Research article Special Issues

A stage structured model for mosquito suppression with immigration

  • Received: 08 July 2024 Revised: 06 October 2024 Accepted: 23 October 2024 Published: 01 November 2024
  • The incompatible insect technique based on Wolbachia is a promising alternative to control mosquito-borne diseases, such as dengue fever, malaria, and Zika, which drives wild female mosquitoes sterility through a mechanism cytoplasmic incompatibility. A successful control program should be able to withstand the perturbation induced by the immigration of fertilized females from surrounding uncontrolled areas. In this paper, we formulated a system of delay differential equations, including larval and adult stages, interfered by Wolbachia-infected males. We classified the release number of infected males and immigration number of fertile females, to ensure that the system displays globally asymptotically stable or bistable dynamics. The immigration of fertile females hinders the maximum possible suppression efficiency so that the wild adults cannot be reduced to a level below A. We identified the permitted most migration number to reduce the wild adults to a target level. To reduce up to 90% of wild adults in the peak season within two months, an economically viable strategy is to reduce the immigration number of wild females less than 0.21% of the carrying capacity of adults in the control area.

    Citation: Mugen Huang, Zifeng Wang, Zixin Nie. A stage structured model for mosquito suppression with immigration[J]. Mathematical Biosciences and Engineering, 2024, 21(11): 7454-7479. doi: 10.3934/mbe.2024328

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  • The incompatible insect technique based on Wolbachia is a promising alternative to control mosquito-borne diseases, such as dengue fever, malaria, and Zika, which drives wild female mosquitoes sterility through a mechanism cytoplasmic incompatibility. A successful control program should be able to withstand the perturbation induced by the immigration of fertilized females from surrounding uncontrolled areas. In this paper, we formulated a system of delay differential equations, including larval and adult stages, interfered by Wolbachia-infected males. We classified the release number of infected males and immigration number of fertile females, to ensure that the system displays globally asymptotically stable or bistable dynamics. The immigration of fertile females hinders the maximum possible suppression efficiency so that the wild adults cannot be reduced to a level below A. We identified the permitted most migration number to reduce the wild adults to a target level. To reduce up to 90% of wild adults in the peak season within two months, an economically viable strategy is to reduce the immigration number of wild females less than 0.21% of the carrying capacity of adults in the control area.



    Of all the tourism segments, cultural tourism is, without a doubt, the one that has grown the most in the last decades. That is why this segment attracts not only the tourists' attention but that of the researchers too. Researchers have studied this segment from an economic, geographic and cultural point of view (Ferrari et al., 2018), considering the marked seasonality of the sector (Cuccia and Rizzo, 2011; Mondéjar-Jiménez et al., 2007). The tourist activity driven by the cultural and heritage elements (McKercher et al., 2005) provides an important source of income for their preservation. These market segments that have existed for years started to develop by the end of the last century (Ferrari et al., 2014). Doubtlessly, an important cultural and heritage offer means an improvement in the image of the destination and has a positive impact on the choice of the consumer (Castro et al., 2007, Pérez-Calderón et al., 2020). This has motivated the researchers to analyze this segment and to clearly define it in the scientific literature (Cetin and Bilgihan, 2016).

    Many of these studies have focused on the cultural motivations of the tourists (Chhabra et al., 2003) to learn the profile and priorities when choosing a destination. However, they have particularly focused on assessing and knowing the main reasons that affect the choice of a destination and the opinion after its visit (Cordente-Rodríguez et al., 2011). This opinion can, doubtlessly, modify the initial idea and favor a return to the destination or its recommendation. Opinion has previously been studied in the literature (Yoon and Uysal, 2005). Nevertheless, there are few studies that manage to reflect, in a consistent manner, the previous motivations to the choice of destination. These motivations must be known in order to adapt the destination to the majority preferences of the visitors (McKercher, 2002; McKercher and du Cros, 2003) which, in many cases, are not managed properly (Garrod and Fyall, 2000).

