# Modelling Anopheles gambiae s.s. Population Dynamics with Temperature- and Age-Dependent Survival

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Model Structures and Parameterisation

**Table 1.**Average duration (in days) of egg, larval, and pupal stages at water temperature Tw according to Parham et al. [69], with corrected coefficients.

Parameter | Functional Form for Average Stage Duration |
---|---|

d_{E} (eggs) | $\left(1.011+\frac{20.212}{1+{\left(Tw/12.096\right)}^{4.839}}\right)$ |

d_{L} (larvae) | $\left(8.13+\frac{13.794}{1+{\left(Tw/20.742\right)}^{8.946}}\right)-\left(1.011+\frac{20.212}{1+{\left(Tw/12.096\right)}^{4.839}}\right)$ |

d_{P} (pupae) | $\left(8.56+\frac{20.654}{1+{\left(Tw/19.759\right)}^{6.827}}\right)-\left(8.13+\frac{13.794}{1+{\left(Tw/20.742\right)}^{8.946}}\right)-\left(1.011+\frac{20.212}{1+{\left(Tw/12.096\right)}^{4.839}}\right)$ |

**Table 2.**Model parameters and parameter values. Parameters marked

*****were inferred as described below.

Parameter | Definition | Unit | Prior | Posterior |
---|---|---|---|---|

q | Proportion of adult females laying eggs | − | 0.61 − 0.85 [65] | * |

n(T_{a}) | Number of eggs laid per female | − | −1.1057 Ta^{2} + 56.208 Ta – 662.1 [65] | |

ρ(T_{w}) | Proportion of eggs hatching | − | −0.0034 Tw^{2} + 0.1719 Tw – 1.248 [65] | |

μ_{E} | Per capita egg mortality rate | days^{−1} | 0.32 − 0.8 [10,70] | * |

μ_{L} | Per capita age-dependent larval mortality rate | days^{−1} | 1/α_{L}β_{L} | |

μ_{LC} | Per capita age-independent larval mortality rate | days^{−1} | 0.0013 Tw^{2} − 0.0704 Tw + 0.9581 | |

μ_{P} | Per capita pupal mortality rate | days^{−1} | 0.25 [11] | |

μ_{A} | Per capita age-dependent adult mortality rate | days^{−1} | 1/α_{A}β_{A} | |

μ_{AC} | Per capita age-independent adult mortality rate | days^{−1} | (5.37 × 10^{−5}) e ^{0.228Ta} | |

μ_{K} | Per capita density- (and rainfall-) dependent larval mortality rate | days^{−1} | ${\text{\mu}}_{C}{\displaystyle \sum _{i=1}^{7}{L}_{i}}/K$ [11] | |

μ_{C} | Constant | days^{−1} | 0–10,000 | * |

K | Carrying capacity | − | [11] | |

τ | Days of rainfall contributing to carrying capacity | days | <10 [11] | * |

α_{L} | Shape parameter of larval gamma hazard function | − | ||

β_{L} | Scale parameter of larval gamma hazard function | days | −0.0112 Tw^{2} + 6.0775 Tw – 6.709 | |

α_{A} | Shape parameter of adult gamma hazard function | − | 3 | |

β_{A} | Scale parameter of adult gamma hazard function | days | 171.26 e^{−0.1191Ta} | |

σ_{E} | Per capita egg development rate | days^{−1} | 1/d_{E} [68] | |

σ_{L} | Per capita larval development rate | days^{−1} | 1/d_{L} [68] | |

σ_{P} | Per capita pupal development rate | days^{−1} | 1/d_{P} [68] | |

σ_{A} | Per capita adult development rate | days^{−1} | 1/d_{A} [68] | |

Δ_{T} | Difference between environmental air and water temperature | °C | 2.9 − 7.6 [71] | * |

_{L}and β

_{L}by subdividing the larval stage into α

_{L}subclasses (the number of sub-classes is determined as defined below) [72,73]. The rate at which larvae progress through the subclasses is set as α

_{L}μ

_{L}, where μ

_{L}is equal to 1/α

_{L}β

_{L}. Upon hatching, eggs will enter the first larval subclass (L

_{1}), in which they either progress to the next subclass (L

_{2}) at temperature-dependent rate 7 μ

_{L}, progress to pupae at temperature-dependent rate σ

_{L}, or die due to overcrowding at density-dependent rate μ

_{K}. This process continues as they progress through all subsequent subclasses.

_{A}and β

_{A}. The adult stage of the model comprises α

_{A}subclasses (the number of subclasses is determined as defined below), and adults progress through the subclasses at daily temperature-dependent rate α

_{A}μ

_{A}, with μ

_{A}equal to 1/α

_{A}β

_{A}. Upon entering the first adult subclass (A

_{1}), female mosquitoes sequentially progress through adult subclasses at rate 3 μ

_{A}, until they drop out of the model. The number of eggs laid in this model is dependent on the total number of adult females in all three adult subclasses.

_{a}), a proportion ρ(T

_{w}) of which will hatch [65] (where the former depends on the environmental (air) temperature of the adults T

_{a}, and the latter depends on the water temperature T

_{w}in which the eggs are laid. Eggs undergo a fixed, temperature-independent daily mortality at rate μ

_{E}, or progress to larvae at a daily rate σ

_{E}, which is given by the inverse of the duration of the egg stage 1/d

_{E}(Table 1) [69] as defined by Bayoh and Lindsay (unpublished data).

_{Lc}in models 1 and 3, or a temperature- and age-dependent daily mortality at rate μ

_{L}in models 2 and 4. In addition, larvae are subjected to density-dependent regulation, which is represented by an additional daily mortality rate μ

_{K}. Larvae that do not die progress to pupae at rate σ

_{E}, which is given by the inverse of the duration of the larval stage (Table 1) [69]. Pupae either die at a fixed, temperature-independent daily mortality rate μ

_{P}or progress to adults at rate σ

_{P}, which is given by the inverse of the duration of the pupal stage (Table 1) [69]. Only adult females are explicitly modelled and it is assumed that half of all pupae developing into adults are females [74]. Adults either die at a temperature-dependent, but age-independent, daily mortality rate μ

_{Ac}in models 1 and 2, or at a temperature- and age-dependent daily mortality rate μ

_{A}, in models 3 and 4. The values of fixed parameters in the models are given in Table 2 together with the references of provenance. In the case of the parameters estimated by fitting the models to data (using Bayesian statistics), the prior values are those used as initial values (informed by the literature where available). The asterisks indicate those values that will be obtained from the posterior distribution.

