The Influence of Anthropogenic and Environmental Disturbances on Parameter Estimation of a Dengue Transmission Model
Abstract
:1. Introduction
2. Methods
2.1. Characteristics of the Study Area
2.2. Experimental Data
2.3. Mathematical Model and Control Actions
2.4. Parameter Estimation
- A.
- We fit one epidemic outbreak over 93 epidemiological weeks, without pulse-type inputs ( in Equation (2)), i.e., we assume that there were no external dynamics that could affect the mosquitoes population (no chemical control or environmental changes);
- B.
- We fit one epidemic outbreak over 93 epidemiological weeks, but with the addition of one pulse-type input, which describes an external change that perturbs the mosquito population through a chemical control ( in Equation (2)). Here, we estimated the parameters of the model and the pulse input together;
- C.
- We fit two epidemic outbreaks over 265 epidemiological weeks (covering 93 weeks of previous cases) and four pulse-type inputs: two positive inputs for two chemical control actions (, ) and two negative inputs (, ) for modeling an increase in mosquito mortality due to some favorable environmental conditions. In addition, in this case, we estimate simultaneously the four inputs and the model parameters.
2.5. Confidence Sub-Contour Box
2.6. Sensitivity and Uncertainty Analyses
3. Results
3.1. Parameter Estimations with Zero, One, and Four Pulse-Type Inputs
Case A (Zero Pulse Input) | Case B (One Pulse Input) | Case C (Four Pulse Inputs) | ||||||
---|---|---|---|---|---|---|---|---|
Factor | Biological Interval | Estimation Interval | Nominal Value | CSB | Nominal Value | CSB | Nominal Value | CSB |
- | (0, 30,000) | 17,000 | (13,000, 23,000) | 21,600 | (18,800, 24,900) | 9610 | (9590, 12,800) | |
- | (0, 30,000) | 3400 | (2400, 4300) | 13,200 | (11,000, 19,000) | 26,000 | (21,000, 35,000) | |
- | (0, 30,000) | 5400 | (3900, 7500) | 12,000 | (9700, 16,000) | 21,900 | (20,900, 22,100) | |
- | (10,000, 10,000,000) | 4,800,000 | (4,400,000, 5,600,000) | 3,400,000 | (2,700,000, 3,800,000) | 8,100,000 | (7,700,000, 10,000,000) | |
- | (100, 1200) | 1000 | (980, 1200) | 310 | (244, 336) | 320 | (280, 330) | |
- | (0, 100) | 0.150000 | (0.110000, 0.210000) | 13 | (12, 16) | 16 | (15, 22) | |
(0, 400,000) | (0, 450,000) | 358,000 | (343,000, 414,000) | 160,000 | (150,000, 190,000) | 180,000 | (170,000, 200,000) | |
- | (0, 100) | 0.28 | (0.21, 0.41) | 10 | (9, 13) | 22 | (21, 25) | |
(65, 165) | (20, 180) | 92 | (64, 120) | 46 | (38, 59) | 49 | (42, 58) | |
C | (6400, 95,000) | (6400, 340,000) | 120,000 | (95,000, 180,000) | 250,000 | (238,000, 290,000) | 231,000 | (199,000, 238,000) |
(0.6, 2.3) | (0, 2.3) | 0.120 | (0.099, 0.170) | 1.29 | (1.10, 1.43) | 1.48 | (1.28, 1.52) | |
- | (0, 1.3) | 0.0078 | (0.0056, 0.0101) | 0.90 | (0.84, 1.30) | 1.23 | (1.14, 1.25) | |
(0.05, 0.5) | (0, 1.6) | 0.42 | (0.32, 0.59) | 0.70 | (0.68, 0.88) | 0.86 | (0.83, 1.07) | |
(0.07, 3.22) | (0, 3.22) | 2.7 | (2.0, 3.9) | 1.53 | (1.45, 1.88) | 1.43 | (1.36, 1.67) | |
(0.1, 1) | (0, 1.7) | 0.497 | (0.415, 0.696) | 0.91 | (0.75, 0.97) | 0.905 | (0.902, 1.110) | |
(0, 1.4) | (0, 1.4) | 1.20 | (0.91, 1.75) | 0.54 | (0.44, 0.65) | 0.61 | (0.60, 0.66) | |
f | (0.4, 0.6) | (0.3, 0.7) | 0.39 | (0.29, 0.52) | 0.49 | (0.42, 0.50) | 0.506 | (0.449, 0.522) |
(0, 4) | (0, 4) | 0.040 | (0.032, 0.052) | 1.52 | (1.50, 1.60) | 2.02 | (2.01, 2.03) | |
(0.06, 0.3) | (0, 0.9) | 0.268 | (0.244, 0.270) | 0.449 | (0.449, 0.456) | 0.5360 | (0.5357, 0.5390) | |
(1, 1.6) | (1, 1.6) | 1.03 | (1.03, 1.07) | 1.44 | (1.44, 1.46) | 1.4770 | (1.4668, 1.4773) | |
(0.58, 0.88) | (0.4, 1.0) | 0.40 | (0.29, 0.51) | 0.634 | (0.630, 0.660) | 0.642 | (0.629, 0.643) | |
