On Temperature-Dependent and Spatially Structured Dengue Transmission Models: A Mathematical Review

Abdullahi Abdu, Admi Nazra, Arrival Rince Putri, Mahdhivan Syafwan

Abstract


Dengue fever remains a major public health concern in tropical and subtropical regions, where transmission dynamics are strongly influenced by environmental variability and human mobil ity. Mathematical modelling provides a rigorous framework for capturing these interactions and informing effective control strategies.

This review presents recent advances in deterministic and spatially structured dengue transmission models that incorporate temperature-dependent parameters and human mo bility. Emphasis is placed on compartmental formulations, including multi-patch and meta population models, where movement between regions plays a key role in disease spread. The influence of temperature on key epidemiological parameters, such as mosquito biting rates, development rates, and survival probabilities, is examined through nonlinear functional relationships.

In addition, common analytical approaches are discussed, including the derivation of the basic reproduction number, stability analysis of equilibria, and sensitivity analysis. The integration of control strategies within these frameworks is also reviewed, demonstrating how intervention policies can be evaluated under varying environmental and mobility conditions.

Overall, the review highlights the importance of combining environmental and spatial effects to better understand dengue transmission and support adaptive control strategies.


Keywords


Dengue transmission; Disease control strategies; Human mobility; Mathematical modelling; Temperature variability.

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References


[1] World Health Organization. Dengue and Severe Dengue. Fact Sheet. Geneva: WHO, 2023.

[2] S. Bhatt et al. “The Global Distribution and Burden of Dengue”. In: Nature 496.7446 (2013), pp. 504–507. doi: 10.1038/nature12060.

[3] J. D. Stanaway et al. “The Global Burden of Dengue: An Analysis from the Global Burden of Disease Study 2013”. In: The Lancet Infectious Diseases 16.6 (2016), pp. 712–723. doi: 10.1016/S1473-3099(16)00026-8.

[4] S. J. Ryan, C. J. Carlson, E. A. Mordecai, and L. R. Johnson. “Global Expansion and Redistribution of Aedes-Borne Virus Transmission Risk with Climate Change”. In: PLoS Neglected Tropical Diseases 13.3 (2019), e0007213. doi: 10.1371/journal.pntd.0007213.

[5] M. U. G. Kraemer et al. “The Global Distribution of the Arbovirus Vectors Aedes aegypti and Aedes albopictus”. In: eLife 4 (2015), e08347. doi: 10.7554/eLife.08347.

[6] F. Rocha, L. Mateus, U. Skwara, M. Aguiar, and N. Stollenwerk. “Understanding Dengue Fever Dynamics: A Study of Seasonality in Vector-Borne Disease Models”. In: International Journal of Computer Mathematics 93.8 (2016), pp. 1405–1422.

[7] M. Aguiar, S. Ballesteros, B. W. Kooi, and N. Stollenwerk. “The Role of Seasonality and Import in Dengue Dynamics”. In: Journal of Theoretical Biology 289 (2011), pp. 181–196. doi: 10.1016/j.jtbi.2011.08.043.

[8] G. R. Phaijoo and D. B. Gurung. “Modeling the Impact of Temperature and Human Movement on the Persistence of Dengue Disease”. In: Computational and Mathematical Methods in Medicine 2017 (2017), p. 1747134. doi: 10.1155/2017/1747134.

[9] M. Andraud, N. Hens, C. Marais, and P. Beutels. “Dynamic Epidemiological Models for Dengue Transmission: A Systematic Review of Structural Approaches”. In: PLoS ONE 7.11 (2012), e49085. doi: 10.1371/journal.pone.0049085.

[10] E. A. Mordecai et al. “Detecting the Impact of Temperature on Transmission of Zika, Dengue, and Chikungunya Using Mechanistic Models”. In: PLoS Neglected Tropical Diseases 11.4 (2017), e0005568. doi: 10.1371/journal.pntd.0005568.

[11] J. Liu-Helmersson, H. Stenlund, A. Wilder-Smith, and J. Rocklöv. “Vectorial Capacity of Aedes aegypti: Effects of Temperature and Implications for Global Dengue Epidemic Potential”. In: PLoS ONE 9.3 (2014), e89783. doi: 10.1371/journal.pone.0089783.

