Since the emergence of the first cases in Wuhan, China, the novel coronavirus (2019-nCoV) infection has been quickly spreading out to other provinces and neighboring countries. Estimation of the basic reproduction number by means of mathematical modeling can be helpful for determining the potential and severity of an outbreak and providing critical information for identifying the type of disease interventions and intensity. A deterministic compartmental model was devised based on the clinical progression of the disease, epidemiological status of the individuals, and intervention measures. The estimations based on likelihood and model analysis show that the control reproduction number may be as high as 6.47 (95% CI 5.71–7.23). Sensitivity analyses show that interventions, such as intensive contact tracing followed by quarantine and isolation, can effectively reduce the control reproduction number and transmission risk, with the effect of travel restriction adopted by Wuhan on 2019-nCoV infection in Beijing being almost equivalent to increasing quarantine by a 100 thousand baseline value. It is essential to assess how the expensive, resource-intensive measures implemented by the Chinese authorities can contribute to the prevention and control of the 2019-nCoV infection, and how long they should be maintained. Under the most restrictive measures, the outbreak is expected to peak within two weeks (since 23 January 2020) with a significant low peak value. With travel restriction (no imported exposed individuals to Beijing), the number of infected individuals in seven days will decrease by 91.14% in Beijing, compared with the scenario of no travel restriction.

The global outbreak of COVID-19 has caused worrying concern amongst the public and health authorities. The first and foremost problem that many countries face during the outbreak is a shortage of medical resources. In order to investigate the impact of a shortage of hospital beds on the COVID-19 outbreak, we formulated a piecewise smooth model for describing the limitation of hospital beds. We parameterized the model while using data on the cumulative numbers of confirmed cases, recovered cases, and deaths in Wuhan city from 10 January to 12 April 2020. The results showed that, even with strong prevention and control measures in Wuhan, slowing down the supply rate, reducing the maximum capacity, and delaying the supply time of hospital beds all aggravated the outbreak severity by magnifying the cumulative numbers of confirmed cases and deaths, lengthening the end time of the pandemic, enlarging the value of the effective reproduction number during the outbreak, and postponing the time when the threshold value was reduced to 1. Our results demonstrated that establishment of the Huoshenshan, Leishenshan, and Fangcang shelter hospitals avoided 22,786 people from being infected and saved 6524 lives. Furthermore, the intervention of supplying hospital beds avoided infections in 362,360 people and saved the lives of 274,591 persons. This confirmed that the quick establishment of the Huoshenshan, Leishenshan Hospitals, and Fangcang shelter hospitals, and the designation of other hospitals for COVID-19 patients played important roles in containing the outbreak in Wuhan.

Based on the report of epidemic data sets for Hubei province and mainland China,the big data from Baidu population migration trends and distributions,we formulated the COVID-19 transmission model on complex networks for Wuhan city and the 15 surrounding cities with severe epidemics, and analyzed the possible times for resumption of work in Wuhan and its surrounding areas and the impact of resumption of work on the risk of a secondary outbreak. Firstly, we estimated the actual cumulative number of cases in Wuhan on January 23rd on the basis of the cumulative number of reported cases in other 15 cities, and obtained the control reproduction numbers for the 16 major cities in Hubei province in different periods. Our research results revealed that the early transmission risk in these areas is high and the current transmission risk is low (due to the control reproduction numbers being less than 1). By simulating the whole network model on the flow network structure and flow volume in the same period of last year, we investigated the impact of the resumption of work on February 17, February 24 and March 2 on disease infection for each city. Main conclusion showed that with strong prevention measures and self-protection the second outbreak will not be caused during a period by the resumption of work on March 2, 2020.

China’s Guangdong Province experienced a major dengue outbreak in 2014. Here we investigate if the weather conditions contributing to the outbreak can be elucidated by multi-scale models. A multi-scale modelling framework, parameterized by available weather, vector and human case data, was used to examine the integrative effect of temperature and precipitation variation on the effective reproduction number (ERN) of dengue fever. With temperature in the range of 25–30 °C, increasing precipitation leads to an increase in the ERN with an average lag of 10 days. With monthly precipitation fixed, the more regular the pattern of rainfall (i.e. higher numbers of rainy days), the larger is the total number of adult mosquitoes. A rainfall distribution peaking in June and July produces a large ERN, beneficial to transmission. Climate conditions conducive to major outbreaks within a season are a combination of relatively high temperature, high precipitation peaking in June and July, and uninterrupted drizzle or regular rainfall. Evaluating a set of weather conditions favourable to a future major dengue outbreak requires near-future prediction of temperature variation, total rainfall and its peaking times. Such information permits seasonal rapid response management decisions due to the lags between the precipitation events and the realisation of the ERN.

Background: Radio/chemotherapy and immune systems provide examples of hormesis, as tumours can be stimulated (or reduced) at low radio/chemical or antibody doses but inhibited (or stimulated) by high doses. Methods: Interactions between effector cells, tumour cells and cytokines with pulsed radio/chemo-immunotherapy were modelled using a pulse differential system. Results: Our results show that radio/chemotherapy (dose) response curves (RCRC) and/or immune response curves (IRC) or a combination of both, undergo homeostatic changes or catastrophic shifts revealing hormesis in many parameter regions. Some mixed response curves had multiple humps, posing challenges for interpretation of clinical trials and experimental design, due to a fuzzy region between an hormetic zone and the toxic threshold. Mixed response curves from two parameter bifurcation analyses demonstrated that low-dose radio/chemotherapy and strong immunotherapy counteract side-effects of radio/chemotherapy on effector cells and cytokines and stimulate effects of immunotherapy on tumour growth. The implications for clinical applications were confirmed by good fits to our model of RCRC and IRC data. Conclusions: The combination of low-dose radio/chemotherapy and high-dose immunotherapy is very effective for many solid tumours. The net benefit and synergistic effect of combined therapy is conducive to the treatment and inhibition of tumour cells.