- | (0.00001, 0.0009) | 0.000021 | (0.000016, 0.000029) | 0.000228 | (0.000190, 0.000302) | 0.000748 | (0.000587, 0.000788) | |
(0, 4) | (0, 4) | 0.227 | (0.216, 0.249) | 1.43 | (1.39, 1.43) | 1.43 | (1.42, 1.44) | |
(0.7, 1.75) | (0.4, 1.8) | 0.400 | (0.290, 0.430) | 0.70 | (0.61, 0.72) | 0.48 | (0.45, 0.49) | |
(0.5, 1.75) | (0.3, 2.0) | 0.328 | (0.322, 0.381) | 1.69 | (1.65, 1.69) | 1.65 | (1.65, 1.67) | |
- | (0, 2) | - | - | 0.48 | (0.45, 0.57) | 0.69 | (0.62, 0.72) | |
- | (32, 38) | - | - | 35.60 | (35.00, 36.00) | 35.80 | (35.60, 36.80) | |
(0, 12) | (0, 12) | - | - | 9.7 | (7.9, 11.5) | 11.99 | (11.39, 12.25) | |
- | (−1.5, 0) | - | - | - | - | −0.46 | (−0.54, 0.45) | |
- | (120, 134) | - | - | - | - | 132 | (125, 145) | |
- | (0, 12) | - | - | - | - | 6 | (5, 7) | |
- | (−1.5, 0) | - | - | - | - | −0.712 | (−0.919, −0.709) | |
- | (210, 235) | - | - | - | - | 231 | (227, 233) | |
- | (0, 12) | - | - | - | - | 5.67 | (4.86, 5.86) | |
- | (0, 2) | - | - | - | - | 0.34 | (0.32, 0.36) | |
- | (240, 260) | - | - | - | - | 243 | (240, 246) | |
(0, 12) | (0, 12) | - | - | - | - | 11 | (10, 12) |
3.2. Estimation of a Sub-Contour Box for Nominal Parameters
3.3. SA: Parameters That Determine the Model Behavior
3.4. Simulation of Control Strategies
- Effect of positive and negative input amplitudes over the vector populations (aquatic and adult stages);
- Variation in pulse-type chemical control input parameters ( and , with j = {1,4});
- Human immunization (vaccination) as a pulse-type input similar to chemical control (see Section 2.3).
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Reproductive Number R 0 and Equilibrium
References
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Factors | Description | Factors | Description |
---|---|---|---|
E | Number of eggs | Oviposition rate | |
L | Number of larvae | C | Egg carrying capacity |
P | Number of pupae | Egg to larva transition rate | |
Number of susceptible mosquitoes | Egg mortality rate | ||
Number of exposed mosquitoes | Larva to pupa transition rate | ||
Number of infected mosquitoes | Larvae mortality rate | ||
Number of susceptible humans | Pupae to mosquito transition rate | ||
Number of exposed humans | Pupae mortality rate | ||
Number of infected humans | f | Fraction of females that emerges | |
Number of recovered humans | Transmission coefficient human-mosquito | ||
M | Total number of mosquitoes | Mosquito mortality rate | |
H | Total number of humans | Change in due to virus infection | |
Egg control input rate | Extrinsic incubation rate | ||
Larvae control input rate | Human mortality rate | ||
Pupae control input rate | Transmission coefficient mosquito-human | ||
Mosquito control input rate | Intrinsic incubation rate | ||
Vaccine control input rate | Human recovery rate | ||
Mosquito control pulse amplitude | |||
Mosquito control initial time | |||
Mosquito control pulse width |
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Catano-Lopez, A.; Rojas-Diaz, D.; Vélez, C.M. The Influence of Anthropogenic and Environmental Disturbances on Parameter Estimation of a Dengue Transmission Model. Trop. Med. Infect. Dis. 2023, 8, 5. https://doi.org/10.3390/tropicalmed8010005
Catano-Lopez A, Rojas-Diaz D, Vélez CM. The Influence of Anthropogenic and Environmental Disturbances on Parameter Estimation of a Dengue Transmission Model. Tropical Medicine and Infectious Disease. 2023; 8(1):5. https://doi.org/10.3390/tropicalmed8010005
Chicago/Turabian StyleCatano-Lopez, Alexandra, Daniel Rojas-Diaz, and Carlos M. Vélez. 2023. "The Influence of Anthropogenic and Environmental Disturbances on Parameter Estimation of a Dengue Transmission Model" Tropical Medicine and Infectious Disease 8, no. 1: 5. https://doi.org/10.3390/tropicalmed8010005