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{{currentCountry.country}}
\n \n \n ‰\n \n \n Facts
\n \n \n Yesterday, {{currentCountry.delta | number}} new cases where reported, {{currentCountry.recoveredDelta}} patients recovered \n and unfortunately {{currentCountry.deathsDelta}} patients died.\n
\n \n Up to now, a total number of {{currentCountry.tests | number}} persons where tested.\n {{currentCountry.cases | number}} results where positive\n ({{100*currentCountry.cases/currentCountry.tests | number:\"1.1-1\"}}% of the tests). Their current state is:\n
\n - {{currentCountry.recovered | number}} recovered and are now immune and not infectious anymore.
\n - {{currentCountry.active | number}} are still active (meaning they are still infected, some of them infectious),\n {{currentCountry.critical | number}} of them in a critical situation1
\n - {{currentCountry.deaths | number}} died2
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1 should stay below the number of ICU and CCB available in your country. \n See \n Wikipedia article List of countries by hospital beds
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2 the estimated mortality rate of your country from the last years \n (before the Corona virus) is \n {{currentCountry.mortalityRate | number}} per year \n ({{currentCountry.mortalityRatePerDay | number}} per day).\n See Wolfram Alpha.\n
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\n Up to now, {{currentCountry.testsPerMille | number:\"1.2-2\"}}‰ of {{currentCountry.country}}'s population\n was tested, {{currentCountry.casesPerMille| number:\"1.2-2\"}}‰ positive \n ({{100*currentCountry.cases/currentCountry.tests | number:\"1.1-1\"}}% of the tests). Their current state is:\n
\n - {{currentCountry.recoveredPerMille | number:\"1.2-2\"}}‰ recovered and are not infectious anymore.
\n - {{currentCountry.activePerMille | number:\"1.2-2\"}}‰ are still active (meaning they are still \n infected, some of them also infectious),\n {{currentCountry.criticalPerMille | number:\"1.2-2\"}}‰ are in a critical situation1
\n - {{currentCountry.deathsPerMille | number:\"1.2-2\"}}‰ died2
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1 should stay below the number of ICU and CCB available in your country. \n See \n Wikipedia article List of countries by hospital beds
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2 the estimated mortality rate for your country from the last years \n (before the Corona virus), is \n {{1000 * currentCountry.mortalityRate / currentCountry.population | number:\"1.2-2\"}}‰ \n of population per year. \n See Wolfram Alpha.\n
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Data and Symbols
\n Covid-19 case data are provided by Johns Hopkins University and retrieved with the APIs provided by \n NovelCOVID.
\n It is important to keep in mind that the reported new cases reflect positive tests performed \n several days before being reported. Further more, the infection took place even some additional days before\n the test.
\n For every day since the beginning of case reporting, we define the following indicators:\n \n - ΔT - new cases; ΔR - new recovered; ΔD - new deaths.
\n - T - cumulated reported cases
\n - R - cumulated recovered cases
\n - A - currently active cases
\n - C - currently critical cases (subset of A)
\n - D - cumulated deaths
\n - R0 (Experimental!) - the expected average number of persons which will be infected by one infected person.\n The estimation of the reproduction number for each day is assuming that on average an infected person is isolated after \n 5 days of being infectious. This is actually different from county to country so the results here are very inaccurate.
\n \n - M - mobility data change is indicating in % how much the mobility of the population has changed \n since january 2020. The data provided by google: \n \n See how your community is moving around differently due to COVID-19 \n
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\n Math
\n \n We are using a very simple but illustrative model to simulate what could happen in the future, \n based on the logistic equation. In our model, we assume that patients tested positive will be isolated \n and cannot infect other peoples anymore. We assume that patients tested positive, before being tested,\n where infectious about 5 days before being isolated. \n
\n Basic reproduction rate and number: r0 and R0
\n \n Let us assume that an infected person, on average, \n is encountering every day a number ρ of other persons.\n For each person he encounters, there is a \n probability φ of infecting him (for instance if they shake hands, \n or the infected person is sneezing while they meet etc.).\n
\n \n Definition:The basic reproduction rate r0 is the number of new infections\n caused directly by an infected person during one day, if all other persons around him are susceptible: \n r0= ρ × φ\n
\n \n If on day n there are In infectious persons, and assuming all of them meet only susceptible persons (meaning: \n persons which can be infected - i.e. they are not yet infected, nor immune) - then during one day, the \n new number of infected persons is: \n
\n \n ΔIn+1 = r0 × In\n
\n \n Notes:
\n 1. If r0 ≤ 1, the disease cannot spread and disappears.
