Article Text

The European COVID-19 drugs calculation tool: an aid for the estimation of the drugs needed during the SARS-CoV 2 pandemic
  1. Daniele Leonardi Vinci1,
  2. Adriano Meccio2,
  3. Alessio Provenzani3,
  4. Maria Ernestina Faggiano4,
  5. Nenad Miljković5,
  6. Despina Makridaki6,
  7. Petr Horák7,
  8. Piera Polidori3
  1. 1 School of Specialization in Hospital Pharmacy, University of Palermo, Palermo, Sicilia, Italy
  2. 2 Chemical Engineering, University of Palermo, Palermo, Sicilia, Italy
  3. 3 Clinical Pharmacy, ISMETT, Palermo, Italy
  4. 4 Pharmacy, AOU Policlinico, Bari, Puglia, Italy
  5. 5 Hospital Pharmacy, Institute of Orthopaedic Surgery "Banjica", Belgrade, Serbia
  6. 6 Pharmacy Services, "Sismanoglio- Amalia Fleming", General Hospital of Attica, Athens, Greece
  7. 7 Hospital Pharmacy, Motol University Hospital, Praha, Praha, Czech Republic
  1. Correspondence to Dr Daniele Leonardi Vinci, School of Specialization in Hospital Pharmacy, University of Palermo, Palermo 90131, Italy; daniele.leo93{at}


Objective To create an informatics supportive tool, which can assist healthcare professionals in estimating potential requirements for essential drug supplies to respond to the current SARS-CoV-2 pandemic based on epidemiological forecasting.

Methods The tool was based on a Susceptible-Infected-Removed (SIR) epidemiological model in which the population is divided into three compartments and transmission parameters are specified to define the rate at which people move between stages. Appropriate data entry was guaranteed by the creation of structured guided paths. The drugs needed for the forecasted patients were estimated according to a list of critical care drugs compiled by consulting previous published scientific works, national and international guidelines. For each drug, an estimation was made of the percentage average ICU uptake for each therapeutic group and active principle.

Results The tool consists of a Microsoft Excel template that is based on the initial epidemiological situation, the non-pharmaceutical interventions applied, the risk of hospitalisation based on the population age distribution, and the hospital beds available. The tool provides a forecast of which patients with COVID-19 will need to be treated in a hospital setting. The number of patients is used to estimate the drugs needed based on the average daily dose and the treatment length of each drug. The possibility of editing the type of distribution (exponential or linear) of the number of patients at the beginning of the analysis, the percentage adherence with non-pharmaceutical interventions and their delayed effect, and all the key epidemiological parameters make the estimation tailorable to different clinical contexts and needs.

Conclusions This model might be an effective supporting tool that could be easily implemented within the workflow of health professionals. All the information reported in this paper could be useful in developing new strategies to tackle the COVID-19 pandemic.

  • public health
  • critical care
  • COVID-19
  • practice guideline
  • health care rationing
  • health care economics and organizations
  • Medical Informatics

Data availability statement

All data relevant to the study are included in the article or uploaded as supplementary information. No patients data included.

This article is made freely available for personal use in accordance with BMJ’s website terms and conditions for the duration of the covid-19 pandemic or until otherwise determined by BMJ. You may use, download and print the article for any lawful, non-commercial purpose (including text and data mining) provided that all copyright notices and trade marks are retained.

Statistics from


The COVID-19 pandemic has proved to be a global health threat, with approximately 100 million people infected and more than 2 million deaths worldwide.1 The pandemic trend is influenced by multiple factors and each nation has adopted specific strategies to impede its spread. National health services have, therefore, been unprecedentedly challenged to assure adequate patient care, despite a constantly escalating demand for supportive drugs. This complex situation requires appropriate planning that is deeply affected by many aspects, such as the long-term unpredictability of the pandemic evolution, the disruption and vulnerability of the supply chains,2 and the timeliness required by the decision-making process. All these aspects can generate misleading estimations, which can deeply impact the efficiency of the assistance provided by healthcare facilities, resulting in either a lack of therapies or placing further pressure on already constrained drugs and the supply chain. For this reason, health professionals should use adequate tools that can support the calculation of therapeutic needs, especially for those patients that require intensive care. With this regard, modelling of the pandemic appears to be crucial. As reported in a previous work,3 every country, province or hospital should carry out proper pandemic modelling based on the epidemiological features and adapted to the local population in terms of number of people and age distribution in order to tailor and optimise the estimates to their specific situation.

