \gamma = 4.97\% $ for$ \Upsilon = (3.85, 3.85, 3.85, 0, 0) $ , and$ \gamma = 4.96\% $ for$ \Upsilon = (2, 3.55, 4.8, 0.3, 0) $ for parallel releasing policy. - Figure 5. The influence of egg bank on the dynamics of natural Aedes albopictus population in Guangzhou. With the same initial number of adults and parameter values as in Fig. 2, the influence on the dynamics of wild Aedes albopictus population of the initial number of larvae mainly focus on the first two periods.
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Figure 6. The influence of egg bank on the suppression dynamics of Aedes albopictus population in Guangzhou. With the initial data
$ \phi(t) = 50000 $ and$ \psi(t) = 100 $ for$ t\in [-35, 0] $ , and all other parameter values as in Fig. 2, the suppression rates$ \gamma_1 = 74.55\% $ and$ \gamma_2 = 4.95\% $ for$ \Re = (20000, 20000, 20000, 200, 0) $ , and$ \gamma_1 = 4.97\% $ and$ \gamma_2 = 3.78\% $ for$ \Re = (7500000, 2000, 2000, 200, 0) $ .