Dynamics and Simulations of Impulsive Population Models Involving Integrated Mosquito Control Strategies and Fractional Derivatives for Dengue Control
Abstract
1. Introduction
- Integrated mosquito management. Traditional chemical pesticide control and Wolbachia-based biological control each has its distinct advantages and disadvantages. Integrated mosquito management that combines the advantages of both approaches is beneficial for quickly and effectively controlling mosquito populations and the transmission of dengue fever. However, current studies on population replacement strategies for controlling mosquitoes or dengue transmission mostly only consider Wolbachia control, while neglecting integrated mosquito management.
- Population replacement with low total mosquito amount. Introducing Wolbachia into wild mosquitoes has the potential to decrease their capacity for transmitting the dengue virus. Nevertheless, the replacement of wild mosquitoes with Wolbachia mosquitoes can cause annoying mosquito bites and the potential risk of transmitting other mosquito-borne viruses. Therefore, during dengue outbreak seasons, it is desirable to achieve population replacement while keeping the overall mosquito population at a lower threshold, or even aiming for eradication. Moreover, the combination of releasing Wolbachia-carrying mosquitoes and spraying insecticide may help to realize the mentioned control objective. Based on a single Wolbachia-based biological control approach, this work aims to further explore integrated mosquito management through modeling. To this end, an integer-order impulsive differential model is proposed to depict the periodic use of insecticides and explore the dynamics of the spread of Wolbachia in wild mosquito populations. We will investigate the threshold dynamics of periodic solutions and the effects of control parameters on strategies for mosquito eradication and replacement.
- Mosquito memory effects. Mosquitoes serve as the vectors for dengue virus transmission, and due to memory effects related to past environmental resources and climate changes throughout their life cycle, their behaviors—such as mating, blood-feeding, and oviposition—may change. These behavioral changes can influence mosquito control strategies. However, most current modeling studies on the spread of Wolbachia in mosquito populations overlook the memory factors within the mosquito life cycle and their effects on mosquito dynamics and control strategies. To further investigate the impact of mosquito memory factors on strategies for mosquito eradication and replacement, we will extend the established integer-order impulsive differential equation model to a Caputo fractional-order impulsive model. We will numerically examine the impact of varying orders on the periodic solutions of the system and the performance of the two control strategies.
2. Model Formulation and Dynamical Analysis
2.1. Model Formulation
2.2. Stability and Permanence Analysis
3. Simulations
3.1. Sensitivity Analysis
3.2. Effectiveness of Pulse-Spraying Insecticide on Control Strategies
3.3. Impacts of Mosquito Memory on the Two Control Strategies
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Definition | Value (Range) | Unit | Source |
---|---|---|---|---|
The ratio of natural birth rates of W to wild mosquitoes, | 0.9 [0.5, 1] | N/A | [5] | |
The ratio of death rates of W to wild mosquitoes, | 1.1 [0, 2] | N/A | [5,33] | |
Natural birth rate of wild mosquitoes | 0.4 [0.25, 0.76] | [20,33] | ||
Natural birth rate of W mosquitoes | 0.36 [0.13, 0.76] | [20,33] | ||
d | Density-dependent mortality rate of mosquitoes | [20,33] | ||
Maternal inheritance rate | N/A | [20,33] | ||
Fitness cost of W mosquitoes, | [20,33] | |||
q | CI intensity | 0.9 [0.6, 1] | N/A | [24] |
T | Pulse period of spraying insecticide | 4 [2, 15] | day | Assumed |
Insecticide killing rate of wild mosquitoes | 0.8 [0.4, 1] | N/A | Assumed | |
Insecticide killing rate of W mosquitoes | 0.8 [0.4, 1] | N/A | Assumed |
Parameter | d | q | T | ||||||
---|---|---|---|---|---|---|---|---|---|
PRCCs | |||||||||
p-values | 0 | 0 | 0 | 0 | 0 |
Scenarios | Strategy | RST | No. of | No. of | No. of | Repl. Level | |
---|---|---|---|---|---|---|---|
, (low fecundity of individuals) | Erad. | 85 | 0 | 0 | 0 | / | |
70 | |||||||
Erad. | 190 | 0 | 0 | 0 | / | ||
140 | |||||||
Repl. | 275 | 26 | 113 | 139 | |||
155 | 4 | 18 | 22 | ||||
, (high fecundity of individuals) | Repl. | 165 | 998 | 4798 | 5796 | ||
155 | 157 | 1437 | 1594 | ||||
Repl. | 90 | 499 | 2317 | 2766 | |||
85 | 78 | 693 | 771 | ||||
Repl. | 50 | 207 | 937 | 1144 | |||
50 | 32 | 280 | 312 |
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Zhang, X.; He, H.; Wang, K.; Zhu, H. Dynamics and Simulations of Impulsive Population Models Involving Integrated Mosquito Control Strategies and Fractional Derivatives for Dengue Control. Fractal Fract. 2024, 8, 624. https://doi.org/10.3390/fractalfract8110624
Zhang X, He H, Wang K, Zhu H. Dynamics and Simulations of Impulsive Population Models Involving Integrated Mosquito Control Strategies and Fractional Derivatives for Dengue Control. Fractal and Fractional. 2024; 8(11):624. https://doi.org/10.3390/fractalfract8110624
Chicago/Turabian StyleZhang, Xianghong, Hua He, Kaifa Wang, and Huaiping Zhu. 2024. "Dynamics and Simulations of Impulsive Population Models Involving Integrated Mosquito Control Strategies and Fractional Derivatives for Dengue Control" Fractal and Fractional 8, no. 11: 624. https://doi.org/10.3390/fractalfract8110624
APA StyleZhang, X., He, H., Wang, K., & Zhu, H. (2024). Dynamics and Simulations of Impulsive Population Models Involving Integrated Mosquito Control Strategies and Fractional Derivatives for Dengue Control. Fractal and Fractional, 8(11), 624. https://doi.org/10.3390/fractalfract8110624