Razi Journal of Medical Sciences

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Infectious diseases significantly distress the physical and mental health as well as economic conditions of the societies. Understanding how a virus spreads, especially the dynamics of an epidemic is critical in order to make proper decisions and take proper measures. System dynamics approach is a scientific and appropriate method for modeling and studying the behavior of epidemics. There are many studies on system dynamics modeling of infectious diseases in the literature. However, in case of Coronavirus, there are few extensive studies on the behavior of this outbreak especially calibrated to the actual situation in a specific region. In this study, we develop an SEIR model of Covid-19 epidemic in Iran that is actually calibrated to the real data. More Importantly Most of the previous studies are focused only on projecting the number of infected people and deaths. In this study, in addition to projecting the simulation results under different scenarios, sensitivity analysis of the influential parameters are performed. Also studying the effect of quarantine measure for patients on the results and isolating the susceptible population as two different yet indirectly connected sections is not largely considered in previous studies. The developed model in this study includes Susceptible and Exposed population, identification and quarantine of infected individuals, number of Recovered cases and Deaths. The effect of asymptomatic infected people has been included as well. The quarantine itself has been expressed by several sub-variables such as required time for a person to be quarantined, the percentage of the infected who are quarantined (testing capabilities) and the efficiency of the process. There is a same decomposition for other variables such as Isolation of susceptible population and contact rate. Contact rate is defined by sub-variables: media impact, initial contact rate and a slope which determines the increase in contact rate based on the population density.  The media Impact also starts at a minimum level and gradually reaches its maximum. This definition demonstrates the gradual growth in public awareness which improves the hygiene and social distancing commitment among the individuals. Isolation process is highly depended on economic pressure. As isolation period last longer, the more resources are required to keep people fed and healthy in isolation. A simple variable to illustrate the economic pressure is defined which based on an assumed function table limits the isolation duration and percentage of the healthy people who remain isolated. Although this relationship requires more research to indicates the economic impact more accurately it is still useful and enough in order to demonstrate a limitation for isolation process.  After developing the model, it is validated through applying it for a previous real epidemic situation of H1N1 and the results are valid. Also, running the model in extreme conditions returns the expected results. It is assumed that infectivity of the virus is constant (the virus does not mutate during the period of the study) so that through a calibration process it can be obtained based on other parameters. The asymptomatic rate (the percent of people who get exposed to the infection but do not develop any symptoms) and the incubation period (average required time for a person from getting exposed to infection until developing the symptoms) are also assumed constant. After validating the model, it is used to study the spread of Covid-19 in Iran and is calibrated to official data. This stage generates a basic simulation in which the results for target variables produce real data pattern and numbers. As the official data are usually lower than the real cases, a variable to introduce the official data is considered. The official data is a portion of the real data and this portion is a given value for the model. Having the basic calibrated model, developing scenarios and performing sensitivity analysis is the next stage. In particular, we study the impacts of people isolation as well as media, quarantine rate and other given variables on spread of the virus. We investigate and advise the required conditions for controlling the spread of the disease mainly based on the testing capabilities and quarantine of the infected people and contact rate. This study includes several sensitivity analysis for important target variables such as number of daily deaths, total deaths, daily new infected, total infected, required hospital beds and ICU rooms. This analysis is based on changes in entry factors such as quarantine of patients, contact rate, media impact, asymptomatic rate, averaged required time for quarantine, recovery time, isolation of susceptible population and quarantine efficiency. The results show that total number of death and infected are highly sensitive to changes in two key factors: Quarantine of patients and contact rate. The sensitivity of mentioned target variables to isolation of susceptible population, however, is considerably less than those two key factors. We developed several scenarios with different values of isolation rate while other variables are constant. The results indicate that in absence of either reliable quarantine measure or desired contact rate level, isolating the susceptible population will only lead to continues oscillation in the target variables unless the isolation remains for a very long time. However, in scenarios where the quarantine rate or contact rate or both are below the desired level the sensitivity of deaths or infected to isolation rate is higher. Therefore, Isolation could help in providing time for applying proper quarantine measures or to reduce contact rate to desired level. These results indicate the priority level of launching the controlling measures. Also, through performing the sensitivity analysis a minimum level of quarantine rate is obtained. The results show a required contact rate level as well. In fact for both contact rate and quarantine, a lower level than the minimum level will cause the epidemic to get out of control. Another important outcome of the study is an important guidance about the contact rate controlling policy. The results show that the contact rate should be sustained at a desired level through media and public awareness. Most models link the contact rate to the daily deaths or total deaths. We developed two scenarios where in the first one contact rate is controlled by policy making and media and in the other one it is defined based on the feedback of number of deaths. The results show that in the latter the outbreak goes out of control and takes a very long time while in the first scenario it will be controlled in an acceptable time. Therefore, although this is true that practically feedbacks from deaths influences the contact rate, the model shows that if this behavior remains uncontrolled, the epidemic will not be controlled. In a third combined scenario the results show by securing the required contact rate through public awareness and media, feedbacks from deaths could be helpful for policy makers to control the outbreak even faster. Therefore, through performing several sensitivity analysis and developing different scenarios, controlling conditions for the epidemic are obtained. There are two main requirements: first a proper testing and quarantine practice in which more than 87 percent of infected are identified and quarantined within a day and a quarantine efficiency level more than 95 percent. Secondly, contact rate must be level downed and sustained at least to the desired level through media and policy making. This is especially important because reaching and sustaining these conditions will suppress the disease and prevent the next waves of the outbreak.

Keywords: Coronavirus, Covid-19, System Dynamics, Contorl Measures, Epidemics

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