key: cord-0852065-viwochvv authors: Sanchez-Taltavull, Daniel; Candinas, Daniel; Roldan, Edgar; Beldi, Guido title: Modelling strategies to organize healthcare workforce during pandemics: application to COVID-19 date: 2020-03-27 journal: nan DOI: 10.1101/2020.03.23.20041863 sha: cd71d794b72ed6273e6fde52fc28faeea50b068f doc_id: 852065 cord_uid: viwochvv Protection of healthcare workforce is of paramount relevance for the care of infected and non-infected patients in the setting of a pandemic such as coronavirus disease 2019 (COVID-19). Healthcare workers are at increased risk to become infected because of contact to infected patients, infected co-workers and their community outside the hospital. The ideal organisational strategy to protect the healthcare workforce in a situation in which social distancing cannot be maintained at the workplace remains to be determined. In this study, we have mathematically modelled strategies for the employment of hospital workforce with the goal to simulate health and productivity of the workers. Therefore, deterministic models were extended to account for stochastic influences potentially occurring in rather small populations. The models were also designed to determine if desynchronization of medical teams by dichotomizing the workers may protect the workforce. Our studies model workforce productivity depending on the infection rate, the presence of reinfection and the efficiency of home office. As an application example, we apply our theory to the case of coronavirus disease 2019 (COVID-19). The results of the models reveal that a desynchronization strategy in which two medical teams work alternating for 7 days reduces the infection rate of the healthcare workforce. In case of immunity to the infectious agent this affect is mainly relevant at early stages of the pandemic. This effect is independent on infection rates and increases the overall workforce productivity under certain situations. In this short report, we perform computer simulations of biophysical models of coronavirus epidemics of COVID-19 in a healthcare working team, and discuss the efficiency of different work strategies during the viral outbreak. Different types of mathematical models have been used to study epidemiology. In the classical Susceptible Infectious Recovered (SIR) model, a susceptible patient (S) can be infected (I), and the infected person can recover (R), without the risk of reinfection. Variants of this model, are the Susceptible Infectious Susceptible (SIS) and Susceptible Exposed Infectious Recovered (SEIR) models (3) . The SEIR model in which the recovered patients are susceptible again, has already been used for modeling purposes during the COVID-19 outbreak (4) . Also in the context of the COVID19, SEIR models have been used to model control of expansion and have been extended to include age and asymptomatic cases (5, 6) . Another extension of SEIR models that have been presented in this context consists on including persons in quarantine (QSEIR model) (7, 8) . Here, we put forward SIS and SIR models by dividing the infectious persons into a latent and infected state in order to account for the potentially long asymptomatic phase of COVID-19. Next, have developed two time-dependent compartmental models with and without reinfection by adapting the SAIR model of (9-11). Next, we add a variable to account for work W and build two mathematical models for To investigate the possible workforce organizations, we use ODE describing the dynamics of the models including time-dependent parameters in which the rate change based on their location, that is, inhospital compared with home office. The rest of the report is organized as follows. We study and compare organizational strategies on the hospital workforce in the situation of a pandemic on productivity in the absence of reinfection and with reinfection (section 2), and present the results of simulations (section 3). Finally, our results are summarized and discussed (section 4). . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint Sketch of the models Figure 1 shows the SLIW and SLIWR models with compartmentalization that we describe in detail in Section 2.1.2 and Section 2.2.2, respectively. In our models, we consider that a group of healthcare workers are divided in two teams of equal size. At any time, one team is at the workplace whereas the other team stays at home. A dichotomous work switch is implemented as follows ( Figure 1A ): during the first week Team 1 stays at the workplace and Team 2 at home; during the second week Team 1 stays at home and Team 2 at the workplace; next the teams continue alternating their location at the end of each week. When at the workplace, each healthy susceptible worker can become latent at a timedependent infection rate that is larger than when staying at home. Latent workers develop the infection at the workplace, at the same rate than at home. Infection of a susceptible by a latent worker can only occur in the workplace. We also assume that infected workers recover at the same rate at the workplace than at home, becoming again susceptible (SLIW) or fully recovered and immune (SLIRW). is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 27, 2020. where is the infection rate, resulting into an infected in a latent state. ( ) is a function accounting for the number of people infected in the city, which we assume is growing in time. is the infection rate when the person is infected by a co-worker, is the activation rate of the sickness, in which a patient in a latent state starts presenting symptoms. is the recovery rate, where an infected patient recovers and becomes healthy. is a function that accounts for the work output of the workers, for simplicity we assume its growth is proportional to the number of available workers. For simplicity, we consider the death rate negligible and we do not consider recoveries coming from latent patients. In our simulations reported below, we set the initial condition to S(0)=300, L(0)=0, I(0)=0, and W(0)=0, thereby representing a large unit with 300 workers. . CC-BY 4.0 International license It is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in (which was not certified by peer review) preprint The copyright holder for this this version posted March 27, 2020. . https://doi.org/10.1101/2020.03.23.20041863 doi: medRxiv preprint In order to study the desynchronization strategy, in which the workers are divided in half, one group works for one week in the hospital while the other works at home, and the week after they change their functions. In doing so, we model it as two groups of healthy persons susceptible to be infected, 1 and 2 , two groups of infected persons in a latent state, 1 and 2 , and two groups of infected persons presenting symptoms, 1 and 2 . The dynamics of each population are described by the following system of ordinary differential equations for the first group and for the second group. The rate of change of the work output obeys For this model, we use the same parameters than in the previous model, except for and (with j=1,2). Group 1 is one week at home and one week at the hospital, and Group 2 the opposite. Therefore we simulate our model for the first seven days with 2 = 0, 2 = 0.1 1 , because the two groups are not in contact with the co-workers, and we assume that the probability to become infected is higher when working in the hospital. For the following seven days, we introduce a switch of the group's location, by exchanging their parameter values. This procedure is repeated every 7 days. We assume that the productivity decreases during home office, therefore we choose A(t)=1 and B(t)