• James Uriel Livingstone Mangobi Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Manado, Indonesia
Keywords: dengue hemorrhagic fever, Aedes albopictus, SEIR model, equilibrium point, stability analysis


Dengue hemorrhagic fever (DHF) is an acute febrile disease caused by the dengue virus, which is transmitted by various species of Aedes mosquitoes. The SEIR model is a mathematical model for studying the spread of dengue fever. In this model, it is assumed that some mosquito eggs have been infected because infected mosquitoes can transmit the virus to their eggs. The main vector of this disease is the Aedes albopictus mosquito. Analysis was carried out to assess the stability of the equilibrium point, and numerical simulations were carried out to see changes in population numbers due to changes in parameter values. A disease-free equilibrium (DFE) point, which is stable given the basic reproductive number . An endemic point whose stability is guaranteed if the value . The numerical simulations show that an increasing mosquito mortality rate decreases the number of exposed, susceptible humans. Furthermore, an increase in the average bite of an infected mosquito will increase the number of exposed, susceptible humans. For the mosquito population, increasing mosquitoes’ mortality rate will decrease the number of exposed, susceptible mosquitoes. Finally, an increase in the average bite of an infected mosquito will increase the number of exposed, susceptible mosquitoes.


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G. Bhuyan, B. Das, P. Panda, and M. Rao Meda, “Dengue and Its Management through Ayurveda,” International Ayurvedic Medical Journal, vol. 2020, no. 2, 2020, Accessed: Apr. 29, 2023. [Online]. Available:

S. Bhatt et al., “The global distribution and burden of dengue,” Nature, vol. 496, no. 7446, pp. 504–507, Apr. 2013, doi: 10.1038/nature12060.

B. Dayal, P. Patel, S. Prasad, B. Shah, B. K. Singh, and P. Bhatta, “Dengue Fever Outbreak in Kathmandu and its Management in Ayurveda,” Journal of Ayurveda Campus, vol. 3, no. 1, pp. 1–4, 2022, doi: 10.51648/jac40.

Anonymous, Dengue - Guidelines for diagnosis, treatment, prevention and control, New Edition. 2009. Accessed: Apr. 29, 2023. [Online]. Available:

P. Jia et al., “A climate-driven mechanistic population model of Aedes albopictus with diapause,” Parasit Vectors, vol. 9, no. 1, p. 175, 2016, doi: 10.1186/s13071-016-1448-y.

E. Vyhmeister, G. Provan, B. Doyle, B. Bourke, G. G. Castane, and L. Reyes-Bozo, “Comparison of time series and mechanistic models of vector-borne diseases,” Spat Spatiotemporal Epidemiol, vol. 41, p. 100478, 2022, doi:

J. Liu-Helmersson, J. Rocklöv, M. Sewe, and Å. Brännström, “Climate change may enable Aedes aegypti infestation in major European cities by 2100,” Environ Res, vol. 172, pp. 693–699, 2019, doi:

M. Aguiar et al., “Mathematical models for dengue fever epidemiology: A 10-year systematic review,” Phys Life Rev, vol. 40, pp. 65–92, 2022, doi:

D. Heymann, Control of Communicable Diseases Manual, 21st ed. Washington, DC: American Public Health Association, 2022. Accessed: Sep. 04, 2023. [Online]. Available:

B. V. Giordano, A. Gasparotto, P. Liang, M. P. Nelder, C. Russell, and F. F. Hunter, “Discovery of an Aedes ( Stegomyia ) albopictus population and first records of Aedes ( Stegomyia ) aegypti in Canada,” Med Vet Entomol, vol. 34, no. 1, pp. 10–16, Mar. 2020, doi: 10.1111/mve.12408.

M. Bonizzoni, G. Gasperi, X. Chen, and A. A. James, “The invasive mosquito species Aedes albopictus: Current knowledge and future perspectives,” Trends in Parasitology, vol. 29, no. 9. pp. 460–468, Sep. 2013. doi: 10.1016/

D. Heriawati, S. S. Umami, D. Supardan, and Suhirman, “Distribution of Aedes albopictus Mosquitoes in Indonesia,” in Proceedings of the 2nd International Conference on Islam, Science and Technology (ICONIST 2019), Paris, France: Atlantis Press, 2020. doi: 10.2991/assehr.k.200220.035.

M. Z. Ndii, N. Anggriani, J. J. Messakh, and B. S. Djahi, “Estimating the reproduction number and designing the integrated strategies against dengue,” Results Phys, vol. 27, p. 104473, Aug. 2021, doi: 10.1016/j.rinp.2021.104473.

M. Z. Ndii, N. Anggriani, J. J. Messakh, and B. S. Djahi, “Estimating the reproduction number and designing the integrated strategies against dengue,” Results Phys, vol. 27, p. 104473, 2021, doi:

H. M. Yang, “The basic reproduction number obtained from Jacobian and next generation matrices – A case study of dengue transmission modelling,” Biosystems, vol. 126, pp. 52–75, Dec. 2014, doi: 10.1016/j.biosystems.2014.10.002.

X.-Q. Zhao, “The Theory of Basic Reproduction Ratios,” 2017. [Online]. Available:

G. O. Fosu, E. Akweittey, and A. Adu-Sackey, “Next-generation matrices and basic reproductive numbers for all phases of the Coronavirus disease,” Open Journal of Mathematical Sciences, vol. 4, no. 1, pp. 261–272, Dec. 2020, doi: 10.30538/oms2020.0117.

O. Diekmann, J. A. P. Heesterbeek, and M. G. Roberts, “The construction of next-generation matrices for compartmental epidemic models,” J R Soc Interface, vol. 7, no. 47, pp. 873–885, Jun. 2010, doi: 10.1098/rsif.2009.0386.

C. W. Castillo-Garsow and C. Castillo-Chavez, “A Tour of the Basic Reproductive Number and the Next Generation of Researchers,” 2020, pp. 87–124. doi: 10.1007/978-3-030-33645-5_2.

M. Z. Ndii, R. I. Hickson, D. Allingham, and G. N. Mercer, “Modelling the transmission dynamics of dengue in the presence of Wolbachia,” Math Biosci, vol. 262, pp. 157–166, Apr. 2015, doi: 10.1016/j.mbs.2014.12.011.

P.-A. Bliman, “A feedback control perspective on biological control of dengue vectors by Wolbachia infection,” Eur J Control, vol. 59, pp. 188–206, 2021, doi:

Y. Li and L. Liu, “The impact of Wolbachia on dengue transmission dynamics in an SEI–SIS model,” Nonlinear Anal Real World Appl, vol. 62, p. 103363, 2021, doi:

M. Z. Ndii, D. Allingham, R. I. Hickson, and K. Glass, “The effect of Wolbachia on dengue outbreaks when dengue is repeatedly introduced,” Theor Popul Biol, vol. 111, pp. 9–15, 2016, doi:

How to Cite
J. Mangobi, “SEIR MODEL SIMULATION WITH PART OF INFECTED MOSQUITO EGGS”, BAREKENG: J. Math. & App., vol. 17, no. 3, pp. 1641-1652, Sep. 2023.