A fractional-order model for CoViD-19 dynamics with reinfection and the importance of quarantine

Abstract

Coronavirus disease 2019 (CoViD-19) is an infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Among many symptoms, cough, fever and tiredness are the most common. People over 60 years old and with associated comorbidities are most likely to develop a worsening health condition. This paper proposes a non-integer order model to describe the dynamics of CoViD-19 in a standard population. The model incorporates the reinfection rate in the individuals recovered from the disease. Numerical simulations are performed for different values of the order of the fractional derivative and of reinfection rate. The results are discussed from a biological point of view.

Dynamics of SARS-CoV-2 infection for distinct immune functions and coexistence space of SARS-CoV-2 endemic and cytotoxic T lymphocytes response-free equilibria

“…The method we use, is a method that uses the same techniques as [37] whose standard error is given by the expression max j |y(t j ) − y j | = O(h 2 ), where h = max j (t j+1 − t j ) and t j ∈ [t 0 , t 0 + t ⋆ ] for some fixed t ⋆ > 0. The FracPECE method was already used by other authors in previous studies, such as [14,38].…”

“…These models allow us to draw a lot of conclusions about how we should act in situations related to epidemics in different countries around the world. For example, these mathematical analysis could help in decision making by government leaders in combating possible economic losses that come from pandemic disasters, particularly due to SARS-CoV-2 [14].…”

“…It is becoming increasingly important to try to understand how the immune system reacts to SARS-CoV-2 in order to find alternatives while non-priority, young and economically disadvantaged people are not vaccinated [2,12,13]. Many mathematicians have proposed several models describing the dynamics of CoViD-19 in the population [14,15,16,17,18]. However, as far as mathematical modelling is concerned, existing studies on dynamical systems involving SARS-CoV-2 and the immune system have not yet been very thorough.…”

A streamlined numerical method to treat fractional nonlinear terminal value problems with multiple delays appearing in biomathematics

“… 2020 ). The predictor-corrector regulation method arising from Adams-Bashford-Moulton type is utilized for the numerical solution of a fractional order CoViD-19 virus model expressing the dynamics of reinfection and the importance of quarantine (Maurício de Carvalho and Moreira-Pinto 2021 ). The optimal treatment problem is solved via the forward-backward iterative method for the combined antiretroviral drug therapy in an HIV infection model (Nath et al.…”

Study of a Nonlinear System of Fractional Differential Equations with Deviated Arguments Via Adomian Decomposition Method

“…Fractional calculus has been included in recent studies on CoViD-19 [3,17,20]. Many studies have been conducted in the field of mathematics, and it has been shown that differential equations using fractional operators are effective in demonstrating epidemic models linked to many infectious illnesses [7,12].…”