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Denoeux proposed an operator called the cautious conjunctive rule (CCR) to combine non-dogmatic belief functions (i.e., the frame is considered a focal element) from reliable dependent sources, which can occur in practice. However, in cases such as uncertain multiple attribute and group decision analyses, belief functions may denote data that vary in importance. This paper extends CCR as a weighted CCR (WCCR) to combine belief functions in consideration of their relative weights in such situations. Properties of WCCR are analyzed, proven, and demonstrated using numerical examples. In particular, the consideration of relative weights enables WCCR to combine dogmatic belief functions. The normalized WCCR is further constructed and used to assess the trustworthiness of a hospital information system employed in many hospitals in Anhui Province, China. [ABSTRACT FROM AUTHOR]

In this paper, we consider a deterministic malaria transmission model with standard incidence rate and treatment. Human population is divided into susceptible, infectious and recovered subclasses, and mosquito population is split into susceptible and infectious classes. It is assumed that, among individuals with malaria who are treated or recovered spontaneously, a proportion moves to the recovered class with temporary immunity and the other proportion returns to the susceptible class. Firstly, it is shown that two endemic equilibria may exist when the basic reproduction number R 0 < 1 and a unique endemic equilibrium exists if R 0 > 1 . The presence of a backward bifurcation implies that it is possible for malaria to persist even if R 0 < 1 . Secondly, using geometric method, some sufficient conditions for global stability of the unique endemic equilibrium are obtained when R 0 > 1 . To deal with this problem, the estimate of the Lozinski ı ˘ measure of a 6 × 6 matrix is discussed. Finally, numerical simulations are provided to support our theoretical results. The model is also used to simulate the human malaria data reported by the Chinese Ministry of Health from 2002 to 2013. It is estimated that the basic reproduction number R 0 ≈ 0.0161 for the malaria transmission in China and it is found that the plan of eliminating malaria in China is practical under the current control strategies. [ABSTRACT FROM AUTHOR]

• Mathematical model for coronavirus disease that fits well the spread in China. • New θ -SEIHRD model taking into account undetected infections. • Validation of the model with the reported data on China. • Estimation of errors when identifying parameters at early stages of the pandemic. • Different scenarios to show the impact of undetected cases on the pandemic. In this paper we develop a mathematical model for the spread of the coronavirus disease 2019 (COVID-19). It is a new θ -SEIHRD model (not a SIR, SEIR or other general purpose model), which takes into account the known special characteristics of this disease, as the existence of infectious undetected cases and the different sanitary and infectiousness conditions of hospitalized people. In particular, it includes a novel approach that considers the fraction θ of detected cases over the real total infected cases, which allows to study the importance of this ratio on the impact of COVID-19. The model is also able to estimate the needs of beds in hospitals. It is complex enough to capture the most important effects, but also simple enough to allow an affordable identification of its parameters, using the data that authorities report on this pandemic. We study the particular case of China (including Chinese Mainland, Macao, Hong-Kong and Taiwan, as done by the World Health Organization in its reports on COVID-19), the country spreading the disease, and use its reported data to identify the model parameters, which can be of interest for estimating the spread of COVID-19 in other countries. We show a good agreement between the reported data and the estimations given by our model. We also study the behavior of the outputs returned by our model when considering incomplete reported data (by truncating them at some dates before and after the peak of daily reported cases). By comparing those results, we can estimate the error produced by the model when identifying the parameters at early stages of the pandemic. Finally, taking into account the advantages of the novelties introduced by our model, we study different scenarios to show how different values of the percentage of detected cases would have changed the global magnitude of COVID-19 in China, which can be of interest for policy makers. [ABSTRACT FROM AUTHOR]