A stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching

The impact of poaching and regime switching on the dynamics of single-species model

It is widely recognized that the criminal act of poaching has brought tremendous damage to biodiversity. This paper employs a stochastic single-species model with regime switching to investigate the impact of poaching. We first carry out the survival analysis and obtain sufficient conditions for the extinction and persistence in mean of the single-species population. Then, we show that the model is positive recurrent by constructing suitable Lyapunov function. Finally, numerical simulations are carried out to support our theoretical results. It is found that: (i) As the intensity of poaching increases, the odds of being at risk of extinction increases for the single-species population. (ii) The regime switching can suppress the extinction of the single-species population. (iii) The white noise is detrimental to the survival of the single-species population. (iv) Increasing the criminal cost of poaching and establishing animal sanctuaries are important ways to protect biodiversity.

National Holidays and Social Mobility Behaviors: Alternatives for Forecasting COVID-19 Deaths in Brazil

In this paper, we investigate the influence of holidays and community mobility on the transmission rate and death count of COVID-19 in Brazil. We identify national holidays and hallmark holidays to assess their effect on disease reports of confirmed cases and deaths. First, we use a one-variate model with the number of infected people as input data to forecast the number of deaths. This simple model is compared with a more robust deep learning multi-variate model that uses mobility and transmission rates (R0, Re) from a SEIRD model as input data. A principal components model of community mobility, generated by the principal component analysis (PCA) method, is added to improve the input features for the multi-variate model. The deep learning model architecture is an LSTM stacked layer combined with a dense layer to regress daily deaths caused by COVID-19. The multi-variate model incremented with engineered input features can enhance the forecast performance by up to 18.99% compared to the standard one-variate data-driven model.