_{Lc}and μ

_{Ac}was plotted and a functional form fitted (Figure 7 and Table 2) to obtain the larval and adult age-independent mortality rates (μ

_{Lc}and μ

_{Ac}respectively). In order to model more realistically age-dependent mortality, the gamma distribution was fitted to the laboratory survival data in [34] (Figure 5 and Figure 6, red lines).

**Figure 5.**Fit of exponential (blue lines) and gamma (red lines) survival functions S(t) to the laboratory survival data in [34] at 27 °C (

**a**,

**c**) and 31 °C (

**b**,

**d**). Here, (

**a**,

**b**) are for larvae, while (

**c**,

**d**) are for adults.

**Figure 6.**Fit of constant- (blue lines) and time (age) dependent (red lines) hazard functions to the laboratory mortality data in [34] at 27 °C (

**a**,

**c**) and 31 °C (

**b**,

**d**). Here, (

**a**,

**b**) are for larvae, while (

**c**,

**d**) are for adults. The constant hazard corresponds to the exponential model, whilst the age-dependent hazard corresponds to the gamma distribution of survival times.

**Figure 7.**Age-independent larval (

**a**) and adult (

**b**) mortality rate as a function of environmental temperature (with the best-fit functional forms given in Table 2).

_{L}μ

_{L}for larvae and α

_{A}μ

_{A}for adults, where μ

_{L}= 1/α

_{L}β

_{L}and μ

_{A}= 1/α

_{A}β

_{A}. This ensures that the average life expectancy of larvae and adults is still 1/β

_{L}and 1/β

_{A}respectively. As described above, α

_{L}= 7 and α

_{A}= 3, and both β

_{L}and β

_{A}depend on temperature.

**Figure 8.**Value of β for the gamma larval (

**a**) and adult (

**b**) hazard rate as a function of environmental temperature.

_{K}) was derived from White et al. [11] as,

_{C}, which quantifies the magnitude of the density dependence, is a free parameter to be optimised in the model fitting. This formulation assumes the density-dependent mortality rate to be linearly proportional to the total number of mosquitoes in the larval stages. Here, K(t) is based on the form that was found to fit best the model of [11] to the Garki dataset [77], namely,

#### 2.2. Longitudinal Data for Model Fitting

#### 2.3. Model Fitting

_{i}) and a standard deviation σ

_{i}equal to the maximum value of all observations for month i. For months with low or no mosquito counts, a minimum standard deviation of 0.1 was assumed. The probability of obtaining the data (D), given a model M and a set of parameters θ is given by:

_{F}is a normalisation factor applied to the simulated data given model M and parameters θ (y

_{i}(θ, M)) and accounts for any systematic differences between observed abundance and model simulations. This normalisation factor also allows for adjustment between the models, which track the number of adult females, and the data, which include the abundance of male and female adults. Mean monthly mosquito numbers were calculated by averaging across daily model simulation results. All initial conditions were set to unity, and simulations were started six months prior to the date of the first observed data point to reduce the impact of the initial conditions (and model transients) on model fitting.

## 3. Results and Discussion

#### 3.1. Datasets of An. gambiae Abundance

Map Ref | Geographical Location | Study Dates | Study Duration (Months) | Mosquito Species and Stage |
---|---|---|---|---|

A | Likoko, Cameroon | October 2002–September 2003 | 12 | An. gambiae s.l. adults |

B | Mutengene, Cameroon [91] | October 2004–September 2005 | 12 | An. gambiae s.s. adults |

C | Ekombitié, Cameroon [92] | January 2007–December 2007 | 12 | An. gambiae s.l. adults |

D | Njabakunda, The Gambia [93] | April 2007–March 2009 | 24 | An. gambiae s.s. adults |

E | Kassena, Ghana [94] | November 2001–October 2004 | 36 | An. gambiae s.s. adults |

F | Kintampo, Ghana [95] | November 2003–November 2005 | 25 | An. gambiae s.s. adults |

G | Banizoumbou, Niger [96] | May 2005–December 2006 | 20 | An. gambiae s.l. adults |

H | Zindarou, Niger [97] | July 2005–December 2006 | 18 | An. gambiae s.l. adults |

I | Ogbakiri, Nigeria [98] | September 2005–August 2006 | 12 | An. gambiae s.l. adults |

J | Fort Ternan, Kenya [99] | March 2006–March 2008 | 25 | An. gambiae s.l. larvae |

#### 3.2. Model Fitting

**Figure 11.**Agreement between data (solid markers) and model predictions (solid lines). Black dots represent the average adult vector counts for each month from November 2001 to November 2004 from [94]. Solid lines show the best-fitting model predictions. Models 1–4 are represented by red, blue, green, and grey lines, respectively.

**Table 4.**Fitting-inferred parameter values. Parameters q, μ

_{E}, μ

_{C}, τ, and ΔT are described in Table 2, and n

_{F}is the normalisation factor applied to the simulated data.

Model | Parameters | |||||
---|---|---|---|---|---|---|

${n}_{F}$ | $q$ | ${\text{\mu}}_{E}$ | ${\text{\mu}}_{C}$ | τ | ΔT | |

1 | 0.466 | 0.636 | 0.481 | 266.915 | 0.472 | 3.066 |

2 | 0.026 | 0.613 | 0.485 | 16.153 | 0.689 | 7.165 |

3 | 34.308 | 0.72 | 0.501 | 5886.43 | 0.087 | 7.196 |

4 | 11.453 | 0.656 | 0.533 | 1753.52 | 0.095 | 7.092 |

**Table 5.**Bayesian Information Criterion (BIC) values for each model, and Pearson correlation coefficient (r) values describing the models’ fits to data from [94].

