Analysis of A Coendemic Model of COVID-19 and Dengue Disease

Authors

  • Hilda Fahlena Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Bandung, Indonesia
  • Widya Oktaviana Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Bandung, Indonesia
  • Farida Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Bandung, Indonesia
  • Sudirman Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Bandung, Indonesia
  • Nuning Nuraini 1) Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Bandung, Indonesia 2) Center for Mathematical Modeling and Simulation, Institut Teknologi Bandung, Bandung, West Java, Indonesia
  • Edy Soewono 1) Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Bandung, Indonesia 2) Center for Mathematical Modeling and Simulation, Institut Teknologi Bandung, Bandung, West Java, Indonesia

DOI:

https://doi.org/10.5614/cbms.2021.4.2.5

Keywords:

COVID-19, dengue, SIR model, coendemic, basic reproductive ratio, hopf bifurcation

Abstract

The coronavirus disease 2019 (COVID-19) pandemic continues to spread aggressively worldwide, infecting more than 170 million people with confirmed cases, including more than 3 million deaths. This pandemic is increasingly exacerbating the burden on tropical and subtropical regions of the world due to the pre-existing dengue fever, which has become endemic for a longer period in the same region. Co-circulation dengue and COVID-19 cases have been found and confirmed in several countries. In this paper, a deterministic model for the coendemic of COVID-19 and dengue is proposed. The basic reproduction ratio is obtained, which is related to the four equilibria, disease-free, endemic-COVID-19, endemic-dengue, and coendemic equilibria. Stability analysis is done for the first three equilibria. Furthermore, a condition for coexistence equilibrium is obtained, which gives a condition for bifurcation analysis. Numerical simulations were carried out to obtain a stable limit-cycle resulting from two Hopf bifurcation points with dengue transmission rate and COVID-19 transmission rate as the bifurcation parameter, representing a stable periodic coexistence of dengue and COVID-19 transmission. We identify the period of limit cycle decreases after reaching the maximum value.

Author Biography

Hilda Fahlena, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Bandung, Indonesia

Industrial and Financial Research Group

References

Felsenstein, S., Herbert, J. A., McNamara, P. S., and Hedrich, C. M., COVID-19: Immunology and treatment options, Clinical immunology, 215, p. 108448, 2020.

Lopes, A. G., Celestino, C. S., Barros, T. T., Fevereiro, A. G., Gejer, D. H., Oliveira, F. M., ... and Amano, M. T., Case Report: A Severe SARS-CoV-2 Infection in a Teenager With Angelman Syndrome, Frontiers in Medicine, 8, p. 108, 2021

?WHO Coronavirus (COVID-19) Dashboard, WHO Coronavirus (COVID-19) DashboardWith Vaccination Data?, https://covid19.who.int/, Accessed on June 09, 2021.

Rasmussen, Sonja. A et al., Coronavirus Disease 2019 (COVID-19) and pregnancy: what obstetricians need to know, American Journal of Obstetrics and Gynecology, 2020. https://doi.org/10.1016/j.ajog.2020.02.017, Accessed on June 12, 2021).

Scientific, W. H. O., Heymann, D. L., and Shindo, N., COVID-19: what is next for public health?. Lancet, 395(10224), pp. 542-545, 2020.

Ali, M. Y., Gatiti, P., The COVID-19 (Coronavirus) pandemic: reflections on the roles of librarians and information professionals, Health information and libraries journal, 37(2), pp.158-162, 2020.

Harapan, H., Ryan, M., Yohan, B., Abidin, R. S., Nainu, F., Rakib, A., ... and Sasmono, R. T., Covid-19 and dengue: Double punches for dengue-endemic countries in Asia, Reviews in medical virology, 31(2), p.e2161, 2021.

Chen, N., Zhou, M., Dong, X., Qu, J., Gong, F., Han, Y., ... & Zhang, L., Epidemiological and clinical characteristics of 99 cases of 2019 novel coronavirus pneumonia in Wuhan, China: a descriptive study, The lancet, 395(10223), pp. 507-513, 2020.

Joob, B., Wiwanitkit, V., COVID-19 can present with a rash and be mistaken for dengue, Journal of the American Academy of Dermatology, 82(5), p. e177, 2020.

World Health Organization, et al. Dengue: guidelines for diagnosis, treatment, prevention and control, World Health Organization, 2009.

Yan, G., Lee, C. K., Lam, L. T., Yan, B., Chua, Y. X., Lim, A. Y., and Tambyah, P. A., Covert COVID-19 and false-positive dengue serology in Singapore, The Lancet Infectious Diseases, 20(5), p. 536, 2020.

