A stochastic analysis for a triple delayed SIQR epidemic model with vaccination and elimination strategies
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A stochastic analysis for a triple delayed SIQR epidemic model with vaccination and elimination strategies Mohamed El Fatini1
· Roger Pettersson2 · Idriss Sekkak1 · Regragui Taki3
Received: 21 January 2020 / Revised: 09 May 2020 / Accepted: 08 June 2020 © Korean Society for Informatics and Computational Applied Mathematics 2020
Abstract In this paper, a delayed SIQR epidemic model with vaccination and elimination hybrid strategies is analysed under a white noise perturbation. We prove the existence and the uniqueness of a positive solution. Afterwards, we establish a stochastic threshold Rs in order to study the extinction and persistence in mean of the stochastic epidemic system. Then we investigate the existence of a stationary distribution for the delayed stochastic model. Finally, some numerical simulations are presented to support our theoretical results. Keywords Extinction · Persistence in mean · Delay · White noise · Epidemic model · Stationary distribution Mathematics Subject Classification 92B05 · 60G51 · 60H30 · 60G57
1 Introduction Governments has always made the public health policy as a priority and adopted decisions, plans and actions to save human lives from deadly infectious diseases. For
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Mohamed El Fatini [email protected] Roger Pettersson [email protected] Idriss Sekkak [email protected] Regragui Taki [email protected]
1
Département de Mathématiques, Faculté des Sciences, Université Ibn Tofail, BP 133, Kénitra, Morocco
2
Department of Mathematics, Linnaeus University, 351 95 Växjö, Sweden
3
Chouaib Doukkali University EST Sidi Bennour, El Jadida, Morocco
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M. E. Fatini et al.
this matter, computational biologists study the dynamics of epidemics to prevent and control the infection from spreading in the population [1,2,6]. Historically, in the 14th century, the authorities of the city of Venice have installed a measure of isolation to enter and exit its ports, where every crew in every ship was inspected, once the whole personal have no symptoms, then they could be cleared out to land. This idea is adopted as a major measure to prevent infectious diseases such as Ebola and Malaria from spreading. Nowadays, every well equipped hospital has a number of rooms and halls dedicated for the isolation of infected individuals. In addition, the authorities can put their people under quarantine. This decision has a significant impact on the basic reproduction number, which leads us to the extinction of the infectious disease. Recently, the quarantine measure has proven to be efficient in the extinction of the COVID19 disease in China, which let many countries to adopt this strategy in absence of vaccine or a cure to the new Corona virus. In order to understand the effect of quarantine on the behavior of the epidemics, Heathcote [13] proposed a model with quarantine to describe isolated individuals in the compartmental model followed by other papers such as [5,27]. On the other hand, a new type of delayed stochastic models are proposed to describe the role of time delay in re
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