Stochastic and Deterministic Dynamic Model of Dengue Transmission Based on Dengue Incidence Data and Climate Factors in Bandung City


  • La Pimpi Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia
  • Sapto Wahyu Indratno Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia
  • Juni Wijayanti Puspita Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia
  • Edi Cahyono Department of Mathematics, Halu Oleo University, Kampus Bumi Tridharma Anduonohu, Kendari 93232, Indonesia



Climate variables, dengue disease transmission, effective reproduction number, Poisson regression model, infected human, infected mosquito


Indonesia, a country in the tropics, is an area of distribution and an endemic area of dengue. The death rate caused by dengue is relatively high In Indonesia. Therefore, the health authority must prioritize preventing and controlling dengue disease for a long-term policy. This study proposes a method based on dynamic climate variables in estimating the proportion of infected human and infected mosquito. We focus on the dengue case in Bandung city, one of the big cities in Indonesia, which is classified as endemic dengue. We applied the Poisson regression method involving dynamic climate variables to estimate the average number of infected human population. We then use these estimation results as the basis for approximating the proportion of infected human and mosquito populations using a deterministic and stochastic model approach. Effective reproduction number is also obtained here. The simulation results show that the stochastic model looks better in capturing dengue incidence data than the deterministic model. Therefore, dengue transmission can be reduced by controlling the abundance of mosquito populations, considering climate conditions and the historical number of infected human.


Word Health Organization (WHO), Dengue and Severe Dengue-Fact sheet,, Accessed on April 1, 2021.

Noordeen, F., Raza, M.R.M., Pitchai., F.N.N., Saranga, W.K.C., Sandeepani, L.K.H.B., Sadamali, L.D., Sanathchandra, MBTT., Samarakoon, K.R.M.H.N., Rukhshana, M.J.F., Ranayake, R.M.M., Ratnayake, R.C.S.B., Ratanayake, R.M.P.M., Seanadheera, H.M.S.M., Distribution of Dengue Vectors, Aedes Aegypti and textitAedes Albopictus, in a Few Selected Semi-urban Areas of the Central Province of Sri Lanka, Journal of Infectious Diseases, 8(1), pp. 36-39, 2018.

Gil, J.F., Palacios, M., Krolewiecki, A.J., Cordata, P., Flores, R., Jaime, C., Arias, L., Villalpando, C., Damato, A.M.A., Nasser, J.R., and Aparicio, J.P., Spatial Spread of Dengue in a Non-endemic Tropical City in Northern Argentina, Acta Tropica, 158, pp. 24-31, 2016.

Gupta, N., Srivastava, S., Jain, A., and Chaturvedi, U.C., Dengue in India, Indian J.Med. Res,. 136(3), pp. 373-390, 2012.

Puspita, J.W, Fakhruddin, M., Fahlena, H., Rohim, F., and Sutimin, On the Reproduction Ratio of Dengue Incidence in Semarang, Indonesia 2015-2018, Commun. Biomath. Sci., 2(2), pp. 118-126, 2019.

Mishra, G., Jain, A., Prakash, O., Prakash, S., Kumar, R., Garg, R.K., Pandey, N., and Singh, M., Molecular Characterization of Dengue Viruses Circulating During 2009-2012 in Uttar Pradesh, India, J. Med. Virol., 87(1), pp. 68-75, 2015.

World Health Organization (WHO), Dengue: Guidelines for Diagnosis, Treatment, Prevention and Control, WHO/TDR, New edition, p. 160, 2009.

Ali, T.M., Kamil, A.A., and Karim, M.F.A., Deterministic Mathematical Model of Dengue Disease Spread, Journal of Mathematical Sciences, 96(4), pp. 419-435, 2015.

WHO/SERO, Concrete Measure Key in Controlling Dengue in South East Asia. Press Release SEA/PR/1479. New Delhi, World Health Organization Regional Office for South-East Asia, 2008,, Accessed on January 14, 2021.

Esteva, L. and Vargas, C., Analysis of a Dengue Disease Transmission Model, Math. Biosci., 150, pp. 131-151, 1998.

Leite, A., Liu-Helmersson, J., Karim, F., and Rocklov, J., Asymptomatic Individuals and Dengue Transmission - Insights from Mathematical Modeling, European Journal of Public Health, 24 (2), 2014.

Supriatna, A. K., Soewono, E., and van Gils, S. A., A two-age-classes dengue transmission model, Mathematical Biosciences, 216(1), pp. 114-121, 2008.

Otero, M. and Solari, H.G., Stochastic Eco-epidemiological Model of Dengue Disease Transmission by Aedes Aegypti Mosquito, Mathematical Biosciences, 223(1), pp. 32-46, 2010.

Fakhruddin, M., Nuraini, N., and Indratno, S. W., Mathematical model of dengue transmission based on daily data in Bandung, AIP Conference Proceedings, 2084(1), p. 020013, 2019.

Champagne, C. and Cazelles, B., Comparison of Stochastic and Deterministic Frameworks in Dengue Modelling, Mathematical Biosciences, 310, pp. 1-12, 2019.

Morin, C.W., Comrie, A.C. and Ernst, K., Climate and Dengue Transmission: Evidence and Implications, Environ. Health Perspect. 121, pp. 1264-1272, 2013.

