Projections of Ebola outbreak size and duration with and without vaccine use in Équateur, Democratic Republic of Congo, as of May 27, 2018.

As of May 27, 2018, 6 suspected, 13 probable and 35 confirmed cases of Ebola virus disease (EVD) had been reported in Équateur Province, Democratic Republic of Congo. We used reported case counts and time series from prior outbreaks to estimate the total outbreak size and duration with and without vaccine use. We modeled Ebola virus transmission using a stochastic branching process model that included reproduction numbers from past Ebola outbreaks and a particle filtering method to generate a probabilistic projection of the outbreak size and duration conditioned on its reported trajectory to date; modeled using high (62%), low (44%), and zero (0%) estimates of vaccination coverage (after deployment). Additionally, we used the time series for 18 prior Ebola outbreaks from 1976 to 2016 to parameterize the Thiel-Sen regression model predicting the outbreak size from the number of observed cases from April 4 to May 27. We used these techniques on probable and confirmed case counts with and without inclusion of suspected cases. Probabilistic projections were scored against the actual outbreak size of 54 EVD cases, using a log-likelihood score. With the stochastic model, using high, low, and zero estimates of vaccination coverage, the median outbreak sizes for probable and confirmed cases were 82 cases (95% prediction interval [PI]: 55, 156), 104 cases (95% PI: 58, 271), and 213 cases (95% PI: 64, 1450), respectively. With the Thiel-Sen regression model, the median outbreak size was estimated to be 65.0 probable and confirmed cases (95% PI: 48.8, 119.7). Among our three mathematical models, the stochastic model with suspected cases and high vaccine coverage predicted total outbreak sizes closest to the true outcome. Relatively simple mathematical models updated in real time may inform outbreak response teams with projections of total outbreak size and duration

Transmission Dynamics of Some Epidemiological Patch Models

As we known, infectious diseases can be transmitted from one region to another due to extensive travel and migration. Meanwhile, different regions have different demographic and epidemiological characteristics. To capture these features, multi-patch epidemic models have been developed to study disease transmission in heterogeneous environments. In Chapter 1, a susceptible-infectious-susceptible patch model with nonconstant transmission coefficients is formulated to investigate the effect of media coverage and human movement on the spread of infectious diseases among patches. In chapter 2, I propose a multi-patch model to study the effects of population dispersal on the spatial spread of malaria between patches. In Chapter 3, based on the classical Ross-Macdonald model, I propose a periodic malaria model to incorporate the effects of temporal and spatial heterogeneity in disease transmission. Chapter 4 is devoted to studying the spatial spread of Rift Valley fever in Egypt. In summary, I propose several epidemic patch models to study the effects of human movement on the spatial spread of infectious diseases. The analytical and numerical results suggest that the migration of humans can influence disease spread in a complicated way and to control or eliminate an infectious disease we need global and regional strategies

An SIS patch model with variable transmission coefficients

In this paper, an SIS patch model with non-constant transmission coefficients is formulated to investigate the effect of media coverage and human movement on the spread of infectious diseases among patches. The basic reproduction number R(0) is determined. It is shown that the disease-free equilibrium is globally asymptotically stable if R(0)≤1, and the disease is uniformly persistent and there exists at least one endemic equilibrium if R(0)>1. In particular, when the disease is non-fatal and the travel rates of susceptible and infectious individuals in each patch are the same, the endemic equilibrium is unique and is globally asymptotically stable as R(0)>1. Numerical calculations are performed to illustrate some results for the case with two patches

A PERIODIC ROSS-MACDONALD MODEL IN A PATCHY ENVIRONMENT

Based on the classical Ross-Macdonald model, in this paper we propose a periodic malaria model to incorporate the effects of temporal and spatial heterogeneity on disease transmission. The temporal heterogeneity is described by assuming that some model coefficients are time-periodic, while the spatial heterogeneity is modeled by using a multi-patch structure and assuming that individuals travel among patches. We calculate the basic reproduction number [Formula: see text] and show that either the disease-free periodic solution is globally asymptotically stable if [Formula: see text] or the positive periodic solution is globally asymptotically stable if [Formula: see text]. Numerical simulations are conducted to confirm the analytical results and explore the effect of travel control on the disease prevalence