Dynamics of Ebola epidemics in West Africa 2014

This paper investigates the dynamics of Ebola virus transmission in West Africa during 2014. The reproduction numbers for the total period of epidemic and for different consequent time intervals are estimated based on a newly suggested linear model. It contains one major variable - the average time of infectiousness (time from onset to hospitalization) that is considered as a parameter for controlling the future dynamics of epidemics. Numerical implementations are carried out on data collected from three countries Guinea, Sierra Leone and Liberia as well as the total data collected worldwide. Predictions are provided by considering different scenarios involving the average times of infectiousness for the next few months and the end of the current epidemic is estimated according to each scenario

Efficiency of prompt quarantine measures on a susceptible-infected-removed model in networks

This study focuses on investigating the manner in which a prompt quarantine measure suppresses epidemics in networks. A simple and ideal quarantine measure is considered in which an individual is detected with a probability immediately after it becomes infected and the detected one and its neighbors are promptly isolated. The efficiency of this quarantine in suppressing a susceptible-infected-removed (SIR) model is tested in random graphs and uncorrelated scale-free networks. Monte Carlo simulations are used to show that the prompt quarantine measure outperforms random and acquaintance preventive vaccination schemes in terms of reducing the number of infected individuals. The epidemic threshold for the SIR model is analytically derived under the quarantine measure, and the theoretical findings indicate that prompt executions of quarantines are highly effective in containing epidemics. Even if infected individuals are detected with a very low probability, the SIR model under a prompt quarantine measure has finite epidemic thresholds in fat-tailed scale-free networks in which an infected individual can always cause an outbreak of a finite relative size without any measure. The numerical simulations also demonstrate that the present quarantine measure is effective in suppressing epidemics in real networks.Comment: 10 pages, 7 figure

Travelling waves for an epidemic model with non-smooth treatment rates

This is the post-print version of the final published paper that is available from the link below. Copyright @ 2010 IOP Publishing Ltd and SISSA.We consider a susceptible–infected–removed (SIR) epidemic model with two types of nonlinear treatment rates: (i) piecewise linear treatment rate with saturation effect, (ii) piecewise constant treatment rate with a jump (Heaviside function). For case (i), we compute travelling front solutions whose profiles are heteroclinic orbits which connect either the disease-free state to an infective state or two endemic states with each other. For case (ii), it is shown that the profile has the following properties: the number of susceptibles is monotonically increasing and the number of infectives approaches zero at infinity, while their product converges to a constant. Numerical simulations are performed for all these cases. Abnormal behaviour like travelling waves with non-monotonic profile or oscillations is observed

A minimal HIV-AIDS infection model with general incidence rate and application to Morocco data

We study the global dynamics of a SICA infection model with general incidence rate. The proposed model is calibrated with cumulative cases of infection by HIV-AIDS in Morocco from 1986 to 2015. We first prove that our model is biologically and mathematically well-posed. Stability analysis of different steady states is performed and threshold parameters are identified where the model exhibits clearance of infection or maintenance of a chronic infection. Furthermore, we examine the robustness of the model to some parameter values by examining the sensitivity of the basic reproduction number. Finally, using numerical simulations with real data from Morocco, we show that the model predicts well such reality.Comment: This is a preprint of a paper whose final and definite form is with 'Statistics Opt. Inform. Comput.', Vol. 7, No 2 (2019). See [http://www.IAPress.org]. Submitted 16/Sept/2018; Revised 10 & 15/Dec/2018; Accepted 15/Dec/201