The Middle East Respiratory Syndrome (MERS) has been identified in 2012 and since then outbreaks have been reported in various localities in the Middle East and in other parts of the world. To help predict the possible dynamics of MERS, as well as ways to contain it, this paper develops a mathematical model for the disease. It has a compartmental structure similar to SARS models and is in the form of a coupled system of nonlinear ordinary differential equations (ODEs). The model predictions are fitted to data from the outbreaks in Riyadh (Saudi Arabia) during 2013-2016. The results reveal that MERS will eventually be contained in the city. However, the containment time and the severity of the outbreaks depend crucially on the contact coefficients and the isolation rate constant. When randomness is added to the model coefficients, the simulations show that the model is sensitive to the scaled contact rate among people and to the isolation rate. The model is analyzed using stability theory for ODEs and indicates that when using only isolation, the endemic steady state is locally stable and attracting. Numerical simulations with parameters estimated from the city of Riyadh illustrate the analytical results and the model behavior, which may have important implications for the disease containment in the city. Indeed, the model highlights the importance of isolation of infected individuals and may be used to assess other control measures. The model is general and may be used to analyze outbreaks in other parts of the Middle East and other areas.

No abstract

This work studies and numerically simulates a logistic-type model for the dynamics of Chagas disease, which is caused by the parasite T. cruzi and affects millions of humans and domestic mammals throughout rural areas in Central and South America. A basic model for the disease dynamics that includes insecticide spraying was developed in Spagnuolo et al. (2010) [27] and consists of a delay-differential equation for the vectors and three nonlinear ordinary differential equations for the populations of the infected vectors, infected humans and infected domestic mammals. In this work, the vector equation is modified by using a logistic term with zero, one or two delays or time lags. The aim of this study is three-fold: to numerically study the effects of using different numbers of delays on the model behavior; to find if twice yearly insecticide spraying schedules improve vector control; and to study the sensitivity of the system to the delays in the case of two delays, by introducing randomness in the delays. It is found that the vector equation with different number of delays has very different solutions. The “best” day of spraying is the middle of Spring and twice annual sprayings cause only minor improvements in disease control. Finally, the model is found to be insensitive to the values of the delays, when the delays are randomly distributed within rather narrow intervals or ranges centered on the parameter values used in Coffield et al. (2014) [8].

Abstract-This work describes a continuous differential equations model for the dynamics of Middle Eastern Respiratory Syndrome (MERS) and provides its computer simulations. It is a continuation of our previous paper Al-Asuoad et al. (Biomath 5, 2016) and it extends the simulations results provided there, which were restricted to the city of Riyadh, to the whole of Saudi Arabia. In addition, it updates the results for the city of Riyadh itself. Using an optimization procedure, the system coefficients were obtained from published data, and the model allows for the prediction of possible scenarios for the transmission and spread of the disease in the near future. This, in turn, allows for the application of possible disease control measures. The model is found to be very sensitive to the daily effective contact parameter, and the presented simulations indicate that the system is very close to the bifurcation of the stability of the Disease Free Equilibrium (DFE) and appearance of the Endemic Equilibrium (EE), which indicates that the disease will not decay substantially in the near future. Finally, we establish the stability of the DFE using only the stability number R c , which simplifies and improves one of the main theoretical results in the previous paper.

BIOMATH h t t p : / / w w w. b i o m a t h f o r u m . o r g / b i o m a t h / i n d e x . p h p / b i o m a t h /Abstract-This work presents and simulates a mathematical model for the dynamics of a population of Wood Frogs. The model consists of a system of five coupled impulsive differential equations for the larvae, juveniles (early, middle, and late) and the mature adult populations. A simulation result depicts possible dynamics of the frogs' population when during one year the larvae population dies out. This provides a tool for the study of the resilience of the population and the conditions that may lead to its survival and flourishing or extinction.