The Analysis of Epidemic Dynamical Models for Dengue Transmission Considering the Mosquito Aquatic Phase

Nur Inayah, Muhammad Manaqib, Nina Fitriyati, Madona Yunita Wijaya, Andrew Fiade, Flori Ratna Sari

Abstract


This  study  generalizes the dengue  transmission model  by  considering the dynamics of the human population and  the Aedes  aegypti mosquito  population.  The  mosquito  population is  devided into  two  phases,  i.e.,  the aquatic  phase and the adult  phase.  From  the model,  we seek the disease-free  equilibrium, endemic  equilibrium, and  basic  reproduction number   (R0) points.    The  model  yields a  single   basic  reproduction number   which determines the system’s  behavior.   If  R0   < 1,  the disease-free  equilibrium is  locally  asymptotically stable, indicating that the disease  will die out.  Conversely, if R0   > 1, an endemic  equilibrium exists,  and  the disease may  persist  in the  population.    Next,   a  numerical simulation  is  performed  to  geometrically  visualize   the resulting analysis  and  also  to  simulate the  dengue   transmission in  DKI Jakarta   Province,  Indonesia.   The resulting  numerical simulation  supports our  analysis.   Meanwhile, the  simulation in  DKI Jakarta  Province suggests that  the dengue  fever  disappears after  60 days  from  the first  case appearance  after  controlling  the mosquito  population through fogging and the use of mosquito  larvae  repellent.  Lastly, the sensitivity analysis of R0   indicates  that  parameters   related  to  the  mosquito’s  aquatic   phase  have  a  strong   influence   on  dengue transmission, meaning that small  changes  in these parameters  can significantly increase or decrease the value  of R0  and thus the potential  for an outbreak.


Keywords


Dengue Fever; Aedes Aegypti; Aquatic Phase; Stability Analysis; Sensitivity Analysis

Full Text:

PDF

References


T. Setiati et al., “Changing epidemiology of dengue haemorrhagic fever in indonesia,” Dengue Bulletin, vol. 30, 2006.

M. R. Karyanti et al., “The changing incidence of dengue haemorrhagic fever in indonesia: a 45-year registry-based analysis,” BMC Infectious Diseases, vol. 14, no. 1, p. 412, 2014. DOI:10.1186/1471-2334-14-412

Kemenkes, Indonesian Health Profile 2019. Jakarta:Kementerian Kesehatan Republik Indonesia, 2020.

BPS, “Hasil Sensus Penduduk 2020,”https://www.bps.go.id/pressrelease/2021, 2020, Accesed on 25 December 2024.

Kemenkes RI, “Situasi Penyakit Demam Berdarah Di Indonesia 2017,” https://www.kemkes.go.id/download.php, 2018, Accesed on 25 December 2024.

A. Candra, “Demam Berdarah Dengue: Epidemiologi, Patogenesis, dan Faktor Risiko Penularan,” Aspirator, vol. 2, no. 2, pp. 110–119, 2016.

T. Blante, J. Jaharuddin, and E. Nugrahani, “Sensitivity analysis of si1i2rs model for dengue fever transmission,” Jambura Journal of Biomathematics (JJBM), vol. 5, no. 1, pp. 19–26, 2024. DOI:10.37905/jjbm.v5i1.23132

M. Kleden, A. Atti, and A. H. Talahatu, “Factors causing dengue hemorrhagic fever (dhf) in sikka district, east nusa tenggara province,” Jambura Journal of Biomathematics (JJBM), vol. 4, no. 1, pp. 80–87, 2023. DOI:10.34312/jjbm.v4i1.19460

U. Achmadi, “Manajemen Demam Berdarah Berbasis Wilayah,” Buletin Jendela Epidemiologi, vol. 2, 2010.

MT. Li et al., “The Driving Force for 2014 Dengue Outbreak in Guangdong, China,” PLOS ONE, vol. 11, no. 11, p. e0166211, 2016. DOI:10.1371/journal.pone.0166211

H. M. Yang et al., “Assessing the effects of temperature on dengue transmission,” Epidemiology and Infection, vol. 137, no. 8, pp. 1179–1187, 2009. DOI:10.1017/S0950268809002052

J. Müller, Mathematical Models in Biology. Munich:Technical University Munich, Centre for Mathematical Sciences, 2004.

D. Aldila, T. Götz, and E. Soewono, “An optimal control problem arising from a dengue disease transmission model,” Mathematical biosciences, vol. 242, no. 1, pp. 9–16, 2013. DOI:10.1016/j.mbs.2012.11.014

L. Esteva and C. Vargas, “Analysis of a dengue disease transmission model,” Mathematical biosciences, vol. 150, no. 2, pp. 131–151, 1998. DOI:10.1016/S0025-5564(98)10003-2

N. Ilmayasinta et al., “An optimal control analysis of dengue fever,” InPrime: Indonesian Journal of Pure and Applied Mathematics, vol. 5, no. 2, pp. 99–114, 2023. DOI:10.15408/inprime.v5i2.30392

T. W. Scott and A. C. Morrison, “Vector dynamics and transmission of dengue virus: implications for dengue surveillance and prevention strategies: vector dynamics and dengue prevention,” in:Rothman, A. (eds) Dengue Virus. Current Topics in Microbiology and Immunology, vol. 338, pp. 115–128, 2010. DOI:10.1007/978-3-642-02215-9_9

