Deterministic and stochastic models for middle east respiratory syndrome (MERS)

World Health Organization (WHO) data stated that since September 2012, there were 1,733 cases of Middle East Respiratory Syndrome (MERS) with 628 death cases that occurred in 27 countries. MERS was first identified in Saudi Arabia in 2012 and the largest cases of MERS outside Saudi Arabia occurred in South Korea in 2015. MERS is a disease that attacks the respiratory system caused by infection of MERS-CoV. MERS-CoV transmission occurs directly through direct contact between infected individual with non-infected individual or indirectly through contaminated object by the free virus. Suspected, MERS can spread quickly because of the free virus in environment. Mathematical modeling is used to illustrate the transmission of MERS disease using deterministic model and stochastic model. Deterministic model is used to investigate the temporal dynamic from the system to analyze the steady state condition. Stochastic model approach using Continuous Time Markov Chain (CTMC) is used to predict the future states by using random variables. From the models that were built, the threshold value for deterministic models and stochastic models obtained in the same form and the probability of disease extinction can be computed by stochastic model. Simulations for both models using several of different parameters are shown, and the probability of disease extinction will be compared with several initial conditions.World Health Organization (WHO) data stated that since September 2012, there were 1,733 cases of Middle East Respiratory Syndrome (MERS) with 628 death cases that occurred in 27 countries. MERS was first identified in Saudi Arabia in 2012 and the largest cases of MERS outside Saudi Arabia occurred in South Korea in 2015. MERS is a disease that attacks the respiratory system caused by infection of MERS-CoV. MERS-CoV transmission occurs directly through direct contact between infected individual with non-infected individual or indirectly through contaminated object by the free virus. Suspected, MERS can spread quickly because of the free virus in environment. Mathematical modeling is used to illustrate the transmission of MERS disease using deterministic model and stochastic model. Deterministic model is used to investigate the temporal dynamic from the system to analyze the steady state condition. Stochastic model approach using Continuous Time Markov Chain (CTMC) is used to predict the future states by us...

[1]  B J Cowling,et al.  Preliminary epidemiological assessment of MERS-CoV outbreak in South Korea, May to June 2015. , 2015, Euro surveillance : bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin.

[2]  T. Madani,et al.  Infection prevention and control guidelines for patients with Middle East Respiratory Syndrome Coronavirus (MERS-CoV) infection. , 2014, Saudi medical journal.

[3]  Linda J S Allen,et al.  Probability of a Disease Outbreak in Stochastic Multipatch Epidemic Models , 2013, Bulletin of mathematical biology.

[4]  D. Hui,et al.  Middle East respiratory syndrome , 2015, The Lancet.

[5]  V. Munster,et al.  Stability of Middle East respiratory syndrome coronavirus (MERS-CoV) under different environmental conditions. , 2013, Euro surveillance : bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin.

[6]  L. Allen,et al.  Extinction thresholds in deterministic and stochastic epidemic models , 2012, Journal of biological dynamics.

[7]  J. Noh,et al.  Viral Shedding and Environmental Cleaning in Middle East Respiratory Syndrome Coronavirus Infection , 2015, Infection & chemotherapy.

[8]  Charles P. Gerba,et al.  Significance of Fomites in the Spread of Respiratory and Enteric Viral Disease , 2007, Applied and Environmental Microbiology.

[9]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[10]  S. Yi,et al.  Epidemiological investigation of MERS-CoV spread in a single hospital in South Korea, May to June 2015. , 2015, Euro surveillance : bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin.

[11]  P van den Driessche,et al.  Relations between deterministic and stochastic thresholds for disease extinction in continuous- and discrete-time infectious disease models. , 2013, Mathematical biosciences.

[12]  Sophie Pénisson.  Conditional limit theorems for multitype branching processes and illustration in epidemiological risk analysis , 2010 .

[13]  M. Castrucci,et al.  Investigation of an imported case of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) infection in Florence, Italy, May to June 2013. , 2013, Euro surveillance : bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin.