The disease leptospirosis is known to be endemic in Malaysia, and it significantly impacts human wellbeing and the national economy. Current surveillance systems are based on morbidity and mortality leptospirosis national data from the Ministry of Health and remain inadequate due to the number of unreported and misdiagnosed cases. A robust surveillance system is needed to monitor temporal and spatial changes which yield improvements in terms of identifying high-risk areas and disease behaviour. The objective of this study is to identify high-risk areas by estimating relative risk using existing models which are the Standardized Morbidity Ratio (SMR), Poisson-gamma, log-normal, Besag, York and Mollié (BYM) and mixture models. An alternative model is also proposed which involves transmission systems and stochastic elements, namely the stochastic Susceptible-Infected-Removed (SIR) transmission model. This estimation of risk is expected to assist in the early detection of high-risk areas which can be applied as a strategy for preventive and control measures. The methodology in this paper applies relative risk estimates to determine the infection risk for all states in Malaysia based on monthly data from 2011 to 2018 using WinBUGS 1.4 software. The results of relative risks are discussed and presented in tables and graphs for each model to disclose high-risk areas across the country. Based on the risk estimates, different models used have different risk interpretations and drawbacks which make each model different in its use depending on the objectives of the study. As a result, the deviance information criteria (DIC) values obtained do not differ greatly from each expected risk which was estimated.

• Andrade, C. (2015). Understanding relative risk, odds ratio, and related terms: as simple as it can get. The Journal of clinical psychiatry, 76(7), 857-861. https://doi.org/10.4088/JCP.15f10150

• Awang, A. C., & Samat, N. A. (2017). Standardized morbidity ratio for leptospirosis mapping in Malaysia. In AIP Conference Proceedings (Vol. 1847, No. 1, p. 020006). AIP Publishing LLC. https://doi.org/10.1063/1.4983861

• Benacer, D., Thong, K. L., Verasahib, K. B., Galloway, R. L., Hartskeerl, R. A., Lewis, J. W., & Mohd Zain, S. N. (2016). Human leptospirosis in Malaysia: reviewing the challenges after 8 decades (1925-2012). Asia Pacific Journal of Public Health, 28(4), 290-302. https://doi.org/10.1177/1010539516640350

• Besag, J., York, J., & Molli, A. (1991). Bayesian image restoration, with two applications in spatial statistics. Annals of the Institute of Statistical Mathematics, 43(1), 1-20. https://doi.org/10.1007/BF00116466

• Brauer, F. (2017, February 4). Mathematical epidemiology: Past, present, and future. Retrieved August 29, 2020, from https://www.ncbi.nlm.nih.gov/pubmed/29928732

• Dey, S., Delampady, M., & Gopalaswamy, A. M. (2019). Bayesian model selection for spatial capture–recapture models. Ecology and evolution, 9(20), 11569-11583. https://doi.org/10.1002/ece3.5551

• Fletcher, W. (1928). Recent work on leptospirosis, tsutsugamushi disease, and tropical typhus in the federated Malay States. Transactions of the Royal Society of Tropical Medicine and Hygiene, 21(4), 265-288. https://doi.org/10.1016/s0035-9203(28)90019-x

• Garba, B., Bahaman, A. R., Bejo, S. K., Zakaria, Z., Mutalib, A. R., & Bande, F. (2017a). Major epidemiological factors associated with leptospirosis in Malaysia. Acta Tropica, 178, 242-247. https://doi.org/10.1016/j.actatropica.2017.12.010.

• Garba, B., Bahaman, A. R., Khairani-Bejo, S., Zakaria, Z., & Mutalib, A. R. (2017b). Retrospective Study of Leptospirosis in Malaysia. EcoHealth, 14(2), 389-398. https://doi.org/10.1007/s10393-017-1234-0

• Haake, D. A., & Levett, P. N. (2014). Leptospirosis in humans. Current Topics in Microbiology and Immunology, (387), 65–97. https://doi.org/10.1007/978-3-662-45059-8_5

• Ideris, S. H., & Samat, N. A. (2015). Comparison of HIV and AIDS diseases mapping in Malaysia based on standardized morbidity ratio and poisson-gamma model. EDUCATUM Journal of Science, Mathematics and Technology, 2(1), 69-81.

• Kermack, W. O., & McKendrick, A. G. (1927). 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), 700-721. https://doi.org/10.1098/rspa.1927.0118

• Kismiantini. (2009, January 25). Relative risk of disease using linear generalized mixed model. Staff Site Universitas. Retrieved August 29, 2020, from http://staff.uny.ac.id/sites/defaultfiles/penelitian/Kismiantini,S.Si.,M.Si/A2009B1.pdf

• Lawson, A. B. (2006). Statistical methods in spatial epidemiology. John Wiley & Sons.

• Lawson, A. B., & Williams, F. L. (2003). An introductory guide to disease mapping. John Wiley.

• Long, N. X. (2012). Clustering problems, mixture models and Bayesian nonparametrics. Lecture presented at Vietnam Institute of Advanced Studies of Mathematics (VIASM), Hanoi. Retrieved December 05, 2020, from http://dept.stat.lsa.umich.edu/~xuanlong/Talks/nguyen_viasm12_part1.pdf

• Meza, J. L. (2003). Empirical Bayes estimation smoothing of relative risks in disease mapping. Journal of Statistical Planning and Inference, 112(1-2), 43-62. https://doi.org/10.1016/S0378-3758(02)00322-1

• Nurmalasari, M., & Pramana, S. (2014). Analysis of appendectomy in Belgium using disease mapping techniques. Proceedings of the 13th Islamic Countries Conference on Statistical Sciences, 27, 417-430.

• Pooley, C. M., & Marion, G. (2018). Bayesian model evidence as a practical alternative to deviance information criterion. Royal Society Open Science, 5(3), Article 171519. https://doi.org/10.1098/rsos.171519

• Richardson, S., Thomson, A., Best, N., & Elliott, P. (2004). Interpreting posterior relative risk estimates in disease-mapping studies. Environmental Health Perspectives, 112(9), 1016-1025. https://doi.org/10.1289/ehp.6740

• Samat, N. A., & Percy, D. F. (2012). Vector-borne infectious disease mapping with stochastic difference equations: An analysis of dengue disease in Malaysia. Journal of Applied Statistics, 39(9), 2029-2046. https://doi.org/10.1080/02664763.2012.700450

• Spiegelhalter, D., Thomas, A., Best, N., & Luun, D. (2003). WinBUGS user manual version 1.4. MRC Biostatistics Unit.

• Sulong, M. R., Shafei, M. N., Yaacob, N. A, Hasan, H., Daud, A., Mohamad, W. M. Z. W., Zaliha, I., & Mohamed, R. A. (2011). Risk factors associated with leptospirosis among town service workers. International Medical Journal, 18(2), 83-88.

• Triampo, W., Baowan, D., Tang, I. M., Nuttavut, N., Wong-Ekkabut, J., & Coungchawee, G. (2008). A simple deterministic model for the spread of leptospirosis in Thailand. International Journal of Medical and Health Sciences, 2(1), 22-26.

• Wahab, Z. A. (2015, September 8-9). Epidemiology and current situation of leptospirosis in Malaysia. In Persidangan Kesihatan Persekitaran Pihak Berkuasa Tempatan 2015. WP