A mathematical model of a diphtheria outbreak in Rohingya settlement in Bangladesh

Document Type : Research Paper


Department of Mathematics, University of Dhaka, Dhaka 1000, Bangladesh


In this paper, we study the dynamics of the diphtheria outbreak among the immunocompromised group of people, the Rohingya ethnic group. Approximately 800,000 Rohingya refugees are living in the Balukhali refugee camp in Cox’s Bazar. The camp is densely populated with the scarcity of proper food, healthcare, and sanitation. Subsequently, in November 2017 a diphtheria epidemic occurred in this camp. To keep up with the pace of the disease spread, medical demands, and disaster planning, we set out to predict diphtheria outbreaks among Bangladeshi Rohingya immigrants. We adopted a modified Susceptible-Latent-Infectious-Recovered (SLIR) transmission model to forecast the possible implications of the diphtheria outbreak in the Rohingya camps of Bangladesh. We discussed two distinct situations: the daily confirmed cases and cumulative data with unique consequences of diphtheria. Data for statistical and numerical simulations were obtained from \cite{Matsuyama}. We used the fourth-order Runge-Kutta method to obtain numerical simulations for varying parameters of the model which would demonstrate conclusive estimates. Daily and cumulative data predictions were explored for alternative values of the parameters i.e., disease transmission rate $(\beta)$ and recovery rate $(\gamma)$. Additionally, the average basic reproduction number for the parameters $\beta$ and $\gamma$ was calculated and displayed graphically. Our analysis demonstrated that the diphtheria outbreak would be under control if the maintenance could perform properly. The results of this research can be utilized by the Bangladeshi government and other humanitarian organizations to forecast disease outbreaks. Furthermore, it might help them to make detailed and practical planning to avoid the worst scenario.