[12] C. W. Morin, A. C. Comrie, and K. Ernst. “Climate and Dengue Transmission: Evidence and Implications”. In: Environmental Health Perspectives 121.11–12 (2013), pp. 1264–1272. doi: 10.1289/ehp.1306556.

[13] O. J. Brady et al. “Modelling Adult Aedes aegypti and Aedes albopictus Survival at Different Temperatures in Laboratory and Field Settings”. In: Parasites & Vectors 6 (2013), p. 351. doi: 10.1186/1756-3305-6-351.

[14] A. S. Siraj et al. “Temperature Modulates Dengue Virus Epidemic Growth Rates Through Its Effects on Reproduction Numbers and Generation Intervals”. In: PLoS Neglected Tropical Diseases 11.7 (2017), e0005797. doi: 10.1371/journal.pntd.0005797.

[15] A. M. Stewart-Ibarra and R. Lowe. “Climate and Non-Climate Drivers of Dengue Epidemics in Latin America and the Caribbean: A Systematic Review”. In: Infectious Diseases of Poverty 2 (2013), pp. 1–11.

[16] A. Wesolowski et al. “Impact of Human Mobility on the Emergence of Dengue Epidemics in Pakistan”. In: Proceedings of the National Academy of Sciences 112.38 (2015), pp. 11887–11892. doi: 10.1073/pnas.1504964112.

[17] S. T. Stoddard et al. “House-to-House Human Movement Drives Dengue Virus Transmission”. In: Proceedings of the National Academy of Sciences 110.3 (2013), pp. 994–999. doi: 10.1073/pnas.1213349110.

[18] A. Wesolowski, C. O. Buckee, K. Engø-Monsen, and C. J. E. Metcalf. “Connecting Mobility to Infectious Diseases: The Promise and Limits of Mobile Phone Data”. In: The Journal of Infectious Diseases 214.Suppl.4 (2016), pp. S414–S420. doi: 10.1093/infdis/jiw273.

[19] T. A. Perkins et al. “Theory and Data for Simulating Fine-Scale Human Movement in an Urban Environment”. In: Journal of the Royal Society Interface 11.99 (2014), p. 20140642. doi: 10.1098/rsif.2014.0642.

[20] S. Naish et al. “Climate Change and Dengue: A Critical and Systematic Review of Quantitative Modelling Approaches”. In: BMC Infectious Diseases 14 (2014), p. 167. doi: 10.1186/1471-2334-14-167.

[21] S. T. Ogunlade, A. B. Ibrahim, and M. A. Yusuf. “A Systematic Review of Mathematical Models of Dengue Transmission and Vector Control: 2010–2020”. In: Viruses 15.1 (2023), p. 254. doi: 10.3390/v15010254.

[22] V. R. Louis et al. “Modeling Tools for Dengue Risk Mapping: A Systematic Review”. In: International Journal of Health Geographics 13 (2014), p. 50. doi: 10.1186/1476-072X-13-50.

[23] R. C. Reiner et al. “A Systematic Review of Mathematical Models of Mosquito-Borne Pathogen Transmission: 1970–2010”. In: Journal of the Royal Society Interface 10.81 (2013), p. 20120921. doi: 10.1098/rsif.2012.0921.

[24] D. Moher, A. Liberati, J. Tetzlaff, D. G. Altman, and The PRISMA Group. “Preferred Reporting Items for Systematic Reviews and Meta-Analyses: The PRISMA Statement”. In: International Journal of Surgery 8.5 (2010), pp. 336–341. doi: 10.1016/j.ijsu.2010.02.007.

[25] T. Götz, N. Altmeier, W. Bock, R. Rockenfeller, Sutimin, and K. P. Wijaya. “Modeling Dengue Data from Semarang, Indonesia”. In: Ecological Complexity 30 (2017), pp. 57–62. doi: 10.1016/j.ecocom.2016.12.010.

[26] M. A. Khan and Fatmawati. “Dengue Infection Modeling and Its Optimal Control Analysis in East Java, Indonesia”. In: Heliyon 7.1 (2021), e06023. doi: 10.1016/j.heliyon.2021.e06023.