Aim of the study

We decide to create an informatics supportive tool, the European COVID-19 Drugs Calculation Tool (ECDCT). This tool is capable of assisting pharmacists, local healthcare institutions, governments, partners and other stakeholder to easily estimate potential requirements for essential drug supplies to respond to the current COVID-19 pandemic based on epidemiological forecasting.

We also wanted to share our methodological approach with other colleagues, so that our work might help to develop future strategies for the management of drug supplies during a pandemic emergency.

Materials and methods

The ECDCT was developed using Microsoft Excel software and was structured as a user-friendly interactive application that allows users, through a series of guided paths, to enter data about the current epidemiological situation in various countries and geographical areas. Based on the data provided, the tool will output a drug needs estimation derived from an epidemiological forecasting model.

Forecasting model

Epidemiological forecasting was based on a susceptible-infected-removed (SIR) model,4 which describes the transmission dynamics as the flow over time of individuals of a given population (N) through three mutually exclusive population compartments (figure 1):

  • Susceptible (S): healthy individuals at risk of becoming infected.

  • Infected (I): individuals who have already been infected by the virus and can transmit it to susceptible individuals.

  • Removed (R): individuals who recovered from the virus and are assumed to be immune, or those who have died.

Figure 1

Schematic visualisation of susceptible-infected-removed (SIR) compartments. The total population (N) is given by the sum of S+I+R compartments. At the early stage of an unprecedented pandemic, S can be approximated to N.

Given the short timespans involved, it is assumed that the total population does not change significantly during the forecasted period as the births and deaths unrelated to the infection can be neglected and the number of deaths from the virus is small compared with the living population. Moreover, no immigration and emigration phenomena were considered, since movements between countries are restricted during outbreaks. We also assumed that the population is well mixed and every person interacts with one another. Finally, we assumed that all infected people are infectious and are spreading the disease among the susceptible population, and that people who are immune will not become susceptible again.

Defining s=S/N, i=I/N, r=R/N as the fraction of the population in each compartment, the rates of change of the three populations are governed by the following system of ordinary differential equations:

Embedded Image (1)

Embedded Image (2)

Embedded Image (3)

where β represents the rate of spread of infection by an infected person per day when they interact with the susceptible population, and ν is the rate of removal that governs the number of removed people. As β and ν can be difficult to obtain by the average user, we calculate the expected infected individuals based on the basic reproduction number (R0), which can be calculated as:

Embedded Image (4)

where τ=infection/contact, c=contact/time, d=time/infection. Since β and ν can be respectively defined as β = τ c and d = ν −1, we calculated β as:

Embedded Image (5)

We augmented our SIR model by including the effects of Non-Pharmaceutical Interventions (NPIs), a series of public health containment measures, on the R effective (Rt) value, as reported by the Covidactnow Response Simulator,5 and by correcting the number of infected people according to the testing capacity, as shown by the WHO COVID-19 Essential Supplies Forecasting Tool.6 Finally, we set the default tuning values of the ECDCT based on what reported in the scientific literature,6–13 as illustrated in table 1.

Table 1

List of assumptions made to tune the susceptible-infected-removed (SIR) model

Although many more complex epidemiological models exist, we adopted the SIR because:

  • it is easier for users with limited epidemiological competences as it requires fewer variables, easily obtained through official sources;

  • it allows removal of many of the complexities associated with the real-time evolution of the virus’ spread, while still providing a good estimation, both quantitatively and qualitatively14;

  • our forecasting needs did not require a highly accurate model on a short-time period, but one that could capture the fundamental human-to-human transmission dynamics of the pandemic, as the final aim of the ECDCT is estimation of drugs needs throughout the whole COVID-19 surge;

  • it is widely adopted in the scientific literature14 15 and other similar forecasting tools,6 7 although with some ad-hoc variations.