    Cultural tourism, although with different grades of motivation of the users (Tsiotsou and Vasaioti, 2006), encompasses several activities that, in many occasions, contribute to the main reason for visiting (McKercher and du Cros, 2003; Lavín et al., 2017). Segmenting the tourists according to new typologies can establish another research line to address in the future (Frochot, 2005; Poria et al., 2003).

    The main objective of this study is assess a theoretical model to identify the main factors that determine the choosing of a tourist destination with an important cultural offer. The motivations of the tourists (parking, restaurants, transport...), together with the services the destination provides and its cultural offer, must affect its choice. The two factors under study shall alter these motivations as well.

    The model proposed intends to measure the effects in different variables and know if the relations among them are statistically significant. For that purpose, the following hypotheses are stated:

    H1: Tourists' motivations have a positive effect on the choice of a destination. Although this connection has been widely studied and previously contrasted (Chen and Rahman, 2018; Chhabra, 2009; Mondéjar-Jiménez and Vargas-Vargas, 2009; Mondéjar-Jiménez et al., 2009; Vergori and Arima, 2020; Xu et al., 2020), its intensity is the key factor to determine potential visitors.

    H2: Services offered by the destination have a positive effect on the choice of said destination and the motivations of the potential tourists have been object of analysis and determine the image and subsequent choice of a tourist destination (García-Pozo et al., 2019; Hossein et al., 2019; Salazar, 2012; Scheyvens and Biddulph, 2018; Ying and Zhou, 2007).

    H2.1: Services offered by the destination have a positive effect on the choice of said destination.

    H2.2: Services offered by the destination have a positive effect on the motivations of the potential tourists.

    H3: Cultural offer of the destination has a positive effect on the choice of said destination and on the motivations of its potential tourists (Hou et al., 2005; Lynch et al., 2011; Mondéjar-Jiménez et al., 2012; Richards, 2018; Secondi et al., 2011; Stylianou-Lambert, 2011). Cultural and heritage offer is possibly the main factor to determine a cultural destination.

    H3.1: Cultural offer of the destination has a positive effect on the choice of said destination.

    H3.2: Cultural offer of the destination has a positive effect on the motivations of the potential tourists.

    These hypotheses shall be contrasted by means of a structural model using Partial Least Squares (PLS) due to its predictive character and the assumption of normality of some the variables (Assaker et al., 2013; Do Valle and Assaker, 2016; Ali et al., 2018; Hair et al., 2019).

    PLS methodology based on variance structure is recommended for these initial models which, even though they are based on previous studies (Secondi et al., 2011), they also introduce some substantial changes. Models shall be adapted to the selected destination, in this case, the city of Malaga. This type of models shows a very solid performance (Henseler et al., 2009).

    Partial Least Squares Path Modeling (PLS) technique analyzes the relation among the suggested latent variables which are measured through different items obtained in a survey of the city tourists. The relation among the latent variables can reflect direct and indirect effects. The sum of both effects is the total effect among latent variables. The number of observations is sufficient since they exceed the minimum needed for the model to function (Hair et al., 2019).

    The city of Malaga has received more than 4.5 million visitors (tourists + hikers) with an economic impact of more than 3000 million euros, according to the city's tourist observatory. They have generated more than 2.5 million hotel overnight stays, with the United Kingdom, Germany and France being the main emitters of international tourists.

    A study was conducted through interviews with visitors to the city of Malaga from June to December 2019. Given the great number of foreign visitors, the questionnaire was provided in Spanish and English. The questionnaire that was used was the one proposed in Mondéjar and Gómez (2009) which shows a breakdown by blocks of Motivations, Services and Cultural Offer of the visited destination.

    Interviewed tourists were selected at random among the visitors of the main city monuments (the Cathedral of Malaga, the Alcazaba, Carmen Thyssen Museum and Picasso Museum) at the exit of their visit. A balance in places of origin, sex, age and nationality was pursued in order to obtain a sample as representative as possible. A total of 416 valid questionnaires have been used. Overall, 600 questionnaires were collected but many of them were not completely filled in. In some cases, because the tourist was in a hurry and could not wait to continue discovering the city; in other cases because it could be one of the first visited monuments and the tourist did not have a full idea of the services and cultural offer of the city.