[1] R. Matsuyama, A. R. Akhmetzhanov, A. Endo, H. Lee, T. Yamaguchi, S. Tsuzuki, and H. Nishiura, Uncertainty and sensitivity analysis of the basic reproduction number of diphtheria: a case study of a Rohingya refugee camp in Bangladesh, November{December 2017, PeerJ, 6:e4583, (2018).
[2] W. O. Kermack, A. G. McKendrick, A contribution to mathematical theory of epidemics, Proc. Roy. Soc. Lond. A., 700-721, (1927).
[3] M. I. Simoya, J. P. Aparicio, Ross-Macdonald Models: Which one should we use? Acta Tropica, 105452, (2020).
[4] A. Zeb, E. Alzahrani, V. S. Ertuk, G. Zaman, Mathematical model for coronavirus disease 2019 (COVID-19) containing isolation class, Biomed Res Int. Jun 25; 2020:3452402, (2020).
[5] Z. Zhang, A. Zeb, E. Alzahrani, S. Iqbal, Crowding e ects on the dynamics of COVID-19 mathematical model, Adv Di er Equ, 675, (2020).
[6] Z. Zhang, R. Gul, A. Zeb, Global sensitivity analysis of COVID-19 mathematical model, Alex. Eng. J., Volume 60, Issue 1, 565-572, (2021).
[7] M. Hassan, M. Mahmud, K. Nipa, M. Kamrujjaman, Mathematical Modeling and COVID-19 Forecast in Texas, USA: A Prediction Model Analysis and the Probability of Disease Outbreak, Disaster Medicine and Public Health Preparedness, 1-27, (2021).
[8] F. Finger, S. Funk, K. White, R. Siddiqui, W. J. Edmunds, and A. J. Kucharski, Real-time analysis of the diphtheria outbreak in forcibly displaced Myanmar nationals in Bangladesh, BMC Med., (2018).
[9] M. Paoluzzi, N. Gnan, F. Grassi, M. Salvetti, N. Vanacore, and A. Crisanti, A single-agent extension of the SIR model describes the impact of mobility restrictions on the COVID-19 epidemic, Sci. Rep., 11:24467, (2021).
[10] M. Torrea, J. L. Torrea, and D. Ortegaz, A modeling of a Diphtheria epidemic in the refugees camps, bioRxiv, (2017).
[11] M. S. Mahmud, M. Kamrujjaman, & M. S. Islam, A spatially dependent vaccination model with therapeutic impact and non-linear incidence. LNME, 323e345, (2021).
[12] M. Kamrujjaman, M. S. Mahmud, & M. S. Islam, Dynamics of a di usive vaccination model with therapeutic impact and non-linear incidence in epidemiology. J. Biol. Dyn., 15(sup1), S105eS133, (2020).
[13] K. Sornbundit, W. Triampo, C. Modchang, Mathematical modeling of diphtheria transmission in Thailand, Comput. Biol. Med, 87, 162{168, (2017).
[14] A. Golaz, I. R. Hardy, P. Strebel, K. M. Bisgard, C. Vitek, T. Popovic, and M. Wharton, Epidemic Diphtheria in the Newly Independent States of the Former Soviet Union: Implications for Diphtheria Control in the United States, J. Infect. Dis. 181(Suppl 1), S237{43, (2000).
[15] M. R. Rahman, K. Islam, Massive diphtheria outbreak among Rohingya refugees: lessons learnt, J. Travel Med., Volume 26, Issue 1, 2019.
[16] J. A. Polonsky, M. Ivey, M. K. A. Mazhar, Z. Rahman, O. l. P. de Waroux, B. Karo, K. Jalava, S. Vong, A. Baidjoe, J. Diaz, F. Finger, Z. H. Habib, C. E. Halder, C. Haskew, L. Kaiser, A. S. Khan, L. Sangal, T. Shirin, Q. A. Zaki, M. A. Salam, K. White,
Epidemiological, clinical, and public health response characteristics of a large outbreak of diphtheria among the Rohingya population in Cox's Bazar, Bangladesh, 2017 to 2019: A retrospective study, PLos Med, 18(4), e1003587, (2021).
[17] S. Ahmed, W. P. Simmons, R. Chowdhury, S. Huq. The sustainability{peace nexus in crisis contexts: how the Rohingya escaped the ethnic violence in Myanmar, but are trapped into environmental challenges in Bangladesh, Springer, 2021.
[18] T. Waezizadeh, A. Mehrpooya, M. Rezaeizadeh, S. Yarahmadian, Mathematical models for the e ects of hypertension and stress on kidney and their uncertainty, Math. Biosci., Vol. 305, 77-95, (2018).
[19] M. Kamrujjaman, M. S. Mahmud, & M. S. Islam, Coronavirus outbreak and the mathematical growth map of COVID-19. Annual Research & Review in Biology, 72e78, (2020).
[20] M. Kamrujjaman, M. S. Mahmud, S. Ahmed, M. O. Qayum, M. M. Alam, M. N. Hassan, M. R. Islam , K. F. Nipa and U. Bulut. SARS-CoV-2 and Rohingya Refugee Camp, Bangladesh: Uncertainty and How the Government Took Over the Situation, Biology, 10, 124, 1-18, (2021).
[21] M. A. Kuddus, and A. Rahman, Analysis of COVID-19 using a modi ed SLIR model with nonlinear incidence, Results Phys., 27, 104478, (2021).
[22] J. J. Tewa, R. Fokouop, B. Mewoli, and S. Bowong, Mathematical analysis of a general class of ordinary di erential equations coming from within-hosts models of malaria with immune e ectors, Appl. Math. Comput., 218, 7347-7361, (2012).
[23] M. Kamrujjaman, P. Saha, M. S. Islam, and U. Ghosh, Dynamics of SEIR Model: A case study of COVID-19 in Italy, Results in Control and Optimization, 7, 100119, (2022).
[26] H. Nishiura, Correcting the Actual Reproduction Number: A Simple Method to Estimate R0 from Early Epidemic Growth Data, IJERPH, 7(1), 291-302, (2010).
[24] J. D. Murray, Mathematical Biology I: An Introduction, third edition, Springer, 2002.
[25] M. Martcheva, An Introduction to Mathematical Epidemiology, Springer, 2015.
[27] M. S. Mahmud, M. kamrujjaman, M. M. I. Y. Adan, M. A. Hossain, M. M. Rahman, M. S. Islam, M. Mohebujjaman, and M. M. Molla, Vaccine ecacy and SARS-CoV-2 control in California and U.S. during the session 2020-2026: A modeling study, Infect. Dis. Model., 7: 62-81, (2021).
[28] TIME. About 60 Rohingya Babies Are Born Every Day in Refugee Camps, the U.N. Says | TIME. 2018. Available online: https://time.com/5280232/myanmar-bangladesh-rohingya-babies-births/ (accessed on 18 September (2020)).
[29] R. L. Burden, R. L. Faires, Numerical Analysis. 9th Edition, Brookscole, Boston, 259-253, 2011.