Drugs selection

The drugs included in the ECDCT were selected by reviewing published scientific works, national and international guidelines,3 6 16–21 and adjusted according to local practices.

As the treatment guidelines for patients with non-critical disease, at the time of writing, are still not exhaustively defined and most of the drugs are used when needed and depending on the patient’s clinical features, such as the need for oxygen supplementation, it is hard to accurately quantify the demand for drugs in this patient population. For this reason, we provide specific drugs need estimations only for patients requiring critical care (ICU).

The calculation method adopted was informed by a previously published scientific work17 considering the patient and treatment characteristics assumptions, such as the percentage uptake of a drug group, treatment duration for each drug, drug dosages and percentage usage within a drug group.

The dosages entered were chosen on the basis of the most likely daily dosages according to what is reported in the scientific literature. When there was uncertainty or in the case of emergency medications for which the dosage ranges can vary widely (eg, naloxone, flumazenil), the Lexicomp maximum dosages were used as reference.

Some of the assumptions made for the drugs needed that are influenced by local practices and availability of drugs (dosages, duration of treatments for specific indications, and others) have been designed to be modifiable by the users in order to better adapt the estimation to their different clinical needs.

Additional data sources

To aid the ECDCT compiling process, we included data about the population and the number of hospital beds by country, extrapolated by the World Bank.22 23 Moreover, the number of people was stratified by age groups based on the age distribution by income, with data extrapolated from the United Nations,24 and the specific income group of each country. These values were used to infer the percentage of patients with symptoms who would require hospitalisation and critical care in the population considered, based on the standard percentages reported by Imperial College.8


The final version of the ECDCT consists of an Excel template in which it is possible, through a guided and structured user form, to enter all the epidemiological data required to perform the forecasting, such as population selection, R0 value, initial epidemiological situation, NPIs and availability of hospital beds. In particular, the population considered can be either chosen from a specific country or manually entered. For the R0 value, it is possible to enter the whole value, or to specify the single epidemiological parameters described in equation 4.

Information about the initial epidemiological situation refers to the total number of patients who tested positive for COVID-19 and those who were admitted to hospital and were logged on the day of the analysis. Because some of the forecasted values (eg, patients admitted to hospital) depend on the epidemiological situation of the previous few days, we achieved better modelling of the early stages of the analysis by including the epidemiological data relating to either 14 days prior to, or the day of the start of the pandemic (when the first cases occurred), if it happened less than 14 days earlier. This last option is especially useful in case there is a resurgence of the SARS-CoV2 infection after a period of no new detected cases. We considered a maximum threshold of 14 days because it corresponds to the average duration of the infection, with an incubating period of 4 days,11 a contagious period of 5 days25 and a convalescence period of 5 days.7 This epidemiological information is used to automatically distribute the number of cases occurring in the aforementioned interval according to an exponential or linear growth, based on the user’s preferences. As reported by Cooper and colleagues,14 at the beginning of the epidemic, when Rt >1 and S ≈ 1, the rate of infection obtained through a SIR model can be described by an exponential increase, and thus equation 2 can be approximated to:

Embedded Image (6)

Embedded Image (7)

which can be rewritten as

Embedded Image (8)

In ECDCT, because the number of people with infection at the beginning and at the end of the interval considered are known, we inferred λ as:

Embedded Image (9)

Where t0 and td are, respectively, the beginning and the end of the interval.

Finally, we fitted the exponential growth of the infected population as:

Embedded Image (10)

The linear growth uniformly distributes the number of cases occurring in the interval considered, and can be used when the exponential growth is not reliable, such as in extremely short timespans or in the mid-late stage of the pandemic surge.