    A total of 18 indicators have been used to define 4 latent factors: Destination (2 indicators), Cultural Offer (3 indicators), Services (6 indicators) and Motivations (7 indicators). The Destination receives the direct effect of all the variables and the indirect effect of Services and Cultural Offer, which also has a direct effect on the Motivations of the tourists. Based on the block structure of the survey and the burden of each item, some have been suppressed from the original survey because they had a very low effect or did not meet the required minimum.

    Table 1.  Study report.
    Latent factor Indicators
    Tourist Destination Destination valuation (V1) Comparative valuation (V2)
    Cultural Offer Kindness (R1) Cultural offer (R2) Heritage (R3)
    City Services Cleaning (S1)Safety (S4) Preservation (S2)Green areas (S5) Sign posts (S3)Access (S6)
    Tourist Motivations Visiting (M4)Nature (M7)Festivals (M10) Languages (M5)Beach (M8) Sport (M6)Relax (M9)

     | Show Table
    DownLoad: CSV

    The SmartPLS 3 software has been used to estimate the model. The established relations among the latent variables can be observed in Figure 1.

    Figure 1.  Structural equation model.

    Table 2 displays the results with the burdens for each indicator, all the recommended weight being sufficient in every latent factor except the factor Motivations. This is largely due to the heterogeneity of the sample and the different starting points of the tourists since, in some cases, the visitors already knew the destination.

    Table 2.  Cross loadings.
    Culture Motivations Destination Services
    M4 0.165 0.537 0.179 0.163
    M5 0.291 0.579 0.131 0.270
    M6 0.185 0.641 0.276 0.233
    M7 0.233 0.521 0.123 0.134
    M8 0.122 0.334 0.131 0.081
    M9 0.100 0.313 0.045 0.056
    M10 0.125 0.488 0.263 0.132
    R1 0.764 0.342 0.315 0.446
    R2 0.794 0.279 0.292 0.484
    R3 0.765 0.198 0.323 0.544
    S1 0.432 0.182 0.327 0.690
    S2 0.502 0.215 0.309 0.642
    S3 0.315 0.187 0.135 0.525
    S4 0.458 0.238 0.310 0.783
    S5 0.384 0.292 0.335 0.667
    S6 0.390 0.177 0.175 0.631
    V1 0.346 0.362 0.907 0.421
    V2 0.360 0.242 0.846 0.311

     | Show Table
    DownLoad: CSV

    The correlation matrix of latent variables is shown in the following table, the highest correlation being between the Cultural Offer and the Services provided by the destination.

    Table 3.  Matrix of correlation between latent variables.
    Culture Motivations Destination Services
    Culture 1
    Motivations 0.3590 1
    Destination 0.4004 0.3509 1
    Services 0.6303 0.3325 0.4235 1

     | Show Table
    DownLoad: CSV

    Table 4 shows the different reliability measures of the model. The obtained R-Square values are high in both cases and the analysis of internal consistency is acceptable (Cronbach's Alpha) except for the latent factor Motivations, as might be expected in the light of the results in Table 2. It is the same with the composite reliability indices. It is in the Motivations variable where no value is higher than 0.8.

    Table 4.  Reliability measurements.
    AVE CompositeReliability R Square Cronbach's Alpha Communality Redundancy
    Culture 0.599 0.817 0.668 0.599
    Motivations 0.250 0.689 0.147 0.520 0.250 0.029
    Destination 0.768 0.869 0.245 0.702 0.768 0.082
    Services 0.436 0.821 0.743 0.436

     | Show Table
    DownLoad: CSV

    Table 5 shows the different reliability measures of the model. The obtained R-Square values are high in both cases and the analysis of internal consistency is acceptable (Cronbach's Alpha) except for the latent factor Motivations, as might be expected in the light of the results in Table 2. It is the same with the composite reliability indices. It is in the Motivations variable where no value is higher than 0.8. shows the hypothesis test for the direct effects, with a significance level of 95% in all cases. Consequently, all null hypotheses and the positive effects that the Motivations, Culture and Services variables have when choosing a destination can be confirmed. Even though Services has the greater intensity, the results align with previous studies. Indeed, the Services of the destination condition the choice together with the diverse Motivations of the tourist; to a lesser extent the Cultural Offer, since in many cases the tourist does not enjoy it fully, depending on the duration of the stay.

    Table 5.  Tests of hypotheses for direct effects between latent variables.
    Total Effects T Statistics
    Culture Motivations 0.247 2.838*
    Culture Destination 0.221 2.706*
    Motivations Destination 0.207 3.000*
    Services Motivations 0.176 1.947
    Services Destination 0.247 3.423*
    Note: *Significant values at the 5% significance level.

     | Show Table
    DownLoad: CSV

    The first of the conclusions is the validity and reliability of the proposed model which, given its predictive character, can be used by public and private agents for policy-making and destination improvement. Thus, some of the lowest-rated indicators, specially sign posts and safety, can be improved.

    The second conclusion is related to the improvement of motivations of tourists when choosing a destination. The lowest rated are Beach and Relax. It is true that Malaga is not the main exponent of the Spanish Costa del Sol (one of the best valued sun-and-sand destinations globally) but the city of Malaga has magnificent unknown beaches that must be promoted. Furthermore, it is a destination where one can get high levels of relaxation, which is another motivation to choose it. It is certain that the exponential growth in tourists, caused mainly by the arrival of cruises, has turn Malaga into a mass destination. Nevertheless, this massification is concentrated in the historic center adjacent to the port and cruise terminals, leaving the rest of the city as a quiet place where one can enjoy.

    The third conclusion is related to the significant increase in cultural offer in the city of Malaga in the last 20 years. Out of the many sporting, cultural and leisure events, we must highlight the approach of Malaga, together with Madrid, as a national referent of "City of Museums". In fact, it has one of the most important offers (at a national and European level) with a total of 40 museums, the most relevant being the following: Picasso Museum, Museum of the City of Malaga, Carmen Thyssen Malaga Museum, Malaga Pompidou Centre and Russian Museum Malaga.

    In this paper, we showed the relative impact that the different tourist resources have on the election of a given destination. Undoubtedly, the strategic planning of the city must consider these results so as to improve them in future years. All the hypotheses and subhypotheses have been confirmed (influence of the Services in the Motivations, only at a 90%). Therefore, we must emphasize direct effects on the latent variable Destination. However, we should highlight that the effects have a similar result, with values around 0.25.

    We must take into account that, among the future research lines to address, one would be the segmentation of the respondents by means of sex or place of residence (national/foreign). We believe that, in both cases, motivations shall be different, and the perception of services and cultural offer could suffer fluctuations.

    All authors declare no conflicts of interest in this paper.



