A Mathematical Model Of The Middle East Respiratory Syndrome (MERS) In Saudi Arabia
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In this work, we use the following Susceptible-Exposed-Infected-Recovered (SEIR) model with "fitted" logistic demographics to model the Middle East Respiratory Syndrome (MERS) in Saudi Arabia. dS/dt=rN(1-N/K)-β SI/N-μS dE/dt=βSI/N-σE-μE dI/dt=σE-ηI-αI-μI dR/dt=ηI-μR where, S represents susceptible individuals, E represents exposed to MERS, I represents infected individuals by MERS and R represents recovered individuals from MERS. We define the model parameters as: μ is the mortality rate, r is the intrinsic growth rate, K is the carrying capacity, β is the infection rate, σ is the progression rate from E to I, η is the recovery rate and α is the death rate due to MERS. We will use population data of Saudi Arabia from 2005-2017 and the least squares method to fit the logistic demographic equation and to estimate demographic model parameters. We will compute the disease free equilibrium points and we will compute the basic reproduction number R_0 of the MERS model in Saudi Arabia. The sensitivity analysis on the basic reproduction number R_0 will be performed. In addition, we will perform computer simulations of the MERS model. The MERS model shows that R_0<1 that is the MERS disease cannot start in a fully susceptible Saudi Arabia population.