The tool also includes a set of NPIs, such as the closure of activities, the use of masks and the sheltering in place of the population. Concerning the type of closure, the users are allowed to choose between a default set of activity closures or assigning each of them individually. As reported in other works,5 26 we included a factor (that we called percentage of closure and adherence), which represents the percentage of compliance with the public health measures on a scale from 0 (no intervention) to 1 (maximum measure’s compliance). We also included an additional parameter relating to the lag time before the NPIs’ full impact on Rt, which is the delay between the date of NPIs’ implementation and the date of their observable maximum impact on the Rt value. In fact, as has been previously reported in another work,26 there are a series of factors (eg, virus incubation and delay in lab testing) that generate a delayed detection of the NPIs’ effect. Therefore, the evaluation of the NPIs’ effect may require an observational period of 2–3 weeks.13 During this time frame, the Rt reduction is step-wisely achieved by subtracting an increasing percentage of the total NPI effect, calculated as follows:

NPI reduction on Rt * (number of days that have passed since the NPI implementation date / the total number of lag days).

Hospital beds were inferred for each country by considering the average number of beds/1000 inhabitants and adjusted by the country’s total population. When calculating critical care bed numbers, or when data were missing, we used the average number of beds/1000 inhabitants for the appropriate country’s income group, as reported by the Imperial College.8

If the forecasting is performed based on a manually entered population, the ECDCT allows one to specify the number of beds available, and whether those beds are used to assist the whole population or just a percentage of it. Using the latter option, drug estimation will be performed only for the specified percentage of the total number forecasted to be infected, which could be useful for single hospitals that are likely to assist only a fraction of all patients who will need hospitalisation within the area considered.

Hospital bed availability is a key parameter in our calculation because it is used to set the maximum amount of drugs needed since the total number of hospital beds corresponds to the maximum number of patients that will be therapeutically assisted (figure 2).

Figure 2

Comparison between the predicted hospital bed demand and the real hospitalisation capacity simulated using the European COVID-19 drugs calculation tool (ECDCT). For this simulation, the following values were used: population=59 132 073, R0=2.35, total number of cases=1 400 000, active cases=700 000, patients in hospital=35 000, new cases=23 000, total number of cases 14 days previously=600 000, new cases 14 days previously=20 000, total hospital beds available=201 049, percentage of mild/moderate cases detected by test=33%. No NPIs (non-pharmaceutical implementation) was considered.

The ECDCT also includes a series of editable epidemiological parameters that are useful to finely tune the tool, as reported in table 1. Among them, the percentage of patients with mild to moderate severity of symptoms that are detected by tests is of particular note because it is used to calculate the number of patients admitted to hospital. According to scientific evidence, the percentage of undocumented infections (not tested) at the beginning of the outbreak ranged between 82% and 90%.12 Because patients with severe to critical symptoms are the least likely to remain undetected, we decided to consider the percentage of undocumented infections as relating exclusively to patients with mild to moderate symptoms. Therefore, the default percentage of mild to moderate cases detected by test is set equal to 10%,6 but it will be updated according to the latest scientific evidence.

To improve data visualisation about the epidemiological progression and hospital bed availability, we introduced a summary dashboard where the information is displayed through both charts and tables.

Finally, the estimation of drugs based on the number of patients obtained with the SIR model is performed considering the list of drugs selected. This list includes 51 drugs belonging to 19 therapeutic groups (online supplemental table). For each drug we specify the active principle, the daily dose, the pharmaceutical form, the percentage uptake of the drug group, the percentage usage within a drug group and the treatment duration for each drug. In case of therapeutically equivalent alternatives, the users are allowed to select their preferred choice. As reported by Hogg and colleagues,17 the total amount of drug is calculated as follows: the adjusted amount of a specific drug used=daily dose * % of use in ICU (according to therapeutic group) * % of use in ICU (according to each active principle) * average treatment length (days). This adjusted amount is then multiplied by the total number of patients in the timeframe considered.

Supplemental material

In our tool, the value obtained is then divided by a specific dosage available on the market (editable by the users) to calculate the total amount of unit doses required. In figure 3 an example of drug estimation output is reported.

Figure 3

A representative example of the drug estimation output. The drugs amount displayed in the ICU table refers to 5015 patients in ICU, as reported in the ′sum of new ICU patients′ field above the timeline.


As previously stated, predictive models for epidemics are fundamental to understand the course of the epidemic and to plan effective strategies.27 In particular, as outlined in a previously published paper,9 some of the features of a forecasting model should be:

  • pragmatic and focusing only on the relevant question for surge capacity;

  • taking into account the most relevant data such as R0 of the virus, the expected or observed rate of hospitalisation, need for ICU, need for mechanical ventilation, ICU length of stay;

  • incorporating the impact of installing social distancing measures in society and their delayed impact on case detection.