[27] O. Diekmann, J. A. P. Heesterbeek, and M. G. Roberts. “The Construction of Next-Generation Matrices for Compartmental Epidemic Models”. In: Journal of the Royal Society Interface 7.47 (2010), pp. 873–885. doi: 10.1098/rsif.2009.0386.

[28] H. S. Rodrigues, M. T. T. Monteiro, and D. F. M. Torres. “Seasonality Effects on Dengue: Basic Reproduction Number, Sensitivity Analysis and Optimal Control”. In: arXiv Preprint arXiv:1409.3928 (2014).

[29] B. Tesla et al. “Temperature Drives Zika Virus Transmission: Evidence from Empirical and Mathematical Models”. In: Proceedings of the Royal Society B: Biological Sciences 285.1884 (2018), p. 20180795. doi: 10.1098/rspb.2018.0795.

[30] J. Rocklöv and R. Dubrow. “Climate Change: An Enduring Challenge for Vector-Borne Disease Prevention and Control”. In: Nature Immunology 21.5 (2020), pp. 479–483. doi: 10.1038/s41590-020-0648-y.

[31] H. Lee and C. Castillo-Chavez. “The Role of Residence Times in Two-Patch Dengue Transmission Dynamics and Optimal Strategies”. In: Journal of Theoretical Biology 374 (2015), pp. 152–164. doi: 10.1016/j.jtbi.2015.03.005.

[32] F. Brauer. Mathematical Epidemiology. Lecture Notes in Mathematics 1945. Berlin: Springer, 2008. doi: 10.1007/978-3-540-78911-6.

[33] S. A. Carvalho, S. O. da Silva, and I. C. Charret. “Mathematical Modeling of Dengue Epidemic: Control Methods and Vaccination Strategies”. In: Theory in Biosciences 138.2 (2019), pp. 223–239. doi: 10.1007/s12064-019-00273-7.

[34] T. Götz, E. Soewono, and K. P. Wijaya. “An Optimal Control Model of Mosquito Reduction Management in a Dengue Endemic Region”. In: International Journal of Biomathematics 7.6 (2014), p. 1450056. doi: 10.1142/S1793524514500569.

[35] D. Aldila, T. Götz, and E. Soewono. “An Optimal Control Problem Arising from a Dengue Disease Transmission Model”. In: Mathematical Biosciences 242.1 (2013), pp. 9–16. doi: 10.1016/j.mbs.2012.11.014.

[36] J. P. Messina et al. “The Current and Future Global Distribution and Population at Risk of Dengue”. In: Nature Microbiology 4.9 (2019), pp. 1508–1515. doi: 10.1038/s41564-019-0476-8.

[37] L. Cattarino et al. “Mapping Global Variation in Dengue Transmission Intensity”. In: Science Translational Medicine 12.528 (2020), eaax4144. doi: 10.1126/scitranslmed.aax4144.

[38] J. Lourenço and M. Recker. “The 2012 Madeira Dengue Outbreak: Epidemiological Determinants and Future Epidemic Potential”. In: PLoS Neglected Tropical Diseases 8.8 (2014), e3083. doi: 10.1371/journal.pntd.0003083.

[39] M. U. G. Kraemer et al. “Past and Future Spread of the Arbovirus Vectors Aedes aegypti and Aedes albopictus”. In: Nature Microbiology 4.5 (2019), pp. 854–863. doi: 10.1038/s41564-019-0376-y.

[40] M. Aguiar, B. W. Kooi, J. Martins, and N. Stollenwerk. “Scaling of Stochasticity in Dengue Hemorrhagic Fever Epidemics”. In: Mathematical Modelling of Natural Phenomena 7.3 (2012), pp. 1–11.

[41] T. Sardar, S. K. Sasmal, and J. Chattopadhyay. “Estimating Dengue Type Reproduction Numbers for Two Provinces of Sri Lanka During the Period 2013–14”. In: Virulence 7.2 (2016), pp. 187–200. doi: 10.1080/21505594.2015.1096470.




DOI: https://doi.org/10.18860/cauchy.v11i1.42040

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