Variables | Model 1 | Model 2 | Model 3 | Model 4 |
---|---|---|---|---|

BIC | 174.22 | 174.18 | 173.82 | 173.82 |

r | 0.65 | 0.66 | 0.81 | 0.81 |

**Figure 12.**Model predictions (solid colour lines) and 95% Bayesian credible intervals (colour shaded areas) for model 1 (

**a**), model 2 (

**b**), model 3 (

**c**), and model 4 (

**d**); black dots are the data and the colour legend is the same as in Figure 11.

_{E}). This is to be expected, as these parameters are crucial in the reproduction, fitness, and survival of the mosquito, and serves to highlight on which entomological parameters we need more detailed and precise data in order to produce more reliable and robust models of disease vectors. All the models are also very sensitive to the difference between environmental air and water temperatures (ΔT), which further emphasises the importance of modelling the higher temperatures of the water bodies in which the immature stages of the mosquito develop, and suggests that models assuming water temperatures are the same as air temperatures may be missing out on a subtle determinant of mortality. This also highlights the necessity of measuring water temperature specifically in experimental work that aims to define the effect of temperature on the survival of An. gambiae aquatic stages, although this observation is likely applicable to other mosquito disease vectors also. The sensitivity of all models to variations in the difference between air and water temperature also emphasise that the population dynamics of An. gambiae are dependent not just on mean environmental temperatures, but also on small temperature fluctuations, which is consistent with previous experimental and theoretical work [9,25]. While models 1, 2, and 4 were robust to variations in the other three inferred parameters, model 3 displayed a greater sensitivity to changes in the values of μ

_{C}, suggesting that mosquito abundance is more sensitive to density-dependent mortality in the larval stages when age-dependent mortality is taken into account in the adult stages only.