Naish, S., Dale, P., Mackenzie, J.S., McBride, J., Mangersen, K. and Tong, S., Climate Change and Dengue: a Critical and Systematic Review of Quantitative Modelling Approaches, BMC Infect. Dis., 14, p. 167, 2014.

Carrington, L.B., Armijos, M.V., Lambrechts, L., and Scott, T.W., Fluctuations at a Low Mean Temperature Accelerate Dengue Virus Transmission by Aedes Aegypti, PloS Negl. Trop. Dis., 7(4), e2190, 2013.

Sirisena, P.D. and Noordeen, F., Evolution of dengue in Sri Lanka-changes in the virus, vector, and climate, Int. J. Infect Dis., 19, pp. 6-12, 2014.

Chen, S.C., Liao, C.M., Chio, C.P., Chou, H.H., You, S.H., and Cheng, Y.H., Lagged Temperature Effect with Mosquito Transmission Potential Explains Dengue Variability in Southern Taiwan: Insights from a Statistical Analysis, Science of the Total Environment, 408, pp. 4069-4075, 2010.

Banu, S., Hu, W., Guo, Y., Hurst, C., and Tong, S., Projecting the impact of climate change on dengue transmission in Dhaka, Bangladesh, Environment International, 63, pp. 137-142, 2014.

Fakhruddin, M., Putra, P. S., Wijaya, K. P., Sopaheluwakan, A., Satyaningsih, R., Komalasari, K. E., Maemun, Sumiati, Indratno, S. W., Nuraini, N., Gotz, T., and Soewono, E., Assessing the interplay between dengue incidence and weather in Jakarta via a clustering integrated multiple regression model, Ecological Complexity, 39, 100768, 2019.

Statistics of Bandung Municipality, Bandung Municipality in Figures 2018,, Accessed on February 20, 2020.

BMKG, Dataonline-Pusat Database 2018,, Accessed on February 1, 2020.

Esteva, L. and Yang, H.M., Mathematical Model to Assess the Control of Aedes Aegypti Mosquito by the Sterile Insect Technique, Mathematical Bioscience, 198, pp. 132-147, 2005.

Zhu, M. and Xu, Y., A Time-periodic Dengue Fever Model in a Heterogeneous Environment, Mathematics and Computers in Simulation, 155, pp. 115-129, 2019.

Esteva, L. and Vargas, C., A Model for Dengue Disease with Variable Human Population, J. Math. Biol. 38, 220-240, 1999.

Hynes, N.A., Dengue: A Reemerging Concern for Travelers, Cleve. Clin. J. Med., 79, pp. 474-482, 2012.

Hii, Y.L., Zhu, H., Ng, N., Ng, L.C., and Rocklov, J., Forecast of Dengue Incidence Using Temperature and Rainfall, PloS Negl. Trop. Dis. 6, e1908, 2012.

Sang, S., Gu, S., Bi, P., Yang, W., Yang, Z., Xu, L., Yang, J., Liu, X., Jiang, T., Wu, H., Chu, C., and Liu, Q., Predicting Unprecedented Dengue Outbreak Using Imported Cases and Climatic Factors in Guangzhou, 2014, PloS Negl. Trop. Dis. 9, e0003808, 2015.

Chowell, G., Diaz-Duenas, P., Miller, J., Alcazar-Velazco, A., Hyman, J., Fenimore, P., and Castillo-Chavez, C., Estimation of the Reproduction Number of Dengue Fever from Spatial Epidemic, Mathematical Biosciences 208, p. 571, 2007.

Choi, Y., Tang, C.S., McIver, L., Hashizume, M., Chan, V., Abeyasinghe, R.R., Iddings, S., and Huy, R., Effects of Weather Factors on Dengue Fever Incidence and Implications for Interventions in Cambodia, BMC Public Health 16(1), p. 241, 2016.

Wijaya, K.P., Gotz, T., and Soewono, E., Advances in Mosquito Dynamics Modeling, Math. Meth. Appl. Sci., 39(16), pp. 4750-4763, 2016.

Diekmann, O., Heesterbeek, J. A. P., and Roberts, M. G., The Construction of Next-Generation Matrices for Compartmental Epidemic Models, Journal of the Royal Society Interface, 7(47), pp. 873-885, 2010.

Zhao, S., Musa, S.S., Hebert, J.T., Cao, P., Ran, J., Meng, J., He, D. and Qin, J., Modelling the Effective Reproduction Number of Vector-borne Diseases: The Yellow Fever Outbreak in Luanda, Angola 2015-2016 as an example, PeerJ, 8, e8601, 2020.

Anderson, R., Donnelly, C., Hollingsworth, D., Keeling, M., Vegvari, C., Baggaley, R., and Maddren, R., Reproduction Number (R) and Growth Rate (r) of the COVID-19 Epidemic in the UK: Methods of Estimation, Data Sources, Causes of Heterogeneity, and Use as a Guide in Policy Formulation, The Royal Society, 2020.

Pliego, E.P., Castro, J.V., and Collar, A.F., Seasonality on the Life Cycle of Aedes Aegypti Mosquito and its Statistical Relation with Dengue Outbreaks, Applied Mathematical Modelling, 50, pp. 484-496, 2017.