We develop a three dimensional compartmental model to investigate the impact of media coverage to the spread and control of infectious diseases (such as SARS) in a given region/area. Stability analysis of the model shows that the disease-free equilibrium is globally-asymptotically stable if a certain threshold quantity, the basic reproduction number (R 0), is less than unity. On the other hand, if R 0 > 1, it is shown that a unique endemic equilibrium appears and a Hopf bifurcation can occur which causes oscillatory phenomena. The model may have up to three positive equilibria. Numerical simulations suggest that when R 0 > 1 and the media impact is stronger enough, the model exhibits multiple positive equilibria which poses challenge to the prediction and control of the outbreaks of infectious diseases.

IntroductionAn accurate early warning system to predict impending epidemics enhances the effectiveness of preventive measures against dengue fever. The aim of this study was to develop and validate a forecasting model that could predict dengue cases and provide timely early warning in Singapore.Methodology and Principal FindingsWe developed a time series Poisson multivariate regression model using weekly mean temperature and cumulative rainfall over the period 2000–2010. Weather data were modeled using piecewise linear spline functions. We analyzed various lag times between dengue and weather variables to identify the optimal dengue forecasting period. Autoregression, seasonality and trend were considered in the model. We validated the model by forecasting dengue cases for week 1 of 2011 up to week 16 of 2012 using weather data alone. Model selection and validation were based on Akaike's Information Criterion, standardized Root Mean Square Error, and residuals diagnoses. A Receiver Operating Characteristics curve was used to analyze the sensitivity of the forecast of epidemics. The optimal period for dengue forecast was 16 weeks. Our model forecasted correctly with errors of 0.3 and 0.32 of the standard deviation of reported cases during the model training and validation periods, respectively. It was sensitive enough to distinguish between outbreak and non-outbreak to a 96% (CI = 93–98%) in 2004–2010 and 98% (CI = 95%–100%) in 2011. The model predicted the outbreak in 2011 accurately with less than 3% possibility of false alarm.SignificanceWe have developed a weather-based dengue forecasting model that allows warning 16 weeks in advance of dengue epidemics with high sensitivity and specificity. We demonstrate that models using temperature and rainfall could be simple, precise, and low cost tools for dengue forecasting which could be used to enhance decision making on the timing, scale of vector control operations, and utilization of limited resources.

Since its incursion into North America in 1999, West Nile virus (WNV) has spread rapidly across the continent resulting in numerous human infections and deaths. Owing to the absence of an effective diagnostic test and therapeutic treatment against WNV, public health officials have focussed on the use of preventive measures in an attempt to halt the spread of WNV in humans. The aim of this paper is to use mathematical modelling and analysis to assess two main anti-WNV preventive strategies, namely: mosquito reduction strategies and personal protection. We propose a single-season ordinary differential equation model for the transmission dynamics of WNV in a mosquito-bird-human community, with birds as reservoir hosts and culicine mosquitoes as vectors. The model exhibits two equilibria; namely the disease-free equilibrium and a unique endemic equilibrium. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if a certain threshold quantity (R 0 ), which depends solely on parameters associated with the mosquito-bird cycle, is less than unity. The public health implication of this is that WNV can be eradicated from the mosquito-bird cycle (and, consequently, population) if the adopted mosquito reduction strategy (or strategies) can make R 0 < 1. On the other hand, it is shown, using a novel and robust technique that is based on the theory of monotone dynamical systems coupled with a regular perturbation argument and a Liapunov function, that if R 0 > 1, then the unique endemic equilibrium is globally stable for small WNV-induced avian mortality. Thus, in this case, WNV persists in the mosquito-bird population.

We use a compartmental model to illustrate a possible mechanism for multiple outbreaks or even sustained periodic oscillations of emerging infectious diseases due to the psychological impact of the reported numbers of infectious and hospitalized individuals. This impact leads to the change of avoidance and contact patterns at both individual and community levels, and incorporating this impact using a simple nonlinear incidence function into the model shows qualitative differences of the transmission dynamics.

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