    [1] World Health Organization, Global strategy for dengue prevention and control 2012–2020, 2012. Available from: https://iris.who.int/bitstream/handle/10665/75303/9789241504034_eng.pdf.
    [2] S. Bhatt, P. W. Gething, O. J. Brady, J. P. Messina, A. W. Farlow, C. L. Moyes, et al., The global distribution and burden of dengue, Nature, 496 (2013), 504–507. https://doi.org/10.1038/nature12060 doi: 10.1038/nature12060
    [3] A. A. Hoffmann, B. L. Montgomery, J. Popovici, I. Iturbe-Ormaetxe, P. H. Johnson, F. Muzzi, et al., Successful establishment of Wolbachia in Aedes populations to suppress dengue transmission, Nature, 476 (2011), 454–457. https://doi.org/10.1038/nature10356 doi: 10.1038/nature10356
    [4] X. Zheng, D. Zhang, Y. Li, C. Yang, Y. Wu, X. Liang, et al., Incompatible and sterile insect techniques combined eliminate mosquitoes, Nature, 572 (2019), 56–61. https://doi.org/10.1038/s41586-019-1407-9 doi: 10.1038/s41586-019-1407-9
    [5] Z. Xi, C. C. Khoo, S. L. Dobson, Wolbachia establishment and invasion in an Aedes aegypti laboratory population, Science, 310 (2005), 326–328. https://doi.org/10.1126/science.1117607 doi: 10.1126/science.1117607
    [6] M. P. Atkinson, Z. Su, N. Alphey, L. S. Alphey, P. G. Coleman, L. M. Wein, Analyzing the control of mosquito-borne diseases by a dominant lethal genetic system, PNAS, 104 (2007), 9540–9545. https://doi.org/10.1073/pnas.0610685104 doi: 10.1073/pnas.0610685104
    [7] B. Zheng, M. Tang, J. Yu, Modeling Wolbachia spread in mosquitoes through delay differential equation, SIAM J. Appl. Math., 74 (2014), 743–770. https://doi.org/10.1137/13093354X doi: 10.1137/13093354X
    [8] L. Hu, M. Huang, M. Tang, J. Yu, B. Zheng, Wolbachia spread dynamics in stochastic environments, Theor. Popul. Biol., 106 (2015), 32–44. https://doi.org/10.1016/j.tpb.2015.09.003 doi: 10.1016/j.tpb.2015.09.003
    [9] L. Hu, M. Tang, Z. Wu, Z. Xi, J. Yu, The threshold infection level for Wolbachia invasion in random environments, J. Diff. Equ., 266 (2019), 4377–4393. https://doi.org/10.1016/j.jde.2018.09.035 doi: 10.1016/j.jde.2018.09.035
    [10] M. Huang, M. Tang, J. Yu, Wolbachia infection dynamics by reaction-diffusion equations, Sci. China Math., 58 (2015), 77–96. https://doi.org/10.1007/s11425-014-4934-8 doi: 10.1007/s11425-014-4934-8
    [11] M. Huang, J. Yu, L. Hu, B. Zheng, Qualitative analysis for a Wolbachia infection model with diffusion, Sci. China Math., 59 (2016), 1249–1266. https://doi.org/10.1007/s11425-016-5149-y doi: 10.1007/s11425-016-5149-y
    [12] M. Huang, J. Lou, L. Hu, B. Zheng, J. Yu, Assessing the efficiency of Wolbachia driven Aedes mosquito suppression by delay differential equations, J. Theor. Biol., 440 (2018), 1–11. https://doi.org/10.1016/j.jtbi.2017.12.012 doi: 10.1016/j.jtbi.2017.12.012
    [13] Y. Hui, G. Lin, J. Yu, J. Li, A delayed differential equation model for mosquito population suppression with sterile mosquitoes, Discrete Contin. Dyn. Syst. B, 25 (2020), 4659–4676. https://doi.org/10.3934/dcdsb.2020118 doi: 10.3934/dcdsb.2020118
    [14] J. Yu, Existence and stability of a unique and exact two periodic orbits for an interactive wild and sterile mosquito model, J. Diff. Equ., 269 (2020), 10395–10415. https://doi.org/10.1016/j.jde.2020.07.019 doi: 10.1016/j.jde.2020.07.019
    [15] M. Huang, M. Tang, J. Yu, B. Zheng, The impact of mating competitiveness and incomplete cytoplasmic incompatibility on Wolbachia-driven mosquito population suppression, Math. Bios. Eng., 16 (2019), 4741–4757. https://doi.org/10.3934/mbe.2019238 doi: 10.3934/mbe.2019238
