Dynamics of a Dengue Transmission Model with Multiple Stages and Fluctuations
Abstract
:1. Introduction
2. Model Formulation
3. Survival Analysis of Infective Mosquitoes and Infective Human Beings
3.1. Fitness
3.2. Persistence in the Mean
3.3. Existence of a Unique Stationary Distribution
3.4. Extinction
4. Sensitivity Analysis and Numerical Simulations
4.1. Sensitivity Analysis of Main Parameters
4.2. Persistence in the Mean
4.3. Extinction
4.4. Application of Dengue in Fuzhou City
5. Conclusions and Discussion
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Variable | Definition |
---|---|
A | Number of aquatic mosquitoes |
Number of susceptible mosquitoes with no dengue infection | |
Number of infective mosquitoes | |
Number of susceptible human beings | |
Number of infective human beings | |
Number of recovered human beings |
Parameter | Unit | Definition | Range | Source |
---|---|---|---|---|
dimensionless | Constant recruitment rates of aquatic mosquitoes | / | ||
dimensionless | Constant recruitment rates of human beings | / | ||
Death rate of aquatic mosquitoes | [21] | |||
Maturity proportion of aquatic mosquitoes | [26] | |||
Death rate of adult mosquitoes | [22] | |||
Average recovery time in human population | [21] | |||
b | Average biting rate | / | ||
dimensionless | Probability of dengue virus transmitted from to | [22] | ||
dimensionless | Probability of dengue virus spread from to | [22] | ||
Death rate of human beings | [10,38] |
Parameter | (I) | (II) | (III) | (IV) | ||||
---|---|---|---|---|---|---|---|---|
Value | Source | Value | Source | Value | Source | Value | Source | |
2000 | Fitted | 100 | Fitted | 2000 | Fitted | 1,800,000 | Fitted | |
(0, 0.06] | Fitted | 0.05 | [22] | 0.03 | [22] | Fitted | ||
b | Fitted | Fitted | Fitted | Fitted | ||||
0 | Fitted | 0 | Fitted | 0 | Fitted | [2] | ||
(0.01, 0.6] | Fitted | 0.01 | [21] | 0.01 | [21] | 0.01 | [21] | |
0.1428 | [21] | 0.1428 | [21] | 0.1428 | [21] | 0.1428 | [21] | |
0.75 | [22] | 0.6 | [22] | 0.75 | [22] | 0.7 | [22] | |
0.5 | [22] | 0.5 | [22] | 0.4 | [22] | 0.5 | [22] | |
0.3 | [26] | 0.1 | [26] | [0.1, 0.7] | Fitted | 0.2 | [26] | |
[10] | [10] | [10] | [38] | |||||
0.56 | Fitted | 100 | Fitted | 0.56 | Fitted | [38,54] |
Variable | (I) | (II) | (III) | (IV) |
---|---|---|---|---|
40,000 | 20,000 | 40,000 | 9,000,000 | |
20,000 | 20,000 | 20,000 | 10,000,000 | |
1,000 | 10 | 1,000 | 15 | |
15,000 | 15,596 | 15,000 | 8,291,266 | |
150 | 2 | 150 | 2 | |
0 | 0 | 0 | 0 |
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Wang, Z.; Cai, S.; Chen, G.; Zheng, K.; Wei, F.; Jin, Z.; Mao, X.; Xie, J. Dynamics of a Dengue Transmission Model with Multiple Stages and Fluctuations. Mathematics 2024, 12, 2491. https://doi.org/10.3390/math12162491
Wang Z, Cai S, Chen G, Zheng K, Wei F, Jin Z, Mao X, Xie J. Dynamics of a Dengue Transmission Model with Multiple Stages and Fluctuations. Mathematics. 2024; 12(16):2491. https://doi.org/10.3390/math12162491
Chicago/Turabian StyleWang, Zuwen, Shaojian Cai, Guangmin Chen, Kuicheng Zheng, Fengying Wei, Zhen Jin, Xuerong Mao, and Jianfeng Xie. 2024. "Dynamics of a Dengue Transmission Model with Multiple Stages and Fluctuations" Mathematics 12, no. 16: 2491. https://doi.org/10.3390/math12162491
APA StyleWang, Z., Cai, S., Chen, G., Zheng, K., Wei, F., Jin, Z., Mao, X., & Xie, J. (2024). Dynamics of a Dengue Transmission Model with Multiple Stages and Fluctuations. Mathematics, 12(16), 2491. https://doi.org/10.3390/math12162491