Bhatt, S., Gething, P. W., Brady, O. J., Messina, J. P., Farlow, A. W., Moyes, C. L., and Hay, S. I., The global distribution and burden of dengue, Nature, 496(7446), pp. 504-507, 2013.

Halstead, S. B., Dengue hemorrhagic fever: two infections and antibody dependent enhancement, a brief history and personal memoir, Revista cubana de medicina tropical, 54(3), pp. 171-179, 2002.

Rothman, A. L., Dengue: defining protective versus pathologic immunity, The Journal of clinical investigation, 113(7), pp. 946-951, 2004.

Halstead, S. B., Katzelnick, L. C., Russell, P. K., Markoff, L., Aguiar, M., Dans, L. R., Dans, A. L., Ethics of a partially effective dengue vaccine: Lessons from the Philippines. Vaccine, 38(35), pp. 5572-5576, 2020.

Aguiar, M., Ballesteros, S., Kooi, B. W., and Stollenwerk, N. The role of seasonality and import in a minimalistic multi-strain dengue model capturing differences between primary and secondary infections: complex dynamics and its implications for data analysis, Journal of theoretical biology, 289, pp. 181-196, 2011.

Pongsumpun, P., and Tang, I. M., Transmission of dengue hemorrhagic fever in an age structured population, Mathematical and Computer Modelling, 37(9-10), pp. 949-961, 2003.

Nuraini, N., Soewono, E., and Sidarto, K. A., Mathematical model of dengue disease transmission with severe DHF compartment, Bulletin of the Malaysian Mathematical Sciences Society, 30(2), 2007.

Nuraini, N., Tasman, H., Soewono, E., and Sidarto, K. A., A with-in host dengue infection model with immune response, Mathematical and Computer Modelling, 49(5-6), pp. 1148-1155, 2009.

Carosella, L. M., Pryluka, D., Maranzana, A., Barcan, L., Cuini, R., Freuler, C., Stryjewski, M. E., Characteristics of Patients Co-infected with Severe Acute Respiratory Syndrome Coronavirus 2 and Dengue Virus, Buenos Aires, Argentina, March?June 2020, Emerging Infectious Diseases, 27(2), p. 348, 2021.

Coronavirus disease 2019 (COVID-19) Situation Report - 69. World Health Organization. https://www.who.int/emergencies/diseases/novelcoronavirus-2019/situation-reports/, published March 29, 2020, Accessed March 30, 2020.

Masyeni, S., Santoso, M. S., Widyaningsih, P. D., Asmara, D. W., Nainu, F., Harapan, H., and Sasmono, R. T, Serological cross-reaction and coinfection of dengue and COVID-19 in Asia: Experience from Indonesia, International Journal of Infectious Diseases, 102, pp. 152-154, 2021.

Yang, H. M., Junior, L. L., Castro, F. F. M., and Yang, A. C., Mathematical model describing CoViD-19 in S?ao Paulo, Brazil?evaluating isolation as control mechanism and forecasting epidemiological scenarios of release, Epidemiology and Infection, 148, 2020.

Anderson, R. M., and May, R. M., Infectious diseases of humans: dynamics and control, Oxford university press, 1992.

Kermack, W. O., McKendrick, A. G., A contribution to the mathematical theory of epidemics, Proceedings of the royal society of London, Series A, Containing papers of a mathematical and physical character, 115(772), pp. 700-721, 1927.

Nuraini, N., Soewono, E., and Sidarto, K. A., A mathematical model of dengue internal transmission process, Journal of the Indonesian Mathematical Society, 13(1), pp. 123-132, 2007.

Samui, P., Mondal, J., and Khajanchi, S., A mathematical model for COVID-19 transmission dynamics with a case study of India, Chaos, Solitons and Fractals, 140, p. 110173, 2020.

Fauzi, I. S., Fakhruddin, M., Nuraini, N., and Wijaya, K. P., Comparison of dengue transmission in lowland and highland area: Case study in Semarang and Malang, Indonesia, Communication in Biomathematical Science, 2(1), pp. 23-37, 2019.

Chavez, J. P., Gotz, T., Siegmund, S., and Wijaya, K. P., An SIR-Dengue transmission model with seasonal effects and impulsive control, Mathematical biosciences, 289, pp. 29-39, 2017.

Van den Driessche, P., and Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical biosciences, 180(1-2), pp. 29-48, 2002.

Diekmann, O., Heesterbeek, J. A. P., and Metz, J. A., On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, Journal of mathematical biology, 28(4), pp. 365-382, 1990.

Downloads

Published

2021-12-31

Issue

Section

Articles