Predicting the number of reported and unreported cases for the COVID-19 epidemics in China, South Korea, Italy, France, Germany and United Kingdom.

We model the COVID-19 coronavirus epidemics in China, South Korea, Italy, France, Germany and the United Kingdom. We identify the early phase of the epidemics, when the number of cases grows exponentially, before government implementation of major control measures. We identify the next phase of the epidemics, when these social measures result in a time-dependent exponentially decreasing number of cases. We use reported case data, both asymptomatic and symptomatic, to model the transmission dynamics. We also incorporate into the transmission dynamics unreported cases. We construct our models with comprehensive consideration of the identification of model parameters. A key feature of our model is the evaluation of the timing and magnitude of implementation of major public policies restricting social movement. We project forward in time the development of the epidemics in these countries based on our model analysis.

A spatial model of honey bee colony collapse due to pesticide contamination of foraging bees.

We develop a model of honey bee colony collapse based on contamination of forager bees in pesticide contaminated spatial environments. The model consists of differential and difference equations for the spatial distributions of the uncontaminated and contaminated forager bees. A key feature of the model is incorporation of the return to the hive each day of forager bees. The model quantifies colony collapse in terms of two significant properties of honey bee colonies: (1) the fraction of contaminated forager bees that fail to return home due to pesticide contamination, and (2) the fraction of forager bees in the total forager bee population that return to the sites visited on the previous day. If the fraction of contaminated foragers failing to return home is high, then the total population falls below a critical threshold and colony collapse ensues. If the fraction of all foragers that return to previous foraging sites is high, then foragers who visit contaminated sites multiple times have a higher probability of becoming contaminated, and colony collapse ensues. This quantification of colony collapse provides guidance for implementing measures for its avoidance.

A COVID-19 epidemic model with latency period.

At the beginning of a COVID-19 infection, there is a period of time known as the exposed or latency period, before an infected person is capable of transmitting the infection to another person. We develop two differential equations models to account for this period. The first is a model that incorporates infected persons in the exposed class, before transmission is possible. The second is a model that incorporates a time delay in infected persons, before transmission is possible. We apply both models to the COVID-19 epidemic in China. We estimate the epidemiological parameters in the models, such as the transmission rate and the basic reproductive number, using data of reported cases. We thus evaluate the role of the exposed or latency period in the dynamics of a COVID-19 epidemic.

SI epidemic model applied to COVID-19 data in mainland China.

The article is devoted to the parameters identification in the SI model. We consider several methods, starting with an exponential fit to the early cumulative data of SARS-CoV2 in mainland China. The present methodology provides a way to compute the parameters at the early stage of the epidemic. Next, we establish an identifiability result. Then we use the Bernoulli-Verhulst model as a phenomenological model to fit the data and derive some results on the parameters identification. The last part of the paper is devoted to some numerical algorithms to fit a daily piecewise constant rate of transmission.

Identifying the number of unreported cases in SIR epidemic models.

An SIR epidemic model is analysed with respect to the identification of its parameters and initial values, based upon reported case data from public health sources. The objective of the analysis is to understand the relationship of unreported cases to reported cases. In many epidemic diseases the reported cases are a small fraction of the unreported cases. This fraction can be estimated by the identification of parameters for the model from reported case data. The analysis is applied to the Hong Kong seasonal influenza epidemic in New York City in 1968-1969.

An Environmental Model of Honey Bee Colony Collapse Due to Pesticide Contamination.

We develop a model of honey bee colony collapse based on the contamination of forager bees in environmental regions contaminated with pesticides. An important feature of the model is the daily homing capacity each day of foragers bees. The model consists of difference equations describing the daily homing of uncontaminated and contaminated forager bees, with an increased homing failure of contaminated bees. The model quantifies colony collapse in terms of the fraction of contaminated bees subject to this increased homing failure. If the fraction is sufficiently high, then the hive falls below a viability threshold population size that leads to rapid disintegration. If the fraction is sufficiently low, then the hive can rise above the viability threshold and attain a stable population level.

A Model for Transfer of P-Glycoproteins in MCF-7 Breast Cancer Cell Line with Multiple Transfer Rules.

In this paper, we consider a direct protein transfer process between cells in co-culture. Assuming that cells continually encounter each other, and from some hypotheses on cell-to-cell rules of transfer, we derive discrete and continuous Boltzmann-like integro-differential equations. The novelty of this model is to take into account multiple transfer rules. This new transfer model is used to fit the experimental data of cell-to-cell protein transfer in breast cancer.

Modelling the transmission dynamics of meticillin-resistant Staphylococcus aureus in Beijing Tongren hospital.

Semi-professional volunteers work in many tertiary care hospitals in China as healthcare assistants. Proper infection control measures are needed to reduce nosocomial transmission involving volunteers. A compartmental model was constructed to describe the transmission characteristics of meticillin-resistant Staphylococcus aureus (MRSA) in the emergency ward (EW) and respiratory intensive care unit (RICU) for volunteers in Beijing Tongren Hospital, Beijing, China. The model consists of components describing uncolonized and colonized patients, uncontaminated and contaminated healthcare workers (HCWs), and uncontaminated and contaminated volunteers. The basic reproduction number (R(0)) was calculated, and the dependence of R(0) on various model parameters was analysed. Moreover, simulations of the model were performed for comparision with the reported data on the numbers of colonized patients in the EW and RICU from 3 March 2009 to 28 February 2010, respectively. Sensitivity analysis of R(0) showed that increasing handwashing compliance among HCWs and volunteers would reduce the risk of transmission dramatically. As volunteers care for patients on a one-to-one basis, this study showed that the number of MRSA-positive patients would increase if volunteers were replaced by HCWs. Therefore, in addition to improving hand hygiene among HCWs, the employment of properly trained volunteers is an attractive alternative to decrease MRSA and other multi-drug resistant bacteria infections in the hospital setting.

A model of Salmonella infection within industrial house hens.

Salmonella is one of the major sources of toxi-infection in humans. Incidences of human salmonellosis have greatly increased over the past 20 years and this can largely be attributed to epidemics of Salmonella enteritidis phage type 4 within poultry. The main concern with this bacterium is the existence of silent carriers, i.e. animals harbouring S. enteritidis without expressing any visible symptoms. In this article, we formulate a model for S. enteritidis transmission in hen houses, considering both the hens and the environmental bacterium contamination. By considering the hen's individual development of the disease, we build a model for the production of eggs contaminated by S. enteritidis. The objectives are to analyse the dynamic of the disease, and to provide understanding of measures to avoid the endemicity of S. enteritidis in industrial hen houses.