## 4. Conclusions

## Supplementary Files

Supplementary File 1## Acknowledgments

## Author Contributions

## Abbreviations

AIC | Akaike Information Criterion |

An. gambiae s.s. | Anopheles gambiae sensu stricto |

BIC | Bayesian Information Criterion |

CI | Credible Interval |

DD | Degree-day |

EMAC | ECHAM5/MESSy2 Atmospheric Chemistry |

IRS | Indoor Residual Spraying |

LSM | Larval Source Management |

MAP | maximum a posteriori |

MLE | Maximum Likelihood Estimation |

MTD | Minimum Temperature for Development |

ODE | Ordinary Differential Equation |

RH | Relative Humidity |

sst | sea-surface temperature |

sic | sea-ice coverage |

VBD | Vector-Borne Disease |

°C | degrees Celsius |

## Conflicts of Interest

## References

- Eckhoff, P.; Bever, C.; Gerardin, J.; Wenger, E. Fun with maths: Exploting implications of mathematical models for malaria eradication. Malar. J.
**2014**, 13, 486–491. [Google Scholar] [CrossRef] [PubMed] - Smith, T.; Killeen, G.; Maire, N.; Ross, A.; Molineaux, L.; Tedioso, F.; Hutton, G.; Utzinger, J.; Dietz, K.; Tanner, M.; et al. Mathematical modeling of the impact of malaria vaccines on the clinical epidemiology and natural history of Plasmodium falciparum malaria: Overview. Amer. J. Trop. Med. Hyg.
**2006**, 75, 1–10. [Google Scholar] - Koella, J.C. On the use of mathematical models of malaria transmission. Acta Trop.
**1991**, 49, 1–25. [Google Scholar] [CrossRef] - Reiner, R.; Perkins, T.; Barker, C.; Niu, T.; Chaves, L.; Ellis, A.; George, D.; Menach, A.; Pulliam, J.; Bisanzio, D.; et al. A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970–2010. J. R. Soc. Interface
**2013**, 10. [Google Scholar] [CrossRef] [PubMed][Green Version] - Pandey, A.; Mubayi, A.; Medlock, J. Comparing vector-host and SIR models for dengue transmission. Math. Biosci.
**2013**, 246, 252–259. [Google Scholar] [CrossRef] [PubMed] - Martens, P. Malaria prevalence. In Health and Climate Change: Modelling the Impacts of Global Warming and Ozone Depletion; Earthscan Publications Ltd.: London, UK, 1998; p. 176. [Google Scholar]
- Rogers, D. The modelling of vector dynamics in disease research. In Modelling vector-borne and other parasitic diseases; International Laboratory for Research on Animal Diseases: Nairobi, Kenya, 1994. [Google Scholar]
- Struchiner, C.; Luz, P.; Codeço, C.; Coelho, F.; Massad, E. Current research issues in mosquito-borne diseases modeling. In Mathematical Studies on Human Disease Dynamics: Emerging Paradigms and Challenges: AMS-IMS-SIAM Joint Summer Research Conference on Modeling the Dynamics of Human Diseases: Emerging Paradigms and Challenges; American Mathematical Society: Snowbird, UT, USA, 2006. [Google Scholar]
- Beck-Johnson, L.M.; Nelson, W.A.; Paaijmans, K.P.; Read, A.F.; Thomas, M.B.; Bjørnstad, O.N. The effect of temperature on Anopheles mosquito population dynamics and the potential for malaria transmission. PLoS One
**2013**. [Google Scholar] [CrossRef] [PubMed] - Lutambi, A.; Penny, M.; Smith, T.; Chitnis, N. Mathematical modelling of mosquito dispersal in a heterogeneous environment. Math. Biosci.
**2013**, 241, 198–216. [Google Scholar] [CrossRef] [PubMed][Green Version] - White, M.T.; Griffin, J.T.; Churcher, T.S.; Ferguson, N.M.; Basáñez, M.-G.; Ghani, A.C. Modelling the impact of vector control interventions on Anopheles gambiae population dynamics. Parasites Vectors
**2011**, 4, 153–153. [Google Scholar] [CrossRef] [PubMed] - Hoshen, M.B.; Morse, A.P. A weather-driven model of malaria transmission. Malar. J.
**2004**, 3. [Google Scholar] [CrossRef] [PubMed][Green Version] - Depinay, J.-M.O.; Mbogo, C.M.; Killeen, G.; Knols, B.; Beier, J.; Carlson, J.; Dushoff, J.; Billingsley, P.; Mwambi, H.; Githure, J.; et al. A simulation model of African Anopheles ecology and population dynamics for the analysis of malaria transmission. Malar. J.
**2004**, 3. [Google Scholar] [CrossRef] [PubMed][Green Version] - Githeko, A.K.; Lindsay, S.W.; Confalonier, U.E.; Patz, J.A. Climate change and vector-borne diseases: A regional analysis. Bull. WHO.
**2000**, 78, 1136–1147. [Google Scholar] [PubMed] - Brower, V. Vector-borne diseases and global warming: Are both on an upward swing? EMBO Rep.
**2001**, 2, 755–757. [Google Scholar] [CrossRef] [PubMed] - Lipp, E.K.; Huq, A.; Colwell, R.R. Effects of global climate on infectious disease: The cholera model. Clin. Microbiol. Rev.
**2002**, 15, 757–770. [Google Scholar] [CrossRef] [PubMed] - Sutherst, R.W. Global change and human vulnerability to vector-borne diseases. Clin. Microbiol. Rev.
**2004**, 17, 136–173. [Google Scholar] [CrossRef] [PubMed] - Parham, P.; Christiansen-Jucht, C.; Pople, D.; Michael, E. Understanding and Modelling the Impact of Climate Change on Infectious Diseases—Progress and Future Challenges. In Climate Change—Socioeconomic Effects; Blanco, J., Kheradmand, H., Eds.; InTech: Rijeka, Croatia, 2011. [Google Scholar]
- Thomson, M. Emerging Infectious Diseases, Vector-Borne Diseases, and Climate Change. In Global Environmental Change; Freedman, B., Ed.; Handbook of Global Environmental Pollution; Springer: Dordrecht, Netherlands, 2014; pp. 623–628. [Google Scholar]
- Guo, C.; Yang, L.; Ou, C.-Q.; Li, L.; Zhuang, Y.; Yang, J.; Zhou, Y.-X.; Qian, J.; Chen, P.-Y.; Liu, Q.-Y.; et al. Malaria incidence from 2005–2013 and its associations with meteorological factors in Guangdong, China. Malar. J.
