Mathematical model for the novel coronavirus (2019-nCOV) with clinical data using fractional operator

Abstract

Coronavirus infection (COVID-19) is a considerably dangerous disease with a high demise rate around the world. There is no known vaccination or medicine until our time because the unknown aspects of the virus are more significant than our theoretical and experimental knowledge. One of the most effective strategies for comprehending and controlling the spread of this epidemic is to model it using a powerful mathematical model. However, mathematical modeling with a fractional operator can provide explanations for the disease's possibility and severity. Accordingly, basic information will be provided to identify the kind of measure and intrusion that will be required to control the disease's progress. In this study, we propose using a fractional-order SEIARPQ model with the Caputo sense to model the coronavirus (COVID-19) pandemic, which has never been done before in the literature. The stability analysis, existence, uniqueness theorems, and numerical solutions of such a model are displayed. All results were numerically simulated using MATLAB programming. The current study supports the applicability and influence of fractional operators on real-world problems.

Keywords: Adams–Bashforth–Moulton method; COVID‐19 disease; existence theorems; numerical simulations; stability analysis; uniqueness theorems.

FIGURE 1

Comparison of solution behavior between infected data and infected population $I(t)$ with different fractional derivative order σ and constant λ ₃

FIGURE 2

Comparison of solution behavior between dead data and dead population $P(t)$ with different fractional derivative order σ and constant λ ₃

FIGURE 3

Solution behavior with time history of susceptible population $S(t)$ and exposed population $E(t)$

FIGURE 4

Solution behavior with time history of infected population $I(t)$ and recovered–exposed population $A(t)$

FIGURE 5

Solution behavior with time history of recovered population $R(t)$ and deceased population $P(t)$

FIGURE 6

Solution behavior with time history of quarantine population $Q(t)$

FIGURE 7

The impact of changing the average of parameter λ ₁ and parameter λ ₂ on all populace stages after some time where the fractional derivative order σ = 0.85

FIGURE 8

The impact of changing the average of parameter β ₁ and parameter β ₂ on all populace stages after some time where the fractional derivative order σ = 0.85

FIGURE 9

The impact of changing the average of parameter α ₁ and parameter α ₂ on all populace stages after some time where the fractional derivative order σ = 0.85

FIGURE 10

The impact of changing the home quarantine rate of $S(t)$ (parameter λ ₃) on all populace stages after some time where the fractional derivative order σ = 0.85