# Quantifying Critical Parameter in Disease Transmission

## Keywords:

Hand, Foot and Mouth Disease, Maximum Likelihood, Parameter Estimation, Susceptible-Infected-Recovered, Statistical Modeling.## Abstract

The values of each parameter introduced in a disease model play important role in providing the prediction of a disease transmission. Some parameters values are easily quantified through collected statistical data usually made available from clinical research. However, there may be some parameters that are not easily found. For such case, the parameters values are estimated through many trial-and-error numerical runs. In this paper, it is shown that a statistical modeling approach coupled with the Maximum Likelihood Estimate method can be used to quantify critical model parameters. A Hand-Foot-Mouth disease (HFMD) model was taken as a case study where infected population data provided by the Sarawak State of Health was fitted onto the SusceptibleInfected-Removal (SIR) model. The concerned parameter is the transmission coefficient of HFMD in the year 2012. Using the mentioned method, it was found that the value for the transmission coefficient of HFMD in 2012 is 1.2654 (CI: 1.15-1.43). It can be concluded that the critical parameter with 95% confidence interval in SIR model has been quantified effectively. Due to the possibility of obtaining other sets of infected population data, a web application called the Disease Modeling Parameter Calculator was developed to assist in estimating the transmission coefficient.## References

Van Lerberghe, W. (2008). The world health report 2008: primary health care: now more than ever. World Health Organization.

Murray, C. J., & Lopez, A. D. (1997). Mortality by cause for eight regions of the world: Global Burden of Disease Study. The lancet, 349(9061), 1269-1276.

Lopez, A. D., Mathers, C. D., Ezzati, M., Jamison, D. T., & Murray, C. J. (2006). Global and regional burden of disease and risk factors, 2001: systematic analysis of population health data. The Lancet, 367(9524), 1747-1757.

Reich, N. G., Lauer, S. A., Sakrejda, K., Iamsirithaworn, S., Hinjoy, S., Suangtho, P., ... & Lessler, J. (2016). Challenges in Real-Time Prediction of Infectious Disease: A Case Study of Dengue in Thailand. PLoS Negl Trop Dis, 10(6), e0004761.

Keeling, M. J., & Rohani, P. (2008). Modeling infectious diseases in humans and animals. Princeton University Press.

Dorjee, S., Poljak, Z., Revie, C. W., Bridgland, J., McNab, B., Leger, E., & Sanchez, J. (2013). A review of simulation modelling approaches used for the spread of zoonotic influenza viruses in animal and human populations. Zoonoses and public health, 60(6), 383-411.

Frances, L. C. (2012). Comparison of Maximum Likelihood, Bayesian, Partial Least Squares, and Generalized Structured Component Analysis Methods for Estimation of Structural Equation Models with Small Samples: An Exploratory Study. Master’s thesis. University of Nebraska, Lincoln, United States. Retrieved from University of Nebraska Digital Commons.

Jae, M. I. (2002). Tutorial on maximum likelihood estimation. Journal of Mathematical Psychology, 47(1), 90-100.

Latha, S. and Lilly, F. (2012). A Comparison of Parameter Best Estimation Method for Software Reliability Models. International Journal of Software Engineering and Applications, 3(5).

Joseph, S. (2007). Statistical Estimation in HLM Models. Retrieved from http://pages.uoregon.edu/stevensj/HLM/data/Estimation_HLM_ models.pdf.

Mahesh, S. K. (2008). Parameter Estimation of Copula Using Maximum Likelihood Estimation Method. ProQuest.

John, A. (1997). R. A. Fisher and the Making of Maximum Likelihood 1912 – 1922. Statistical Science, 12(2), 162-176.

Dong, L., Wu, K., & Tang, G. (2016). A Data-Centric Approach to Quality Estimation of Role Mining Results. IEEE Transactions on Information Forensics and Security, 11(12), 2678-2692.

Lechner, J., & Günthner, W. A. (2016, September). A tool for a fast evaluation of UHF RFID installations. In RFID Technology and Applications (RFID-TA), 2016 IEEE International Conference on (pp. 117-122). IEEE.

Kaveh, A., & Farhoudi, N. (2011). A unified approach to parameter selection in meta-heuristic algorithms for layout optimization. Journal of Constructional Steel Research, 67(10), 1453-1462.

Ooi, M. H., Wong, S. C., Podin, Y., Akin, W., Del Sel, S., Mohan, A., ... Solomon, T. (2007). Human enterovirus 71 disease in Sarawak, Malaysia: a prospective clinical, virological, and molecular epidemiological study. Clinical Infectious Diseases, 44(5), 646-656.

Chuo, F., Tiing, S., & Labadin, J. (2008). A simple deterministic model for the spread of hand, foot and mouth disease (HFMD) in Sarawak. In Proceedings of the Second Asia International Conference on Modeling & Simulation, 2008. AIMS 08. (pp. 947-952). IEEE.

Barnes, B., & Fulford, G. R. (2011). Mathematical modelling with case studies: a differential equations approach using Maple and MATLAB. CRC Press.

Bolker, B. M. (2008). Ecological Models and Data in R. New Jersey, US: Princeton University Press.

Gustafsson, L., & Sternad, M. (2007). Bringing consistency to simulation of population models–Poisson Simulation as a bridge between micro and macro simulation. Mathematical biosciences, 209(2), 361-385.

Draganescu, A., Knottenbelt, W., & Heinis, T. (2015). Uncertainty Quantification of Epidemic Phenomena and the Parallel Simulator Tool.

Gholampour, A. A., Ghassemieh, M., & Razavi, H. (2011). A time stepping method in analysis of nonlinear structural dynamics. Applied and Computational Mechanics, 5(2).

Kok, W. C., Labadin, J., Mohammad, A., Wong, K. S., & Chang, Y. L. (2016, May). Android-based Disease Monitoring. In Information and Communication Technology (ICICTM), International Conference on (pp. 97-103). IEEE.

Lofgren, E., Fefferman, N. H., Naumov, Y. N., Gorski, J., & Naumova, E. N. (2007). Influenza seasonality: underlying causes and modeling theories. Journal of virology, 81(11), 5429-5436.

Alaa, E. (2013). Transmission Rate in Partial Differential Equation in Epidemic Models. Degree Thesis. Marshall University. Retrieved from Marshall University Digital Theses.

## Downloads

## Published

## How to Cite

*Journal of Telecommunication, Electronic and Computer Engineering (JTEC)*,

*9*(2-9), 163–168. Retrieved from https://jtec.utem.edu.my/jtec/article/view/2692

## Issue

## Section

## License

**TRANSFER OF COPYRIGHT AGREEMENT**

The manuscript is herewith submitted for publication in the Journal of Telecommunication, Electronic and Computer Engineering (JTEC). It has not been published before, and it is not under consideration for publication in any other journals. It contains no material that is scandalous, obscene, libelous or otherwise contrary to law. When the manuscript is accepted for publication, I, as the author, hereby agree to transfer to JTEC, all rights including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the author(s) specifically retain(s):

- All proprietary right other than copyright, such as patent rights
- The right to make further copies of all or part of the published article for my use in classroom teaching
- The right to reuse all or part of this manuscript in a compilation of my own works or in a textbook of which I am the author; and
- The right to make copies of the published work for internal distribution within the institution that employs me

I agree that copies made under these circumstances will continue to carry the copyright notice that appears in the original published work. I agree to inform my co-authors, if any, of the above terms. I certify that I have obtained written permission for the use of text, tables, and/or illustrations from any copyrighted source(s), and I agree to supply such written permission(s) to JTEC upon request.