**2015**, 14, 116–141. [Google Scholar] [CrossRef] [PubMed] - Parham, P.; Waldock, J.; Christophides, G.; Hemming, D.; Agusto, F.; Evans, K.; Fefferman, N.; Gaff, H.; Gumel, A.; LaDeau, S.; et al. Climate, environmental, and socio-economic change: Weighing up the balance in vector-borne disease transmission. Philos. Trans. R. Soc. B
**2015**. [Google Scholar] [CrossRef] [PubMed] - Gullan, P.; Cranston, P. Chapter 6: Insect development and life histories. In The Insects: An Outline of Entomology; Wiley-Blackwell: Oxford, UK, 2010; pp. 151–188. [Google Scholar]
- Gutierrez, A.; Ponti, L.; d’Oultremont, T.; Ellis, C. Climate change effects on poikilotherm tritrophic interactions. Clim. Chang.
**2008**, 87, 167–192. [Google Scholar] [CrossRef] - Lee, S.H.; Nam, K.W.; Jeong, J.Y.; Yoo, S.J.; Koh, Y.-S.; Lee, S.; Heo, S.T.; Seong, S.-Y.; Lee, K.H. The effects of climate change and globalization on mosquito vectors: Evidence from Jeju Island, South Korea on the potential for Asian tiger mosquito (Aedes albopictus) influxes and survival from Vietnam rather than Japan. PLoS One
**2013**. [Google Scholar] [CrossRef] [PubMed] - Lyons, C.; Coetzee, M.; Chown, S. Stable and fluctuating temperature effects on the development rate and survival of two malaria vectors, Anopheles arabiensis and Anopheles funestus. Parasites Vectors
**2013**, 6. [Google Scholar] [CrossRef] [PubMed] - Couret, J.; Benedict, M. A meta-analysis of the factors influencing development rate variation in Aedes aegypti (Diptera: Culicidae). BMC Ecol.
**2014**, 14. [Google Scholar] [CrossRef] [PubMed] - Chang, L.-H.; Hsu, E.-L.; Teng, H.-J.; Ho, C.-M. Differential survival of Aedes aegypti and Aedes albopictus (Diptera: Culicidae) larvae exposed to low temperatures in Taiwan. J. Med. Entomol.
**2007**, 44, 205–210. [Google Scholar] [CrossRef] [PubMed] - Farjana, T.; Tuno, N.; Higa, Y. Effects of temperature and diet on development and interspecies competition in Aedes aegypti and Aedes albopictus. Med. Vet. Entomol.
**2012**, 26, 210–217. [Google Scholar] [CrossRef] [PubMed] - Mills, J.N.; Gage, K.L.; Khan, A.S. Potential influence of climate change on vector-borne and zoonotic diseases: A review and proposed research plan. Environ Health Perspect.
**2010**, 118, 1507–1514. [Google Scholar] [CrossRef] [PubMed] - Mourya, D.T.; Yadav, P.; Mishra, A.C. Effect of temperature stress on immature stages and susceptibility of Aedes aegypti mosquitoes to Chikungunya virus. Amer. J. Trop. Med. Hyg.
**2004**, 70, 346–350. [Google Scholar] - Moller-Jacobs, L.; Murdock, C.; Thomas, M. Capacity of mosquitoes to transmit malaria depends on larval environment. Parasites Vectors
**2014**, 7, 593–604. [Google Scholar] [CrossRef] [PubMed] - Lambrechts, L.; Paaijmans, K.; Fansiri, T.; Carrington, L.; Kramer, L.; Thomas, M.; Scott, T. Impact of daily temperature fluctuations on dengue virus transmission by Aedes aegypti. Proc. Natl. Acad. Sci. USA
**2011**, 108, 7460–7465. [Google Scholar] [CrossRef] [PubMed] - Ciota, A.T.; Matacchiero, A.C.; Kilpatrick, A.M.; Kramer, L.D. The Effect of temperature on life history traits of Culex mosquitoes. J. Med. Entomol.
**2014**, 51, 55–62. [Google Scholar] [CrossRef] [PubMed] - Christiansen-Jucht, C.; Parham, P.E.; Saddler, A.; Koella, J.C.; Basáñez, M.-G. Temperature during larval development and adult maintenance influences the survival of Anopheles gambiae s.s. Parasites Vectors
**2014**, 7. [Google Scholar] [CrossRef] - Macdonald, G. Epidemiological basis of malaria control. Bull. WHO.
**1956**, 15, 613–626. [Google Scholar] [PubMed] - Garrett-Jones, C.; Shidrawi, G.R. Malaria vectorial capacity of a population of Anopheles gambiae. Bull. WHO.
**1969**, 40, 531–545. [Google Scholar] [PubMed] - Kurtenbach, K.; Hanincová, K.; Tsao, J.I.; Margos, G.; Fish, D.; Ogden, N.H. Fundamental processes in the evolutionary ecology of Lyme borreliosis. Nat. Rev. Microbiol.
**2006**, 4, 660–669. [Google Scholar] [CrossRef] [PubMed] - Brady, O.J.; Johansson, M.A.; Guerra, C.A.; Bhatt, S.; Golding, N.; Pigott, D.M.; Delatte, H.; Grech, M.G.; Leisnham, P.T.; Maciel-de-Freitas, R.; et al. Modelling adult Aedes aegypti and Aedes albopictus survival at different temperatures in laboratory and field settings. Parasites Vectors
**2013**, 6. [Google Scholar] [CrossRef] [PubMed][Green Version] - Gage, K.L.; Burkot, T.R.; Eisen, R.J.; Hayes, E.B. Climate and vectorborne diseases. Amer. J. Prev. Med.
**2008**, 35, 436–450. [Google Scholar] [CrossRef] [PubMed] - Morin, C.W.; Comrie, A.C. Regional and seasonal response of a west Nile virus vector to climate change. Proc. Natl. Acad. Sci. USA
**2013**, 110, 15620–15625. [Google Scholar] [CrossRef] [PubMed] - Talla, C.; Diallo, D.; Dia, I.; Ba, Y.; Ndione, J.-A.; Sall, A.A.; Morse, A.; Diop, A.; Diallo, M. Statistical modeling of the abundance of vectors of West African Rift Valley Fever in Barkédji, Senegal. PLoS One
**2014**. [Google Scholar] [CrossRef] [PubMed] - Azil, A.H.; Long, S.A.; Ritchie, S.A.; Williams, C.R. The development of predictive tools for pre-emptive dengue vector control: A study of Aedes aegypti abundance and meteorological variables in north Queensland, Australia. Trop. Med. Int. Health
**2010**, 15, 1190–1197. [Google Scholar] [CrossRef] [PubMed] - Roiz, D.; Ruiz, S.; Soriguer, R.; Figuerola, J. Climatic effects on mosquito abundance in Mediterranean wetlands. Parasites Vectors
**2014**, 7. [Google Scholar] [CrossRef] [PubMed] - Tran, A.; L’Ambert, G.; Lacour, G.; Benoît, R.; Demarchi, M.; Cros, M.; Cailly, P.; Aubry-Kientz, M.; Balenghien, T.; Ezanno, P.; et al. A rainfall- and temperature-driven abundance model for Aedes albopictus populations. Int. J. Environ. Res. Public Health
**2013**, 10, 1698–1719. [Google Scholar] [CrossRef] [PubMed][Green Version] - Lunde, T.; Bayoh, M.; Lindtjørn, B. How malaria models relate temperature to malaria transmission. Parasites Vectors
**2013**, 6. [Google Scholar] [CrossRef] [PubMed] - Bessell, P.R.; Searle, K.R.; Auty, H.K.; Handel, I.G.; Purse, B.V.; deC Bronsvoort, B.M. Epidemic potential of an emerging vector borne disease in a marginal environment: Schmallenberg in Scotland. Sci. Rep.
