Abstract
In this paper, we present a new approach for Covid-19 Pandemic spreading simulation based on fuzzy multi agents. The agent parameters consider distribution of the population according to age, and the index of socio-economic fragility. Medical knowledge affirms that the COVID-19 main risk factors are age and obesity. The worst medical situation is caused by the combination of these two risk factors which in almost 99% of cases finish in ICU. The appearance of virus variants is another aspect parameter by our simulation through a simplified modeling of the contagiousness. Using real data from people from West Indies (Guadeloupe, F.W.I.), we modeled the infection rate of the risk population, if neither vaccination nor barrier gestures are respected. The results show that hospital capacities are exceeded, and the number of deaths exceeds 2% of the infected population, which is close to the reality.
Keywords: MAS: Multi Agent-based System; ICU: Intensive Care Units
Introduction
COVID-19 is an unprecedented pandemic outbreak by the high rate of infection and the global spreading. Besides coping with possible physical illness, a pandemic outbreak can cause employees anxiety and fear. Neither country was prepared to face this outbreak, especially for low and middle-income countries the number of ICU beds are insufficient to combat Covid-19 pandemic [1]. Mathematical and numerical simulation models could be a helpful decision tool to manage the crisis by predicting the number of infections [2]. Many of these tools consider analytical-based models, using for example, the SIR epidemic differential equations [3-6] or linear regression [7]. Using deep learning [8] or fuzzy neural networks [9] is possible to have a data-driven approach. The effects of the lockdown during the pandemic have been analyzed by estimating the number of deaths [10,11]. In this paper we present a Multi Agent-based System (MAS), which incorporates several parameters as risk factors. Elder age is the main risk factor for the severe or critical case of infected [12-14]; and obesity (measured by BMI) seems to be the second main risk factor [15-17]. In before the cited articles the risk factors are introduced in the form of probabilities driven by medical and statistical knowledge. In comparison, in this article, we are interested in the number of critical cases due to the risk factors, by handling the uncertainty using fuzzy logic (Fuzzy Multi-Agent Simulation). This approach seems to be appropriate in a context where many countries do not have enough Intensive Care Units (ICU) to manage the crisis [18].
Fuzzy Multi-Agent Simulation
We adapted the model, implemented in NetLogo platform, epiDEM Travel and Control [19]. In our model the agents have two main characteristics: age and obesity. To do that the population has been classified in 3 fuzzy groups (mild, severe, critical) according to their age and their body mass index BMI (Figure 1). The elder age is the main risk factor for the severe or critical case and obesity is the second main risk factor. According to demographic data, the population is divided into three age groups: young people, adults, and elderly. The severity of COVID-19 disease roughly corresponds to these three groups [20,21]. Statistically, the covid-infected young people have a mild form of the disease, adults have a more serious form and correspond to the group of severe patients, and elderly people represent most critical cases. Obviously, this classification does not consider comorbidities. We introduced in our model the variants of this virus, delta, which is at least 50% more contagious than the “classic” COVID-19 [22,23]. Therefore, we defined in our MAS simulation a zone of transmissibility. The transmissibility zone is represented by a bigger centroid around the infected agent than in the case of a non-infected agent (Figure 2).
Results
The fuzzy MAS simulation presented in this article supposed a missing situation of social distancing or barrier gestures. Therefore, the agents can circulate freely transmitting the disease to everyone with whom it comes into contact. Regarding the characteristics of COVID-19, the parameters are adapted to be directly linked to the disease. Average-recovery-time representing the average duration of the disease has been set to 25. Figure 3 displays a comparison of real number of infected people per day (orange curve) and simulated number via our method (blue curve). We know that the lockdown started the day 19 and our simulation shows what it could happened without lockdown [24-28].
Conclusion
In this paper, we presented a simulation model of COVID-19 spreading in an insular context, considering a non-respect of social distancing and barrier gestures. The model of the spread of the COVID-19 pandemic used a MAS and was based on demographic data and medical knowledge based on two risk factors: age and obesity. These two aggravating risk factors were defined as parameters of agents by using fuzzy logic: fuzzy sets and aggregation fuzzy operators. Further the agents will be defined by considering the vaccination as barrier gesture. In addition, new variant of the virus more contagious will be modelled in this Fuzzy-MAS simulator.
Acknowledgment
The authors of this article would like to thank the Agence Régionale de Santé de Guadeloupe (Regional Health Agency of Guadeloupe) and specially Service Analyse des Données de Santé de la Direction d’Evaluation et de Réponse aux Besoins des Populations (Health Data Analysis Department of the Department of Assessment and Response to Populations’ Needs) for the provision of epidemiological data (incidence rate).
References
- Ma X, Vervoort D (2020) Critical care capacity during the covid-19 pandemic: Global availability of intensive care beds. Journal of Critical Care 58: 96-97.
- Caussy C, François Pattou, Florent Wallet, Chantal Simon, Sarah Chalopin, et al. (2020) Prevalence of obesity among adult inpatients with covid-19 in france. The Lancet Diabetes & Endocrinology 8(7): 562-564.
- Cai Q, Fengjuan Chen, Tao Wang, Fang Luo, Xiaohui Liu, et al. (2020) Obesity and covid-19 severity in a designated hospital in shenzhen, china. Diabetes Care 43(7): 1392-1398.