In the ECDCT, we sought to implement all these features to create a tool that could represent a useful aid to estimate potential requirements for essential drug supplies to respond to the current COVID-19 pandemic.

The main goal of our work was to find a compromise between the creation of an accessible and user-friendly interface and an adequate capacity to capture the fundamental dynamics of the pandemic and thus capable of performing reliable drugs estimation. This aim has informed every developmental decision, such as the choice of basing our epidemiological forecasting on a SIR model, and the adoption of a well defined drugs calculation methodology, which can be easily personalised according to the users’ needs, through a series of editable parameters.

However, it should be considered that the reference values used to tune our model, as with every other model, are often the result of data of questionable quality and homogeneity. As suggested by Casella,26 there can be remarkable differences between countries’ standards and capacity for swab testing, data lost due to clerical errors, and the NPIs′ effectiveness that is still quite uncertain.

Particularly, the NPIs′ effectiveness, in order to be statistically significant, is evaluated by grouping together countries with very different social habits and interpretations of the same measure (eg, lockdown) in the same dataset. Additionally, it should be noted that the impact of NPIs can differ according to a country’s income group.28

Another critical aspect to consider is the fast evolution of available data, which require constant updating of the relevant parameters to ensure that the forecasting always mirrors the current epidemiological and clinical situation. This is particularly true for the lab testing capacity, which has increased since the beginning of the pandemic,29 and the list of drugs included because the therapeutic guidelines and protocols for patients with SARS-CoV-2 have extensively changed over time.30


Despite its intrinsic limitations, we believe that the ECDCT can still be an effective aid for the health professionals’ workflow. Moreover, all the information reported in this paper can represent a useful aid to guide our colleagues in the development of their own methods and tools to tackle the COVID-19 pandemic. The evaluation of the possible benefits derived from the introduction of ECDCT in daily drug management will be an interesting subject for future works.

What this paper adds

What is already known on this subject

  • the COVID-19 pandemic represents a global health emergency that has exacerbated pharmaceutical demand

  • the emergency aspect of the pandemic makes it necessary to estimate pharmaceutical needs in a short time

  • considering that it is a new virus, it is not possible to use historical consumption data as a reference

What this study adds

  • the description of an informatics tool that allows users to make a timely estimate of pharmaceutical needs

  • a drugs forecasting method based on an epidemiological model that can be customised to different settings, needs or other future pandemics

Data availability statement

All data relevant to the study are included in the article or uploaded as supplementary information. No patients data included.

Ethics statements

Patient consent for publication


Supplementary materials

  • Supplementary Data

    This web only file has been produced by the BMJ Publishing Group from an electronic file supplied by the author(s) and has not been edited for content.


  • EAHP Statement 2: Selection, Procurement and Distribution.

  • Contributors DLV and AM developed the tool and wrote the manuscript. PP and AP contributed in the bibliographic research and writing of the manuscript. MEF, NM, DM and PH revised the manuscript.

  • Funding The authors have not declared a specific grant for this research from any funding agency in the public, commercial or not-for-profit sectors.

  • Competing interests None declared.

  • Provenance and peer review Not commissioned; externally peer reviewed.

  • Supplemental material This content has been supplied by the author(s). It has not been vetted by BMJ Publishing Group Limited (BMJ) and may not have been peer-reviewed. Any opinions or recommendations discussed are solely those of the author(s) and are not endorsed by BMJ. BMJ disclaims all liability and responsibility arising from any reliance placed on the content. Where the content includes any translated material, BMJ does not warrant the accuracy and reliability of the translations (including but not limited to local regulations, clinical guidelines, terminology, drug names and drug dosages), and is not responsible for any error and/or omissions arising from translation and adaptation or otherwise.

Request Permissions

If you wish to reuse any or all of this article please use the link below which will take you to the Copyright Clearance Center’s RightsLink service. You will be able to get a quick price and instant permission to reuse the content in many different ways.