**2013**, 3. [Google Scholar] [CrossRef] [PubMed] - Gething, P.; van Boeckel, T.; Smith, D.; Guerra, C.; Patil, A.; Snow, R.; Hay, S. Modelling the global constraints of temperature on transmission of Plasmodium falciparum and P. vivax. Parasites Vectors
**2011**, 4. [Google Scholar] [CrossRef] [PubMed] - Hollingsworth, T.; Pulliam, J.; Funk, S.; Truscott, J.; Isham, V.; Lloyd, A. Seven challenges for modelling indirect transmission: Vector-Borne diseases, macroparasites and neglected tropical diseases. Epidemics
**2015**, 10, 16–20. [Google Scholar] [CrossRef] [PubMed] - Smith, D.; Battle, K.; Hay, S.; Barker, C.; Scott, T.; McKenzie, F. Ross, macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens. PLoS Pathog.
**2012**, 8. [Google Scholar] [CrossRef] [PubMed] - Chabot-Couture, G.; Nigmatulina, K.; Eckhoff, P. An environmental data set for vector-borne disease modeling and epidemiology. PLoS One
**2014**, 9. [Google Scholar] [CrossRef] [PubMed] - Rumisha, S.F.; Smith, T.; Abdulla, S.; Masanja, H.; Vounatsou, P. Modelling heterogeneity in malaria transmission using large sparse spatio-temporal entomological data. Glob. Health Action
**2014**, 7. [Google Scholar] [CrossRef] [PubMed] - Crespo-Pérez, V.; Dangles, O.; Régnière, J.; Chuine, I. Modeling temperature-dependent survival with small datasets: Insights from tropical mountain agricultural pests. Bull. Entomol. Res.
**2013**, 103, 336–343. [Google Scholar] [CrossRef] [PubMed] - Harrington, L.; Françoisevermeylen; Jones, J.; Kitthawee, S.; Sithiprasasna, R.; Edman, J.; Scott, T. Age-dependent survival of the dengue vector Aedes aegypti (Diptera: Culicidae) demonstrated by simultaneous release-recapture of different age cohorts. J. Med. Entomol.
**2008**, 45, 307–313. [Google Scholar] [CrossRef] [PubMed] - Styer, L.; Minnick, S.; Sun, A.; Scott, T. Mortality and reproductive dynamics of Aedes aegypti (Diptera: Culicidae) fed human blood. Vector-Borne Zoonotic Dis.
**2007**, 7, 86–98. [Google Scholar] [CrossRef] [PubMed] - Styer, L.; Carey, J.; Wang, J.-L.; Scott, T. Mosquitoes do senesce: Departure from the paradigm of constant mortality. Amer. J. Trop. Med. Hyg.
**2007**, 76, 111–117. [Google Scholar] - Sylvestre, G.; Gandini, M.; Maciel-de-Freitas, R. Age-dependent effects of oral infection with dengue virus on aedes aegypti (Diptera: Culicidae) feeding behavior, survival, oviposition success and fecundity. PLoS ONE
**2013**, 8. [Google Scholar] [CrossRef] [PubMed] - MacDonald, G. The analysis of the sporozoite rate. Trop. Bull.
**1952**, 49, 569–586. [Google Scholar] - Alto, B.W.; Richards, S.L.; Anderson, S.L.; Lord, C.C. Survival of West Nile virus-challenged Southern house mosquitoes, Culex pipiens quinquefasciatus, in relation to environmental temperatures. J. Vector Ecol.
**2014**, 39, 123–133. [Google Scholar] [CrossRef] [PubMed] - Bellan, S.E. The importance of age dependent mortality and the extrinsic incubation period in models of mosquito-borne disease transmission and control. PLoS ONE
**2010**, 5. [Google Scholar] [CrossRef] [PubMed] - Arifin, S.N.; Zhou, Y.; Davis, G.J.; Gentile, J.E.; Madey, G.R.; Collins, F.H. An agent-based model of the population dynamics of Anopheles gambiae. Malar. J.
**2014**, 13, 1–20. [Google Scholar] [CrossRef] [PubMed] - Clements, A.; Paterson, G. The analysis of mortality and survival rates in wild populations of mosquitoes. J. Appl. Ecol.
**1981**, 18, 373–399. [Google Scholar] [CrossRef] - Dawes, E.J.; Churcher, T.S.; Zhuang, S.; Sinden, R.E.; Basáñez, M.-G. Anopheles mortality is both age- and Plasmodium-density dependent: Implications for malaria transmission. Malar. J.
**2009**, 8. [Google Scholar] [CrossRef] [PubMed] - Hancock, P.; Thomas, M.; Godfray, H.C. An age-structured model to evaluate the potential of novel malaria-control interventions: A case study of fungal biopesticide sprays. Proc. R. Soc. B. Biol. Sci.
**2009**, 276, 71–80. [Google Scholar] [CrossRef] [PubMed] - Takken, W.; Koenraadt, C.J.M. Ecology of Parasite-Vector Interactions; Springer: Dordrecht, Netherlands, 2013. [Google Scholar]
- Christiansen-Jucht, C.; Parham, P.; Saddler, A.; Koella, J.; Basáñez, M.-G. Temperature during larval development and adult maintenance influences the survival of Anopheles gambiae s.s. Parasite Vector
**2014**. Available online: http://www.biomedcentral.com/content/pdf/s13071-014-0489-3.pdf (accessed 13 February 2015). [Google Scholar] - Bukhari, T.; Takken, W.; Koenraadt, C.J.M. Biological tools for control of larval stages of malaria vectors—A review. Biocontrol Sci. Technol.
**2013**, 23, 987–1023. [Google Scholar] [CrossRef] - Yamana, T.; Eltahir, E. Incorporating the effects of humidity in a mechanistic model of Anopheles gambiae mosquito population dynamics in the Sahel region of Africa. Parasites Vectors
**2013**, 6. [Google Scholar] [CrossRef] [PubMed] - Warrell, D.; Gilles, H. Essential Malariology, 4th ed.; Hodder Arnold: London, UK, 2002. [Google Scholar]
- Parham, P.; Pople, D.; Christiansen-Jucht, C.; Lindsay, S.; Hinsley, W.; Michael, E. Modeling the role of environmental variables on the population dynamics of the malaria vector Anopheles gambiae sensu stricto. Malar. J.