    [16] B. Zheng, J. Yu, Z. Xi, M. Tang, The annual abundance of dengue and Zika vector Aedes albopictus and its stubbornness to suppression, Ecol. Model., 387 (2018), 38–48. https://doi.org/10.1016/j.ecolmodel.2018.09.004 doi: 10.1016/j.ecolmodel.2018.09.004
    [17] D. Li, H. Wan, The threshold infection level for Wolbachia invasion in a two-sex mosquito population model, Bulletin Math. Biol., 81 (2019), 2596–2624. https://doi.org/10.1007/s11538-019-00620-1 doi: 10.1007/s11538-019-00620-1
    [18] B. Zheng, M. Tang, J. Yu, J. Qiu, Wolbachia spreading dynamics in mosquitoes with imperfect maternal transmission, J. Math. Biol., 76 (2018), 235–263. https://doi.org/10.1007/s00285-017-1142-5 doi: 10.1007/s00285-017-1142-5
    [19] X. Zhang, S. Tang, R. A. Cheke, Birth-pulse models of Wolbachia-induced cytoplasmic incompatibility in mosquitoes for dengue virus control, Nonlinear Anal. Real World Appl., 22 (2015), 236–258. https://doi.org/10.1016/j.nonrwa.2014.09.004 doi: 10.1016/j.nonrwa.2014.09.004
    [20] J. Yu, J. Li, Global asymptotic stability in an interactive wild and sterile mosquito model, J. Diff. Equ., 269 (2020), 6193–6215. https://doi.org/10.1016/j.jde.2020.04.036 doi: 10.1016/j.jde.2020.04.036
    [21] J. Yu, J. Li, A delay suppression model with sterile mosquitoes release period equal to wild larvae maturation period, J. Math. Biol., 84 (2022), 14. https://doi.org/10.1007/s00285-022-01718-2 doi: 10.1007/s00285-022-01718-2
    [22] M. Huang, M. Tang, J. Yu, B. Zheng, A stage structured model of delay differential equations for Aedes mosquito population suppression, Discrete Contin. Dyn. Syst., 40 (2020), 3467–3484. https://doi.org/10.3934/dcds.2020042 doi: 10.3934/dcds.2020042
    [23] P. I. Bliman, Y. Dumont, Robust control strategy by the sterile insect technique for reducing epidemiological risk in presence of vector migration, Math. Biosci., 350 (2022), 108856. https://doi.org/10.1016/j.mbs.2022.108856 doi: 10.1016/j.mbs.2022.108856
    [24] M. Huang, J. Yu, Modeling the impact of migration on mosquito population suppression, Qual. Theor. Dyn. Syst., 22 (2023), 134. https://doi.org/10.1007/s12346-023-00834-8 doi: 10.1007/s12346-023-00834-8
    [25] T. Prout, The joint effects of the release of sterile males and immigration of fertilized females on a density regulated population, Theor. Popul. Biol., 13 (1978), 40–71. https://doi.org/10.1016/0040-5809(78)90035-7 doi: 10.1016/0040-5809(78)90035-7
    [26] G. L. Goff, D. Damiens, A. H. Ruttee, L. Payet, C. Lebon, J. Dehecq, et al., Field evaluation of seasonal trends in relative population sizes and dispersal pattern of Aedes albopictus males in support of the design of a sterile male release strategy, Paras. Vectors, 12 (2019), 81. https://doi.org/10.1186/s13071-019-3329-7 doi: 10.1186/s13071-019-3329-7
    [27] F. Liu, C. Zhou, P. Lin, Studies on the population ecology of Aedes albopictus–-The seasonal abundance of natural population of Aedes albopictus in Guangzhou, Acta Sci. Natur. Universitatis Sunyatseni, 29 (1990), 118–122.
    [28] A. Tr'ajer, T. Hammer, I. Kacsala, B. Tánczos, N. Bagi, J. Padisák, Decoupling of active and passive reasons for the invasion dynamics of Aedes albopictus Skuse (Diptera: Culicidae): Comparisons of dispersal history in the Apennine and Florida peninsulas, J. Vect. Ecol., 42 (2017), 233–242. https://doi.org/10.1111/jvec.12263 doi: 10.1111/jvec.12263
    [29] Y. Li, F. Kamara, G. Zhou, S. Puthiyakunnon, C. Li, Y. Liu, et al., Urbanization increases Aedes albopictus larval habitats and accelerates mosquito development and survivorship, PLoS Negl. Trop. Dis., 8 (2014), e3301. https://doi.org/10.1371/journal.pntd.0003301 doi: 10.1371/journal.pntd.0003301