E. Banni et al., “Estimasi reproduction number model matematika penyebaran malaria di sumba tengah, indonesia,” Jambura Journal of Biomathematics (JJBM), vol. 2, no. 1, pp. 13–19, 2021. DOI:10.34312/jjbm.v2i1.9971

A. Ahkrizal, J. Jaharuddin, and E. Nugrahani, “Dynamics system in the seir-si model of the spread of malaria with recurrence,” Jambura Journal of Biomathematics (JJBM), vol. 4, no. 1, pp. 31–36, 2023. DOI:10.34312/jjbm.v4i1.18754

M. C. Eisenberg et al., “Examining rainfall and cholera dynamics in Haiti using statistical and dynamic modeling approaches,” Epidemics, vol. 5, no. 4, pp. 197–207, 2013. DOI:10.1016/j.epidem.2013.09.004

J. H. Tien and D. J. Earn, “Multiple transmission pathways and disease dynamics in a waterborne pathogen model,” Bulletin of Mathematical Biology, vol. 72, no. 6, pp. 1506–1533, 2010. DOI:10.1007/s11538-010-9507-6

E. Chikaki and H. Ishikawa, “A dengue transmission model in Thailand considering sequential infections with all four serotypes,” Journal of infection in developing countries, vol. 3, no. 9, pp. 711–722, 2009. DOI:10.3855/jidc.616

M. Andraud et al., “Dynamic Epidemiological Models for Dengue Transmission: A Systematic Review of Structural Approaches,” PLOS ONE, vol. 7, no. 11, p. e49085, 2012. DOI:10.1371/journal.pone.0049085

M. Amaku et al., “A comparative analysis of the relative efficacy of vector-control strategies against dengue fever,” Bulletin of mathematical biology, vol. 76, no. 3, pp. 697–717, 2014. DOI:10.1007/s11538-014-9939-5

E. Massad et al., “Modeling the impact of global warming on vector-borne infections,” Physics of life reviews, vol. 8, no. 2, pp. 169–199, 2011. DOI:10.1016/j.plrev.2011.01.001

M. Chan and M. A. Johansson, “The Incubation Periods of Dengue Viruses,” PLOS ONE, vol. 7, no. 11, p. e50972, 2012. DOI:10.1371/journal.pone.0050972

H. Delatte et al., “Influence of Temperature on Immature Development, Survival, Longevity, Fecundity, and Gonotrophic Cycles of Aedes albopictus, Vector of Chikungunya and Dengue in the Indian Ocean ,” Journal of Medical Entomology, vol. 46, no. 1, pp. 33–41, 2009. DOI:10.1603/033.046.0105

T. W. Scott et al., “Longitudinal Studies of Aedes aegypti (Diptera: Culicidae) in Thailand and Puerto Rico: Blood Feeding Frequency ,” Journal of Medical Entomology, vol. 37, no. 1, pp. 89–101, 2000. DOI:10.1603/0022-2585-37.1.89

Q. Cheng et al., “Climate and the Timing of Imported Cases as Determinants of the Dengue Outbreak in Guangzhou, 2014: Evidence from a Mathematical Model,” PLOS Neglected Tropical Diseases, vol. 10, no. 2, 2016. DOI:10.1371/journal.pntd.0004417

P. van den Driessche and J. Watmough, “Further Notes on the Basic Reproduction Number,” in Mathematical Epidemiology. Victoria:Springer, 1945. DOI:10.1007/978-3-540-78911-6_6

L. Esteva and C. Vargas, “Analysis of a dengue disease transmission model,” Mathematical Biosciences, vol. 150, no. 2, pp. 131–151, 1998. DOI:10.1016/S0025-5564(98)10003-2

H. M. Yang et al., “Assessing the effects of temperature on dengue transmission,” Epidemiology and Infection, vol. 137, no. 8, pp. 1188–1202, 2009. DOI:10.1017/S0950268809002052

WHO, “Dengue: Guidelines for Diagnosis, Treatment, Prevention and Control,” https://apps.who.int/iris/handle/10665/44188, 2009, Accesed on 25 December 2024.

N. Chitnis, J. M. Hyman, and J. M. Cushing, “Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model,” Bulletin of mathematical biology, vol. 70, no. 5, pp. 1272–1296, 2008. DOI:10.1007/s11538-008-9299-0

R. Resmawan and L. Yahya, “Sensitifity Analysis of Mathematical Model of Coronavirus Disease (COVID-19) Transmission,” Cauchy, vol. 6, no. 2, p. 91, 2020. DOI:10.18860/ca.v6i2.9165




DOI: https://doi.org/10.37905/jjbm.v6i3.29332

Copyright (c) 2025 Nur Inayah, Muhammad Manaqib, Nina Fitriyati, Madona Yunita Wijaya, Andrew Fiade, Flori Ratna Sari

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Jambura Journal of Biomathematics (JJBM) has been indexed by:

EDITORIAL OFFICE OF JAMBURA JOURNAL OF BIOMATHEMATICS

 Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Gorontalo
Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango 96554, Gorontalo, Indonesia
 Email: [email protected]
 Jambura Journal of Biomathematics (JJBM) by Department of Mathematics Universitas Negeri Gorontalo is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Powered by Public Knowledge Project OJS.