\n 2. The reproduction rate is influenced by the social habits and behavior of the people \n (by ρ: how many \n other people are met; by φ: do they shake hands? Do they embrace each other?\n Do they wash their hands on a regular base?).
\n 3. It is also influenced by the disease itself (by ρ: how it is transmitted?).
\n 4. It is NOT influenced by the status of the other persons - i.e. if they are already immune or not. \n
\n \n Definition: The Infectious period τ is the average duration an infected person remains\n infectious and can infect others (before being isolated). We use the value of 5 days in our calculation.\n
\n \n Definition: The Active period ε is the average total duration an infected person remains\n infected. We use the value of 14 days in our calculations.\n
\n \n Definition: The basic reproduction number R0 is the number of persons directly infected\n by an infected person during his infection period.\n
\n \n R0 = r0 × τ\n
\n Effective reproduction rate and number: rt and Rt
\n \n Both r0 and R0 are defined under ideal conditions: it is assumed that \n all other persons are susceptible. This is the case in the beginning of an epidemy, when the number of\n infectious and immune persons is negligible. \n But after some time, our imaginary infected person will not only encounter susceptible persons, but also \n active or immune persons.\n If the population of the country is P, the number of current infected persons is A (active), \n R the recovered persons, then number of susceptible \n persons is S = P - A - R, and the probability for our imaginary infected person to encounter a \n susceptible person is s = S / P. The probability s will decrease from 1 towards 0 during an epidemy (we will see later that \n often it will not reach 0).
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\n Definition:The effective reproduction rate rt and the effective reproduction number \n Rt are defined as:\n
\n \n rt = r0 × s
\n Rt = R0 × s
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\n \n If we consider the number of persons who die, D, the population will decrease over time, \n and on day n+1 we can write:\n The newly infected persons on day n can be written as:\n
\n \n ΔIn = r0 × In-1 × sn-1
\n sn = (Pn - An - Rn) / Pn
\n Pn = Pn-1 - Dn\n
\n \n The number of recovered persons on day n can be written as \n
\n \n Rn = Rn-1 + ΔIn-τ\n
\n And the number of infectious and infected persons on day n is:\n \n In = In-1 + ΔIn- ΔIn-τ
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\n An = An-1 + ΔIn - ΔIn-ε
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\n For now we assume there are no deaths:\n \n Dn = 0 for all n\n
\n \n Our result is a slightly more complex form of the \n logistic map. \n Below we plot the series for the 2 indicators: An and Rn. \n We quickly observe that the values of R and S have an asymptotic behavior so that not the whole population\n will be infected. A - the number of simultaneously ill persons - is growing exponential in the beginning, \n reaches a maximum and the falls down exponentially back to 0. The amplitude of this maximum, the point \n in time when is reached and the final values of R and S depends on the two unknown parameters of our\n series: τ and r0.\n
\n Take your time and try out a few combinations for the values for of τ and r0. \n The population P is chosen to be that \n of {{currentCountry.country}}: {{currentCountry.population | number:\"1.0-0\"}}.\n
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\n R0: {{reproductionNumber | number:\"1.2-2\"}}\n \n \n
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\n τ: {{infectionPeriod | number:\"1.0-0\"}} days\n \n \n
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\n simulation period: {{simulationDays | number:\"1.0-0\"}} days\n \n \n
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\n \n Covid-19's basic reproduction number R0 is estimated between 1.4 and 5.7, under \"natural\" \n social behavior of the population, as we used to live before or during the start of this pandemic (see \n \n Wikipedia article on basic reproduction number).
\n Social distancing and other (also hygienic) measures are reducing the basic reproduction number, attempting to\n bring it and keep it at a value lower than or around 1.
\n Probably you can see in the simulation that any number larger than 1.4 is leading to a fast\n increase of simultaneously ill people, which would cause an overloaded health system.\n Probably it is going to take a long time until we will have the freedom to live as before...\n
\n Disclaimer & Credits
\n Implemented by Artur Pusztai
\n The application is work in progress, not sufficiently tested, and not suitable for decision making.\n
\n \n Covid-19 case data are provided by\n Johns Hopkins University\n and retrieved with the APIs provided by\n NovelCOVID\n
\n Mobility profiles are provided by google:\n \n See how your community is moving around differently due to COVID-19\n
\n \n Mortality rates are taken from\n Wolfram Alpha.\n
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