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| 1 | Estimating the basic reproductive ratio for the Ebola outbreak in Liberia and Sierra Leone显示文摘Background:Ebola virus disease has reemerged as a major public health crisis in Africa,with isolated cases also observed globally,during the current outbreak.Methods:To estimate the basic reproductive ratio R0,which is a measure of the severity of the outbreak,we developed a SEIR(susceptible-exposed-infected-recovered)type deterministic model,and used data from the Centers for Disease Control and Prevention(CDC),for the Ebola outbreak in Liberia and Sierra Leone.Two different data sets are available:one with raw reported data and one with corrected data(as the CDC suspects under-reporting).Results:Using a deterministic ordinary differential equation transmission model for Ebola epidemic,the basic reproductive ratio R0 for Liberia resulted to be 1.757 and 1.9 for corrected and uncorrected case data,respectively.For Sierra Leone,R0 resulted to be 1.492 and 1.362 for corrected and uncorrected case data,respectively.In each of the two cases we considered,the estimate for the basic reproductive ratio was initially greater than unity leading to an epidemic outbreak.Conclusion:We obtained robust estimates for the value of R0 associated with the 2014 Ebola outbreak,and showed that there is close agreement between our estimates of R0.Analysis of our model also showed that effective isolation is required,with the contact rate in isolation less than one quarter of that for the infected non-isolated population,and that the fraction of high-risk individuals must be brought to less than 10%of the overall susceptible population,in order to bring the value of R0 to less than 1,and hence control the outbreak. | Adnan Khan Mahim Naveed Muhammad Dur-e-Ahmad Mudassar Imran | 2015 | Infectious Diseases of Poverty2015，4，1： | 5 |
| 2 | Estimating the basic reproduction number for single-strain dengue fever epidemics显示文摘Background:Dengue,an infectious tropical disease,has recently emerged as one of the most important mosquito-borne viral diseases in the world.We perform a retrospective analysis of the 2011 dengue fever epidemic in Pakistan in order to assess the transmissibility of the disease.We obtain estimates of the basic reproduction number R0 from epidemic data using different methodologies applied to different epidemic models in order to evaluate the robustness of our estimate.Results:We first estimate model parameters by fitting a deterministic ODE vector-host model for the transmission dynamics of single-strain dengue to the epidemic data,using both a basic ordinary least squares(OLS)as well as a generalized least squares(GLS)scheme.Moreover,we perform the same analysis for a direct-transmission ODE model,thereby allowing us to compare our results across different models.In addition,we formulate a direct-transmission stochastic model for the transmission dynamics of dengue and obtain parameter estimates for the stochastic model using Markov chain Monte Carlo(MCMC)methods.In each of the cases we have considered,the estimate for the basic reproduction number R0 is initially greater than unity leading to an epidemic outbreak.However,control measures implemented several weeks after the initial outbreak successfully reduce R0 to less than unity,thus resulting in disease elimination.Furthermore,it is observed that there is strong agreement in our estimates for the pre-control value of R0,both across different methodologies as well across different models.However,there are also significant differences between our estimates for the post-control value of the basic reproduction number across the two different models.Conclusion:In conclusion,we have obtained robust estimates for the value of the basic reproduction number R0 associated with the 2011 dengue fever epidemic before the implementation of public health control measures.Furthermore,we have shown that there is close agreement between our estimates for the post-control value of R0 across the different methodologies.Nevertheless,there are also significant differences between the estimates for the post-control value of R0 across the two different models. | Adnan Khan Muhammad Hassan Mudassar Imran | 2014 | Infectious Diseases of Poverty2014，3，1： | 3 |
| 3 | Optimal control analysis of Ebola disease with control strategies of quarantine and vaccination显示文摘Background:The 2014 Ebola epidemic is the largest in history,affecting multiple countries in West Africa.Some isolated cases were also observed in other regions of the world.Method:In this paper,we introduce a deterministic SEIR type model with additional hospitalization,quarantine and vaccination components in order to understand the disease dynamics.Optimal control strategies,both in the case of hospitalization(with and without quarantine)and vaccination are used to predict the possible future outcome in terms of resource utilization for disease control and the effectiveness of vaccination on sick populations.Further,with the help of uncertainty and sensitivity analysis we also have identified the most sensitive parameters which effectively contribute to change the disease dynamics.We have performed mathematical analysis with numerical simulations and optimal control strategies on Ebola virus models.Results:We used dynamical system tools with numerical simulations and optimal control strategies on our Ebola virus models.The original model,which allowed transmission of Ebola virus via human contact,was extended to include imperfect vaccination and quarantine.After the qualitative analysis of all three forms of Ebola model,numerical techniques,using MATLAB as a platform,were formulated and analyzed in detail.Our simulation results support the claims made in the qualitative section.Conclusion:Our model incorporates an important component of individuals with high risk level with exposure to disease,such as front line health care workers,family members of EVD patients and Individuals involved in burial of deceased EVD patients,rather than the general population in the affected areas.Our analysis suggests that in order for R0(i.e.,the basic reproduction number)to be less than one,which is the basic requirement for the disease elimination,the transmission rate of isolated individuals should be less than one-fourth of that for non-isolated ones.Our analysis also predicts,we need high levels of medication and hospitalization at the beginning of an epidemic.Further,optimal control analysis of the model suggests the control strategies that may be adopted by public health authorities in order to reduce the impact of epidemics like Ebola. | Muhammad Dure Ahmad Muhammad Usman Adnan Khan Mudassar Imran | 2016 | Infectious Diseases of Poverty2016，5，1： | 1 |
| 4 | Modeling transmission dynamics of Ebola virus disease显示文摘 | Mudassar Imran Adnan Khan Ali R. Ansari Syed Touqeer Hussain Shah | 2017 | International Journal of Biomathematics2017，10，4： | 1 |
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