- Roda WC, Varughese MB, Han D, Li MYR (2020) Why is it difficult to accurately predict the covid-19 epidemic? Infectious Disease Modelling 5: 271-281.
- Giordano G, Blanchini F, Bruno R, Patrizio Colaneri, Alessandro Di Filippo, et al. (2020) Modelling the covid-19 epidemic and implementation of population-wide interventions in italy. Nature Medicine 26: 855-860.
- Jagodnik KM, Ray F, Giorgi FM, Lachmann A (2020) Correcting under-reported covid-19 case numbers: estimating the true scale of the pandemic. Med Rxiv preprint.
- Roques L, Klein EK, Papaïx J, Sara A, Soubeyrand S (2020) Using early data to estimate the actual infection fatality ratio from covid-19 in france. Biology 9(5): 97.
- Chimmula VKR, Zhang L (2020) Time series forecasting of covid-19 transmission in canada using lstm network. Chaos, Solitons and Fractals 135: 109864.
- Al qaness MAA, Ewees AA, Fan H, Abualigah L, Elaziz MA (2020) Marine predators algorithm for forecasting confirmed cases of covid-19 in italy, usa, iran and korea. International Journal of Environmental Research and Public Health 17(10): 3520.
- Shuja J, Alanazi E, Alasmary W, Alashaikh A (2020) Covid-19 open source data sets: a comprehensive survey. Applied Intelligence 21: 1-30.
- Silva P, Batista P, Lima H, Alves M, Guimaraes F, et al. (2020) Covid-abs: An agent-based model of covid-19 epidemic to simulate health and economic effects of social distancing interventions. Chaos, Solitons and Fractals 139: 110088.
- Dong Ensheng, Du Hongru, Gardner Lauren (2020) An interactive web based dashboard to track covid-19 in real time. The Lancet Infectious Diseases 20(5): 533-534.
- Tatapudi H, Das R, Das T (2020) Impact assessment of full and partial stay-at-home orders, face mask usage, and contact tracing: An agent-based simulation study of covid-19 for an urban region. Global Epidemiology 2: 100036.
- Cuevas E (2020) An agent-based model to evaluate the covid-19 transmission risks in facilities. Computers in Biology and Medicine 121: 103827.
- Pettit NN, Erica L Mac Kenzie, Jessica P Ridgway, Kenneth Pursell, Daniel Ash, et al. (2020) Obesity is associated with increased risk for mortality among hospitalized patients with covid-19. Obesity 28(10): 1806-1810.
- Kass DA, Duggal P, Cingolani O (2020) Obesity could shift severe covid-19 disease to younger ages. The Lancet 395(10236): 1544-1545.
- Banerjee A, Laura Pasea, Steve Harris, Arturo Gonzalez Izquierdo, Ana Torralbo, et al. (2020) Estimating excess 1-year mortality associated with the covid-19 pandemic according to underlying conditions and age: a population-based cohort study. The Lancet 395(10238): 1715-1725.
- Bouchnita A, Jebrane A (2020) A hybrid multi-scale model of covid-19 transmission dynamics to assess the potential of non-pharmaceutical interventions. Chaos, Solitons and Fractals 138: 109941.
- Yang C, Wilensky U (2011) Netlogo epidem travel and control model.
- Ali M, Shah STH, Lmran M, Khan A (2020) The role of asymptomatic class, quarantine and isolation in the transmission of covid-19, journal of biological dynamics. Journal of Biological Dynamics 14(1): 389-408.
- Davies N, Abbott S, Barnard R, Jarvis C, Kucharski A, et al. (2021) Estimated transmissibility and impact of sars-cov-2 lineage b. 1.1. 7 in england. Science 372(6538).
- Vyklyuk Y, Manylich M, Skoda M, Radovanovic MM, Petrovic MD (2021) Modeling and analysis of different scenarios for the spread of covid-19 by using the modified multi-agent systems – evidence from the selected countries. Results in Physics 20: 103662.
- Smith MC, Broniatowski DA (2016) Modeling influenza by modulating flu awareness. In: K Xu, D Reitter, D Lee, N Osgood (Eds.)., Social, Cultural, and Behavioral Modeling. SBP-BRiMS, Lecture Notes in Computer Science, vol. 9708, Washington, DC, USA.
- Wang Z, Zhao H, Lai Z, Qin X (2016) Improved sir epidem model of social network marketing effectiveness and experimental simulation. Xitong Gongcheng Lilun yu Shijian/System Engineering Theory and Practice 36(8): 2024-2034.
- Yang C, Wilensky U (2011) Netlogo epidem basic.
- McLennan AK, Ulijaszek SJ (2015) Obesity emergence in the pacific islands: why understanding colonial history and social change is important. Public Health Nutrition 18(8).
- Miyahira SA, Araujo E (2008) Fuzzy obesity index for obesity treatment and surgical indication. In 2008 IEEE International Conference on Fuzzy Systems.
- Miyahira SA, De Azevedo JL, Moreira Coutinho, Araujo E (2011) Fuzzy obesity index (mafoi) for obesity evaluation and bariatric surgery indication. Journal of Translational Medicine 9: 134.