Stability and optimal control strategies for a novel epidemic model of COVID-19

Lü, Xing; Hui, Hong wen; Liu, Fei fei; Bai, Ya li

doi:10.1007/s11071-021-06524-x

Cited by 128 publications

(29 citation statements)

References 39 publications

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“…With the introduction of public health interventions for inhibiting COVID-19, some mathematical models begin to consider the impact of interventions to re-estimate the course of COVID-19 [ 22 – 31 ]. Zhou et al [ 32 ] use a deterministic dynamical model to study the interaction between media publicity and disease progression so as to investigate the effectiveness of media publicity in combating the COVID-19 epidemic.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling for COVID-19 with focus on intervention strategies and cost-effectiveness analysis

Deng

Zhao

2022

Nonlinear Dyn

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The realistic assessments of public health intervention strategies are of great significance to effectively combat the COVID-19 epidemic and the formation of intervention policy. In this paper, an extended COVID-19 epidemic model is devised to assess the severity of the pandemic and explore effective control strategies. The model is characterized by ordinary differential equations with seven-state variables, and it incorporates some parameters associated with the interventions (i.e., media publicity, home isolation, vaccination and face-mask wearing) to investigate the impacts of these interventions on the spread of the COVID-19 epidemic. Some dynamic behaviors of the model, such as forward and backward bifurcation, are analyzed. Specifically, we calibrate the model parameters using actual COVID-19 infected data in Brazil by Markov Chain Monte Carlo algorithm such that we can study the effects of interventions on a practical case. Through a comprehensive exploration of model design and analysis, model calibration, sensitivity analysis, implementation of optimal control problems and cost-effectiveness analysis, the rationality of our model is verified, and the effective strategies to combat the epidemic in Brazil are revealed. The results show that the asymptomatic infected individuals are the main drivers of COVID-19 transmission, and rapid detection of asymptomatic infections is critical to combat the COVID-19 epidemic in Brazil. Interestingly, the effect of the vaccination rate associated with pharmaceutical intervention on the basic reproduction number is much lower than that of non-pharmaceutical interventions (NPIs). Our study also highlights the importance of media publicity. To reduce the infected individuals, the multi-pronged NPIs have considerable positive effects on controlling the outbreak of COVID-19. The infections are significantly decreased by the early implementation of media publicity complemented with home isolation and face-mask wearing strategy. When the cost of implementation is taken into account, the early implementation of media publicity complemented with a face-mask wearing strategy can significantly mitigate the second wave of the epidemic in Brazil. These results provide some management implications for controlling COVID-19.

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Section: Introductionmentioning

confidence: 99%

Mathematical modeling for COVID-19 with focus on intervention strategies and cost-effectiveness analysis

Deng

Zhao

2022

Nonlinear Dyn

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“…The dynamics of COVID-19 has been assessed by numerous mathematical models since the starting of the pandemic [ 40 , 41 ]. In the present study, we did not incorporate the explicit dynamics of COVID-19 in the mathematical model formulation to investigate its direct influence on HIV-TB dual epidemic.…”

Section: Discussionmentioning

confidence: 99%

Impact of saturated treatments on HIV-TB dual epidemic as a consequence of COVID-19: optimal control with awareness and treatment

2022

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In this study, we propose an HIV-TB co-infection model by considering the treatment provision limitation induced by recent COVID-19 pandemic that impacts this dual epidemic immensely, assimilating the significance of educational attempts. We analyze the model and its submodels with single infections individually. We obtain the awareness-induced basic reproduction numbers and discuss the global stability of disease-free equilibrium when provision limitation is zero. We observe that the submodels exhibit forward as well as backward bifurcations under provision restriction. Further, we derive thresholds for resource limitations regulating the dynamical behavior of the systems while analyzing the stability of endemic equilibrium of the models with single infections. Sophisticated simulation approaches are implemented to discover the influences of provision-restricted medication and awareness on dual epidemic. Our findings convey the persistence of co-infection though the basic reproduction number is below unity, if the provision restriction remains uncurbed. An observable insight is that, in spite of having epidemic threshold less than unity and no limitation in TB treatment, co-infection relapses and persists in the population, when there is no awareness attempt. Numerical findings emphasize the urgent need of increased treatment accessibility and importance of awareness in the current situation. Moreover, an optimization problem incorporating treatment and awareness controls is formulated and solved to find the ideal strategy to manage HIV-TB co-epidemic that recommends to diminish the medical resource limitation to get the enormous impact in dominating the adversity caused by COVID-19.

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“…Infectious diseases have been a severe threat to human health. Many disasters in history have been due to the outbreak of contagious diseases, such as the plague pandemic, smallpox, the Black Death, AIDS, SARS [1], and recently COVID-19 [2,3]. Mathematical models are effective ways to investigate the spread of epidemics.…”

Section: Introductionmentioning

confidence: 99%

“…In the model ( 2), (1p)ηI corresponds to the infected individuals who lost immunity after recovery, while pηI represents the infected individuals who gain immunity after recovery. In particular, if p = 1 and ϕ(I) = 1, then the model ( 1) is a special case of the model (2). Define the basic reproduction number as…”

Section: Introductionmentioning

confidence: 99%

Dynamics and stationary distribution of a stochastic SIRS epidemic model with a general incidence and immunity

Chen

2022

Bound Value Probl

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Infected individuals often obtain or lose immunity after recovery in medical studies. To solve the problem, this paper proposes a stochastic SIRS epidemic model with a general incidence rate and partial immunity. Through an appropriate Lyapunov function, we obtain the existence and uniqueness of a unique globally positive solution. The disease will be extinct under the threshold criterion. We analyze the asymptotic behavior around the disease-free equilibrium of a deterministic SIRS model. By using the Khasminskii method, we prove the existence of a unique stationary distribution. Further, solutions of the stochastic model fluctuate around endemic equilibrium under certain conditions. Some numerical examples illustrate the theoretical results.

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Stability and optimal control strategies for a novel epidemic model of COVID-19

Cited by 128 publications

References 39 publications

Mathematical modeling for COVID-19 with focus on intervention strategies and cost-effectiveness analysis

Mathematical modeling for COVID-19 with focus on intervention strategies and cost-effectiveness analysis

Impact of saturated treatments on HIV-TB dual epidemic as a consequence of COVID-19: optimal control with awareness and treatment

Dynamics and stationary distribution of a stochastic SIRS epidemic model with a general incidence and immunity

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