    [30] F. Liu, C. Yao, P. Lin, C. Zhou, Studies on life table of the natural population of Aedes albopictus, Acta Sci. Natur. Universitatis Sunyatseni, 31 (1992), 84–93.
    [31] P. A. Ross, N. M. Endersby, H. L. Yeap, A. A. Hoffmann, Larval competition extends developmental time and decreases adult size of wMelPop Wolbachia infected Aedes aegypti, Am. J. Trop. Med. Hyg., 9 (2014), 198–205. https://doi.org/10.4269/ajtmh.13-0576 doi: 10.4269/ajtmh.13-0576
    [32] R. K. Walsh, L. Facchinelli, J. M. Ramsey, J. G. Bond, F. Gould, Assessing the impact of density dependence in field populations of Aedes aegypti, J. Vector Ecol., 36 (2011), 300–307. https://doi.org/10.1111/j.1948-7134.2011.00170.x doi: 10.1111/j.1948-7134.2011.00170.x
    [33] D. Zhang, X. Zheng, Z. Xi, K. Bourtzis, J. R. L. Gilles, Combining the sterile insect technique with the incompatible insect technique: I-impact of Wolbachia infection on the fitness of triple- and double-infected strains of Aedes albopictus, PLoS One, 10 (2015), e0121126. https://doi.org/10.1371/journal.pone.0121126 doi: 10.1371/journal.pone.0121126
    [34] P. Cailly, A. Tran, T. Balenghien, G. L'Ambert, C. Toty, P. Ezanno, A climate driven abundance model to assess mosquito control strategies, Ecol. Model., 227 (2012), 7–17. https://doi.org/10.1016/j.ecolmodel.2011.10.027 doi: 10.1016/j.ecolmodel.2011.10.027
    [35] H. I. Freedman, Deterministic mathematical models in population ecology, 2nd edition, HIFR Consulting LTD, Edmonton, 1987.
    [36] H. L. Smith, An introduction to delay differential equations with applications to the life sciences, Springer, New York, 2011.
    [37] J. Yu, Modeling mosquito population suppression based on delay differential equations, SIAM J. Appl. Math., 78 (2018), 3168–3187. https://doi.org/10.1137/18M1204917 doi: 10.1137/18M1204917
    [38] D.R. Curtiss, Recent extensions of Descartes' Rule of signs, Annals of Math., 19 (1918), 251–278. https://doi.org/10.2307/1967494 doi: 10.2307/1967494
    [39] J. Waldock, N. L. Chandra, J. Lelieveld, Y. Proestos, E. Michael, G. Christophides, et al., The role of environment variables on Aedes albopictus biology and Chikungunya epidemiology, Pathog. Glob. Health., 107 (2013), 224–240. https://doi.org/10.1179/2047773213Y.0000000100 doi: 10.1179/2047773213Y.0000000100
    [40] Z. Zhong, G. He, The life table of laboratory Aedes albopictus under various temperatures, Academic J. Sun Yat-sen Univ. Med. Sci., 9 (1988), 35–39.
    [41] A. Tran, G. L'Ambert, G. Lacour, R. Benoît, M. Demarchi, M. Cros, et al., A rainfall and temperature driven abundance model for Aedes albopictus populations, Int. J. Environ. Res. Public Health, 10 (2013), 1698–1719. https://doi.org/10.3390/ijerph10051698 doi: 10.3390/ijerph10051698
    [42] P. A. Hancock, V. L. White, A. G. Callahan, C. H. J. Godfray, A. A. Hoffmann, S. A. Ritchie, Density-dependent population dynamics in Aedes aegypti slow the spread of wMel Wolbachia, J. Appl. Ecol., 53 (2016), 785–793. https://doi.org/10.1111/1365-2664.12620 doi: 10.1111/1365-2664.12620
    [43] P. J. Huxley, K. A. Murray, S. Pawar, L. J. Cator, Competition and resource depletion shape the thermal response of population fitness in Aedes aegypti, Commun. Biol., 5 (2022), 66. https://doi.org/10.1038/s42003-022-03030-7 doi: 10.1038/s42003-022-03030-7
    [44] P. E. Parham, E. Michael, Modeling the effects of weather and climate change on malaria transmission, Environ. Health Perspect., 118 (2010), 620–626. https://doi.org/10.1289/ehp.0901256 doi: 10.1289/ehp.0901256
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