**2012**. [Google Scholar] [CrossRef] [PubMed][Green Version] - Okogun, G.R.A. Life-table analysis of Anopheles malaria vectors: generational mortality as tool in mosquito vector abundance and control studies. J. Vector Borne Dis.
**2005**, 42, 45–53. [Google Scholar] [PubMed] - Paaijmans, K.P.; Jacobs, A.F.G.; Takken, W.; Heusinkveld, B.G.; Githeko, A.K.; Dicke, M.; Holtslag, A.A.M. Observations and model estimates of diurnal water temperature dynamics in mosquito breeding sites in western Kenya. Hydrol. Process.
**2008**, 22, 4789–4801. [Google Scholar] [CrossRef] - Wearing, H.J.; Rohani, P.; Keeling, M.J. Appropriate models for the management of infectious diseases. PLoS Med.
**2005**, 2. [Google Scholar] [CrossRef] [PubMed][Green Version] - Lloyd, A. Realistic distributions of infectious periods in epidemic models: Changing patterns of persistence and dynamics. Theor. Popul. Biol.
**2001**, 60, 59–71. [Google Scholar] [CrossRef] [PubMed] - Kirby, M.J.; Lindsay, S.W. Effect of temperature and inter-specific competition on the development and survival of Anopheles gambiae sensu stricto and An. arabiensis larvae. Acta Trop.
**2009**, 109, 118–123. [Google Scholar] [CrossRef] [PubMed] - Gilpin, M.E.; McClelland, G.A. Systems analysis of the yellow fever mosquito Aedes aegypti. Fortschr. Zool.
**1979**, 25, 355–388. [Google Scholar] [PubMed] - Legros, M.; Lloyd, A.L.; Huang, Y.; Gould, F. Density-dependent intraspecific competition in the larval stage of Aedes aegypti (Diptera: Culicidae): Revisiting the current paradigm. J. Med. Entomol.
**2009**, 46, 409–419. [Google Scholar] [CrossRef] [PubMed] - Molineaux, L.; Gramiccia, G. The Garki Project; World Health Organization: Geneva, Switzerland, 1980. [Google Scholar]
- Zwiefelhofer, D. Find Latitude and Longitude. Available online: http://www.findlatitudeandlongitude.com (accessed on 13 February 2015).
- Batch Geo LLC. Available online: http://batchgeo.com/ (accessed on 13 February 2015).
- Collett, D. Modelling survival data in medical research, 2nd ed.; Chapman and Hall/CRC: London, UK, 2003. [Google Scholar]
- Kass, R.; Raftery, A. Bayes factors. J. Amer. Stat. Assoc.
**1995**, 90, 773–795. [Google Scholar] [CrossRef] - Bolker, B. Chapter 6: Likelihood and all that. In Ecological Models and Data in R; Princeton University Press: Princeton, NJ, USA, 2008; p. 408. [Google Scholar]
- Kirk, P.; Thorne, T.; Stumpf, M.P.H. Model selection in systems and synthetic biology. Curr. Opin. Biotechnol.
**2013**, 24, 767–774. [Google Scholar] [CrossRef] [PubMed] - Brooks, S.; Gelman, A.; Jones, G.; Meng, X.-L. Handbook of Markov Chain Monte Carlo, 1st ed.; Chapman and Hall/CRC: London, UK, 2011. [Google Scholar]
- Gutenkunst, R.N.; Waterfall, J.J.; Casey, F.P.; Brown, K.S.; Myers, C.R.; Sethna, J.P. Universally sloppy parameter sensitivities in systems biology models. PLoS Comput. Biol.
**2007**, 3. [Google Scholar] [CrossRef] [PubMed] - Erguler, K.; Stumpf, M.P.H. Practical limits for reverse engineering of dynamical systems: A statistical analysis of sensitivity and parameter inferability in systems biology models. Mol. Biosyst.
**2011**, 7, 1593–1602. [Google Scholar] [CrossRef] [PubMed] - Roeckner, E.; Bäuml, G.; Bonaventura, L.; Brokopf, R.; Esch, M.; Giorgetta, M.; Hagemann, S.; Kirchner, I.; Kornblueh, L.; Manzini, E.; et al. Part I: Model Description. The Atmospheric General Circulation Model ECHAM5; Max Planck Institut für Meteorologie: Hamburg, Germany, 2003; p. 127. [Google Scholar]
- Jöckel, P.; Tost, H.; Pozzer, A.; Brühl, C.; Buchholz, J.; Ganzeveld, L.; Hoor, P.; Kerkweg, A.; Lawrence, M.G.; Sander, R.; et al. The atmospheric chemistry general circulation model ECHAM5/MESSy1: Consistent simulation of ozone from the surface to the mesosphere. Atmos. Chem. Phys.
**2006**, 6, 5067–5104. [Google Scholar] [CrossRef] - Proestos, Y.; Christophides, G.K.; Ergüler, K.; Tanarhte, M.; Waldock, J.; Lelieveld, J. Present and future projections of habitat suitability of the Asian tiger mosquito, a vector of viral pathogens, from global climate simulation. Philos. Trans. R. Soc. Lond. B Biol. Sci.
**2015**, 370. [Google Scholar] [CrossRef] [PubMed] - Taylor, K.; Williamson, D.; Zwiers, F. The Sea Surface Temperature and Sea-Ice Concentration Boundary Conditions for AMIP II Simulations; Climate and Global Dynamics Division, UCAR: Boulder, Co, USA, 2000; p. 25. [Google Scholar]
- Tanga, M.C.; Ngundu, W.I.; Tchouassi, P.D. Daily survival and human blood index of major malaria vectors associated with oil palm cultivation in Cameroon and their role in malaria transmission. Trop. Med. Int. Health
