ABSTRACT
Throughout the last few decades, fractional-order models have been used in many fields of science and engineering, applied mathematics, and biotechnology. Fractional-order differential equations are beneficial for incorporating memory and hereditary properties into systems. Our paper proposes an asymptomatic COVID-19 model with three delay terms τ1,τ2,τ3 and fractional-order α. Multiple constant time delays are included in the model to account for the latency of infection in a vector. We study the necessary and sufficient criteria for stability of steady states and Hopf bifurcations based on the three constant time-delays, τ1, τ2, and τ3. Hopf bifurcation occurs in the addressed model at the estimated bifurcation points τ10, τ20, τ30, and τ10*. The numerical simulations fit to real observations proving the effectiveness of the theoretical results. Fractional-order and time-delays successfully enhance the dynamics and strengthen the stability condition of the asymptomatic COVID-19 model. © 2023 World Scientific Publishing Company.
ABSTRACT
In this paper, we develop a fractional-order differential model for the dynamics of immune responses to SARS-CoV-2 viral load in one host. In the model, a fractional-order derivative is incorporated to represent the effects of temporal long-run memory on immune cells and tissues for any age group of patients. The population of cytotoxic T cells (CD8+), natural killer (NK) cells, and infected viruses is unknown in this model. Some interesting sufficient conditions that ensure the asymptotic stability of the steady states are obtained. This model indicates some complex phenomena in COVID-19 such as “immune exhaustion” and “long COVID.” Sensitivity analysis is also investigated for model parameters to determine the parameters that are effective in disease control and future treatment as well as vaccine design. The model is verified with clinical and experimental data of 5 patients with COVID-19.
ABSTRACT
In this paper, we study the dynamics of COVID-19 in the UAE with an extended SEIR epidemic model with vaccination, time-delays, and random noise. The stationary ergodic distribution of positive solutions is examined, in which the solution fluctuates around the equilibrium of the deterministic case, causing the disease to persist stochastically. It is possible to attain infection-free status (extinction) in some situations, in which diseases die out exponentially and with a probability of one. The numerical simulations and fit to real observations prove the effectiveness of the theoretical results. Combining stochastic perturbations with time-delays enhances the dynamics of the model, and white noise intensity is an important part of the treatment of infectious diseases.
ABSTRACT
In this paper, we provide a fractional-order delay differential model for coronavirus (CoV) infection to give us best understand what causes the intensity of symptoms and illness of contaminated lung and respiratory system. A fractional-order and time-delays are incorporated in the model to naturally represent the effects of both long-run and short-run memory in the dynamics of cells and tissues of immune system. Some interesting sufficient conditions that ensure the asymptotic stability of the steady states are obtained. Sensitivity analyses such as sensitivity to variations in the rate of interferon, rate of innate immunity cells, rate of adaptive immunity cells, and variation in pathogen virulence are investigated to provide insight into the role of each and most effective parameter of the model. This consideration may deliver experiences into respiratory infections and define the foremost compelling parameters for treatment. © 2021. NSP Natural Sciences Publishing Cor
ABSTRACT
Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of coronavirus COVID-19 to humans. In this chapter, we use a stochastic epidemic SIRC model, with cross-immune class and time-delay in transmission terms, for the spread of COVID-19. We analyze the model and prove the existence and uniqueness of positive global solution. We deduce the basic reproduction number R0s for the stochastic model which is smaller than R0 of the corresponding deterministic model. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov function, and conditions for the extinction of the disease are obtained. We provide a stochastic SIRC model with time delay in Sect. 13.2. In Sect. 13.3, we study the existence and uniqueness of a global positive solution for the stochastic delayed SIRC model. In Sects. 13.4 and 13.5, a stationary distribution and extinction analysis of the underlying model are investigated. Some virtual numerical examples are presented in Sect. 13.6. Finally, concluding remarks are provided in Sect. 13.7. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
ABSTRACT
Public health science is increasingly focusing on understanding how COVID-19 spreads among humans. For the dynamics of COVID-19, we propose a stochastic epidemic model, with time-delays, Susceptible-Infected-Asymptomatic-Quarantined-Recovered (SIAQR). One global positive solution exists with probability one in the model. As a threshold condition of persistence and existence of an ergodic stationary distribution, we deduce a generalized stochastic threshold R 0 s < R 0 . To estimate the percentages of people who must be vaccinated to achieve herd immunity, least-squares approaches were used to estimate R 0 from real observations in the UAE. Our results suggest that when R 0 > 1 , a proportion max ( 1 - 1 / R 0 ) of the population needs to be immunized/vaccinated during the pandemic wave. Numerical simulations show that the proposed stochastic delay differential model is consistent with the physical sensitivity and fluctuation of the real observations.
ABSTRACT
Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of the new strain coronavirus COVID-19 to humans. In this paper, we use a stochastic epidemic SIRC model, with cross-immune class and time-delay in transmission terms, for the spread of COVID-19. We analyze the model and prove the existence and uniqueness of positive global solution. We deduce the basic reproduction number R 0 s for the stochastic model which is smaller than R 0 of the corresponding deterministic model. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov function, and conditions for the extinction of the disease are obtained. Our findings show that white noise plays an important part in controlling the spread of the disease; When the white noise is relatively large, the infectious diseases will become extinct; Re-infection and periodic outbreaks can occur due to the existence of feedback time-delay (or memory) in the transmission terms.