The effects of containment measures in the Italian outbreak of COVID-19

The COVID-19 pandemic is spreading worldwide. Italy emerged early on as the country with the largest outbreak outside Asia. The outbreak in Northern Italy demonstrates that it is fundamental to contain the virus’ spread at a very early stage of diffusion. At later stages, no containment measure, even if strict, can prevent the saturation of the hospitals and of the intensive care units in any country. Here we show that it is possible to predict when the intensive care units will saturate, within a few days from the beginning of the exponential growth of COVID-19 intensive care patients. Using early counts of intensive care patients, we predict the saturation for Lombardy, Italy. We also assess short-term and long-term lockdown effects on intensive care units and number of deaths. Governments should use the Italian outbreak as a precedent and implement appropriate containment measures to prevent the saturation of their intensive care units and protect their population, also, and above all, in anticipation of a possible second exponential spread of infections.

Angiogenesis and vessel co-option in a mathematical model of diffusive tumor growth: The role of chemotaxis

This work considers the propagation of a tumor from the stage of a small avascular sphere in a host tissue and the progressive onset of a tumor neovasculature stimulated by a pro-angiogenic factor secreted by hypoxic cells. The way new vessels are formed involves cell sprouting from pre-existing vessels and following a trail via a chemotactic mechanism (CM). Namely, it is first proposed a detailed general family of models of the CM, based on a statistical mechanics approach. The key hypothesis is that the CM is composed by two components: i) the well-known bias induced by the angiogenic factor gradient; ii) the presence of stochastic changes of the velocity direction, thus giving rise to a diffusive component. Then, some further assumptions and simplifications are applied in order to derive a specific model to be used in the simulations. The tumor progression is favored by its acidic aggression towards the healthy cells. The model includes the evolution of many biological and chemical species. Numerical simulations show the onset of a traveling wave eventually replacing the host tissue with a fully vascularized tumor. The results of simulations agree with experimental measures of the vasculature density in tumors, even in the case of particularly hypoxic tumors.

The dynamics of tumour-vasculature interaction suggests low-dose, time-dense anti-angiogenic schedulings

OBJECTIVES

The administration schedule appears to be a particularly relevant factor in determining the effectiveness of an antiangiogenic drug. A better quantitative knowledge of the interactions between tumour growth and the development of its vasculature could help to design effective therapies.

MATERIAL AND METHODS

Biological and clinical inferences were derived from the analysis of a mathematical model proposed by Hahnfeldt et al. (1999), and some of its variants. In particular, we compared the effect of constant continuous infusion of an anti-angiogenic drug that induces vascular loss, to the effect of periodic, bolus-based therapy.

RESULTS AND CONCLUSIONS

The role of drug elimination rate and of dose fractionation was investigated, and we show that different schedulings, guaranteeing the same mean value of drug concentration, may exhibit very different long-term responses according to their concentration vs. time profile. For a large class of tumour growth laws, the profiles that approach the constant one are the most effective. This behaviour appears to depend on the 'cooperativity' of the tumour-vasculature interaction and on the functional form of the relationship between tumour growth and vasculature extent. Moreover, we suggest that a therapy approaching constant drug infusion might be advantageous also in the case of cytostatic anti-angiogenic drugs.

Measuring progress against cancer in Europe: has the 15% decline targeted for 2000 come about?

BACKGROUND

Against a background of increasing cancer rates in the mid-1980s, Europe Against Cancer launched an ambitious programme aiming to reduce cancer mortality by 15% by the year 2000. A programme of activities and research, focussing on three major themes [prevention (particularly tobacco control), screening, and education and training], was developed together with the European Code Against Cancer.

METHODS

To evaluate the outcome of the programme, all cancer mortality data were abstracted for each member state of the European Union (EU) until the most recent year available. For each gender group in each member state, age-specific rates were estimated for 2000. For each country-gender grouping, the standardized mortality rate (SMR) and expected numbers of deaths in 2000 were calculated based on the age-specific rates for 1985 and the population estimates for 2000. The ratio of the SMR in 2000 to that of 1985, was used as the measure to compare mortality rates.

RESULTS

In 1985, there were 850 194 cancer deaths in the EU. Based solely on demographic considerations, this number was expected to rise to 1 033 083 in the year 2000. Between 1985 and 2000, the number of cancer deaths increased in both men (+12%) and women (+9%). The target of a 15% reduction in the expected numbers of cancer deaths in the EU was not met, although the 10% reduction in number of deaths expected in men and 8% in women, along with a 11% reduction in risk of cancer death in men and a 10% reduction in women, was noteworthy. Only Austria and Finland achieved the 15% reductions in deaths in both men and women. The UK and Luxembourg (where the small population and annual number of deaths make interpretation difficult) came close to meeting these targets, as did Italy. Portugal and Greece had the poorest performance, with increases in each gender group.

CONCLUSIONS

Cancer deaths in the EU were expected to rise from 850 194 in 1985 to 1 033 083 in 2000. It is estimated that there will be 940 510 cancer deaths that year, due to the decline in risk observed since 1985. The Europe Against Cancer programme appears to have been associated with the avoidance of 92 573 cancer deaths in the year 2000. With few exceptions, most countries are experiencing declining trends in cancer death rates, which seem set to continue, at least in the near future. Renewed tobacco control efforts are clearly needed for women, and there is a strong case for the introduction of organized breast and cervix screening programmes in all member states. Continuing to emphasize prevention within cancer control will help to promote the continuing decline in death rates in the future.

Cancer mortality trends in the EU and acceding countries up to 2015

BACKGROUND

Examination of trends in cancer mortality in Europe over the past 30 years has shown that, after long-term rises, age-standardised mortality from most common cancer sites has fallen in the EU since the late 1980s. This study aimed to examine trends in the age-specific and age-standardised cancer mortality rates and numbers of cancer deaths up to 2020 for all cancers and various specific sites for all 15 EU countries, the 10 acceding countries, Bulgaria and Romania (currently applicant countries, along with Turkey), and Iceland, Norway and Switzerland of the four EEA countries.

PATIENTS AND METHODS

Mortality rates were modelled as a function of age, calendar period and birth cohort. Birth cohort was calculated as age subtracted from calendar period.

RESULTS

As a consequence of the generally decreasing trends in the age-standardised rates, the best estimate is that there will be approximately 1.25 million cancer deaths in 2015, which is almost 130,000 (11%) more deaths than in 2000, but 155,000 (11%) fewer deaths than the 1.4 million projected in 2015 on the basis of demographic changes alone. The increases in the forecast numbers of cancer deaths in 2015 are proportionally larger in males than in females (13% and 10%, respectively) and proportionally larger in the acceding countries than in the current EU member countries (14% and 11%, respectively).

CONCLUSIONS

Our forecasts are conservative best estimates of future cancer mortality. There is clearly scope for large improvements in survival, and hence reductions in cancer mortality, in some countries, through eliminating these differences using existing knowledge and treatment regimes.