**2011**, 16, 447–457. [Google Scholar] [CrossRef] [PubMed] - Fils, E.; Ntonga, P.; Belong, P.; Messi, J. Contribution of mosquito vectors in malaria transmission in an urban district of southern Cameroon. J. Entomol. Nematol.
**2010**, 2, 13–17. [Google Scholar] - Nwakanma, D.C.; Neafsey, D.E.; Jawara, M.; Adiamoh, M.; Lund, E.; Rodrigues, A.; Loua, K.M.; Konate, L.; Sy, N.; Dia, I.; et al. Breakdown in the process of incipient speciation in anopheles gambiae. Genetics
**2013**, 193, 1221–1231. [Google Scholar] [CrossRef] [PubMed] - Kasasa, S.; Asoala, V.; Gosoniu, L.; Anto, F.; Adjuik, M.; Tindana, C.; Smith, T.; Owusu-Agyei, S.; Vounatsou, P. Spatio-temporal malaria transmission patterns in Navrongo demographic surveillance site, northern Ghana. Malar. J.
**2013**, 12. [Google Scholar] [CrossRef] [PubMed][Green Version] - Dery, D.B.; Brown, C.; Asante, K.P.; Adams, M.; Dosoo, D.; Amenga-Etego, S.; Wilson, M.; Chandramohan, D.; Greenwood, B.; Owusu-Agyei, S.; et al. Patterns and seasonality of malaria transmission in the forest-savannah transitional zones of Ghana. Malar. J.
**2010**, 9. [Google Scholar] [CrossRef] [PubMed] - Gianotti, R.L.; Bomblies, A.; Dafalla, M.; Issa-Arzika, I.; Duchemin, J.-B.; Eltahir, E.A. Efficacy of local neem extracts for sustainable malaria vector control in an African village. Malar. J.
**2008**, 7. [Google Scholar] [CrossRef] [PubMed] - Bomblies, A.; Duchemin, J.-B.; Eltahir, E.A. A mechanistic approach for accurate simulation of village scale malaria transmission. Malar. J.
**2009**, 8. [Google Scholar] [CrossRef] [PubMed] - Uttah, E.C.; Ibe, D.; Wokem, G.N. Filariasis control in coastal Nigeria: Predictive significance of baseline entomological indices of Anopheles. gambiae s.l. (Diptera: Culicidae). Int. Sch. Res. Not.
**2013**, 2013. [Google Scholar] [CrossRef] - Imbahale, S.S.; Paaijmans, K.P.; Mukabana, W.R.; van Lammeren, R.; Githeko, A.K.; Takken, W. A longitudinal study on Anopheles mosquito larval abundance in distinct geographical and environmental settings in western Kenya. Malar. J.
**2011**, 10. [Google Scholar] [CrossRef] [PubMed] - Churcher, T.S.; Trape, J.-F.; Cohuet, A. Human-to-mosquito transmission efficiency increases as malaria is controlled. Nat. Commun.
**2015**, 6. [Google Scholar] [CrossRef] [PubMed] - Tebaldi, C.; Knutti, R. The use of the multi-model ensemble in probabilistic climate projections. Philos. Trans. R. Soc. Lond. Math. Phys. Eng. Sci.
**2007**, 365, 2053–2075. [Google Scholar] [CrossRef] [PubMed] - Webster, M.; Sokolov, A. Quantifying the Uncertainty in Climate Predictions; Joint Program on the Science and Polocy of Global Change, Massachusetts Institute of Technology: Boston, MA, USA, 1998. [Google Scholar]
- Bilcke, J.; Beutels, P.; Brisson, M.; Jit, M. Accounting for methodological, structural, and parameter uncertainty in decision-analytic models. Med. Decis. Mak.
**2011**, 31, 675–692. [Google Scholar] [CrossRef] [PubMed] - Olayemi, I.K.; Ande, A.T. Life table analysis of Anopheles gambiae (Diptera: Culicidae) in relation to malaria transmission. J. Vector Borne Dis.
**2009**, 46, 295–298. [Google Scholar] [PubMed] - Bayoh, M.N.; Lindsay, S.W. Effect of temperature on the development of the aquatic stages of Anopheles gambiae sensu stricto (Diptera: Culicidae). Bull. Entomol. Res.
**2003**, 93, 375–381. [Google Scholar] [CrossRef] [PubMed] - Bayoh, M.; Lindsay, S. Temperature-related duration of aquatic stages of the Afrotropical malaria vector mosquito Anopheles gambiae in the laboratory. Med. Vet. Entomol.
**2004**, 18, 174–179. [Google Scholar] [CrossRef] [PubMed] - Nisbet, R.M.; Gurney, W.S.C. The systematic formulation of population models for insects with dynamically varying instar duration. Theor. Popul. Biol.
**1983**, 23, 114–135. [Google Scholar] [CrossRef] - Eckhoff, P. A malaria transmission-directed model of mosquito life cycle and ecology. Malar. J.
**2011**, 10. [Google Scholar] [CrossRef] [PubMed] - Young, L.; Young, J. Degree-day models. In Statistical Ecology: A Population Perspective; Kluwer Academic Publishers: Boston, MA, USA, 2002; pp. 421–439. [Google Scholar]
- Ahumada, J.A.; Lapointe, D.; Samuel, M.D. Modeling the population dynamics of Culex quinquefasciatus (Diptera: Culicidae), along an elevational gradient in Hawaii. J. Med. Entomol.
**2004**, 41, 1157–1170. [Google Scholar] [CrossRef] [PubMed] - Jones, V.; Brunner, J. Degree-day models. In Orchard Pest Management; Washington State University: Washington, DC, USA, 2015. [Google Scholar]
- Egizi, A.; Fefferman, N.H.; Fonseca, D.M. Evidence that implicit assumptions of “no evolution” of disease vectors in changing environments can be violated on a rapid timescale. Philos. Trans. R. Soc. Lond. B Biol. Sci.
**2015**, 370. [Google Scholar] [CrossRef] [PubMed] - Sinka, M.; Bangs, M.; Manguin, S.; Coetzee, M.; Mbogo, C.; Hemingway, J.; Patil, A.; Temperley, W.; Gething, P.; Kabaria, C.; et al. The dominant Anopheles vectors of human malaria in Africa, Europe and the Middle East: Occurrence data, distribution maps and bionomic précis. Parasites Vectors
**2010**, 3. [Google Scholar] [CrossRef] [PubMed]

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**MDPI and ACS Style**

Christiansen-Jucht, C.; Erguler, K.; Shek, C.Y.; Basáñez, M.-G.; Parham, P.E.
Modelling *Anopheles gambiae s.s.* Population Dynamics with Temperature- and Age-Dependent Survival. *Int. J. Environ. Res. Public Health* **2015**, *12*, 5975-6005.
https://doi.org/10.3390/ijerph120605975

**AMA Style**

Christiansen-Jucht C, Erguler K, Shek CY, Basáñez M-G, Parham PE.
Modelling *Anopheles gambiae s.s.* Population Dynamics with Temperature- and Age-Dependent Survival. *International Journal of Environmental Research and Public Health*. 2015; 12(6):5975-6005.
https://doi.org/10.3390/ijerph120605975

**Chicago/Turabian Style**

Christiansen-Jucht, Céline, Kamil Erguler, Chee Yan Shek, María-Gloria Basáñez, and Paul E. Parham.
2015. "Modelling *Anopheles gambiae s.s.* Population Dynamics with Temperature- and Age-Dependent Survival" *International Journal of Environmental Research and Public Health* 12, no. 6: 5975-6005.
https://doi.org/10.3390/ijerph120605975