Abstract:In this paper, the uncertainty quantification and sensitivity analysis of a mathematical model of the SARS-CoV-2 virus transmission dynamics with mass vaccination strategy has been carried out. More specifically, a compartmental epidemic model has been considered, in which vaccination, social distance measures, and testing of susceptible individuals have been included. Since the application of these mitigation measures entails a degree of uncertainty, the effects of the uncertainty about the application of soc… Show more
“…It is important however to note that while therapeutic measures, vaccination, and treatment are very effective in curtailing the spread of the epidemic, more control efforts are required to eradicate the disease when R 0 ( v ) > 1. Thus, continuously and concurrently applying both pharmaceutical and nonpharmaceutical public health interventions such as face mask, hand washing, and social distancing should be encouraged [ 64 ].…”
We formulate and theoretically analyze a mathematical model of COVID-19 transmission mechanism incorporating vital dynamics of the disease and two key therapeutic measures—vaccination of susceptible individuals and recovery/treatment of infected individuals. Both the disease-free and endemic equilibrium are globally asymptotically stable when the effective reproduction number
R
0
v
is, respectively, less or greater than unity. The derived critical vaccination threshold is dependent on the vaccine efficacy for disease eradication whenever
R
0
v
>
1
, even if vaccine coverage is high. Pontryagin’s maximum principle is applied to establish the existence of the optimal control problem and to derive the necessary conditions to optimally mitigate the spread of the disease. The model is fitted with cumulative daily Senegal data, with a basic reproduction number
R
0
=
1.31
at the onset of the epidemic. Simulation results suggest that despite the effectiveness of COVID-19 vaccination and treatment to mitigate the spread of COVID-19, when
R
0
v
>
1
, additional efforts such as nonpharmaceutical public health interventions should continue to be implemented. Using partial rank correlation coefficients and Latin hypercube sampling, sensitivity analysis is carried out to determine the relative importance of model parameters to disease transmission. Results shown graphically could help to inform the process of prioritizing public health intervention measures to be implemented and which model parameter to focus on in order to mitigate the spread of the disease. The effective contact rate
b
, the vaccine efficacy
ε
, the vaccination rate
v
, the fraction of exposed individuals who develop symptoms, and, respectively, the exit rates from the exposed and the asymptomatic classes
σ
and
ϕ
are the most impactful parameters.
“…It is important however to note that while therapeutic measures, vaccination, and treatment are very effective in curtailing the spread of the epidemic, more control efforts are required to eradicate the disease when R 0 ( v ) > 1. Thus, continuously and concurrently applying both pharmaceutical and nonpharmaceutical public health interventions such as face mask, hand washing, and social distancing should be encouraged [ 64 ].…”
We formulate and theoretically analyze a mathematical model of COVID-19 transmission mechanism incorporating vital dynamics of the disease and two key therapeutic measures—vaccination of susceptible individuals and recovery/treatment of infected individuals. Both the disease-free and endemic equilibrium are globally asymptotically stable when the effective reproduction number
R
0
v
is, respectively, less or greater than unity. The derived critical vaccination threshold is dependent on the vaccine efficacy for disease eradication whenever
R
0
v
>
1
, even if vaccine coverage is high. Pontryagin’s maximum principle is applied to establish the existence of the optimal control problem and to derive the necessary conditions to optimally mitigate the spread of the disease. The model is fitted with cumulative daily Senegal data, with a basic reproduction number
R
0
=
1.31
at the onset of the epidemic. Simulation results suggest that despite the effectiveness of COVID-19 vaccination and treatment to mitigate the spread of COVID-19, when
R
0
v
>
1
, additional efforts such as nonpharmaceutical public health interventions should continue to be implemented. Using partial rank correlation coefficients and Latin hypercube sampling, sensitivity analysis is carried out to determine the relative importance of model parameters to disease transmission. Results shown graphically could help to inform the process of prioritizing public health intervention measures to be implemented and which model parameter to focus on in order to mitigate the spread of the disease. The effective contact rate
b
, the vaccine efficacy
ε
, the vaccination rate
v
, the fraction of exposed individuals who develop symptoms, and, respectively, the exit rates from the exposed and the asymptomatic classes
σ
and
ϕ
are the most impactful parameters.
“…Models developed by Olivares and Stafetti (2021) showed that even a mass vaccination with one million inoculations per week during six months would only produce 15–18% of acquired immunity. That would add the proportion of immunized individuals to 46–59% of the total population that is still not sufficient for reaching herd immunity [ 24 ]. With limited vaccine availability and health care capacity, optimal protection could not be reached.…”
With a limited number of vaccines and healthcare capacity shortages, particularly in low- and middle-income countries, vaccination programs should seek the most efficient strategy to reduce the negative impact of the COVID-19 pandemics. This study aims at assessing several scenarios of delivering the vaccine to people in Indonesia. We develop a model for several scenarios of delivering vaccines: without vaccination, fair distribution, and targeted distribution to five and eight districts with the highest COVID-19 incidence in West Java, one of the most COVID-19-affected regions in Indonesia. We calculate the needs of vaccines and healthcare staff for the program, then simulate the model for the initial 4-month and one-year scenarios. A one-year vaccination program would require 232,000 inoculations per day by 4833 vaccinators. Targeted vaccine allocation based on the burden of COVID-19 cases could benefit the COVID-19 vaccination program by lowering at least 5000 active cases. The benefits would increase by improving the number of vaccines and healthcare staff. Amidst lacking available vaccines, targeted vaccine allocation based on the burden of COVID-19 cases could increase the benefit of the COVID-19 vaccination program but still requires progressive efforts to improve healthcare capacity and vaccine availability for optimal protection for people.
“…A modified SEIR compartmental model, introduced in [13] and denoted as SEIsIaQR, is used in this paper to represent the COVID-19 transmission dynamics, in which, following [16] , a vaccination term is added to the model as shown in Figure 1 . Fig.…”
Background and Objective:
Assuming the availability of a limited amount of effective COVID-19 rapid tests, the effects of various vaccination strategies on SARS-CoV-2 virus transmission are compared for different vaccination scenarios characterized by distinct limitations associated with vaccine supply and administration.
Methods:
The vaccination strategies are defined by solving optimal control problems of a compartmental epidemic model in which the daily vaccination rate and the daily testing rate for the identification and isolation of asymptomatic subjects are the control variables. Different kinds of algebraic constraints are considered, representing different vaccination scenarios in which the total amount of vaccines available during the time period under consideration is limited or the number of daily available vaccines is limited. These optimal control problems are numerically solved by means of a direct transcription technique, which allows both equality and inequality constraints to be straightforwardly included in the formulation of the optimal control problems.
Results:
Several numerical experiments are conducted, in which the objective functional to be minimized is a combination of the number of symptomatic and asymptomatic infectious subjects with the cost of vaccination of susceptible subjects and testing of asymptomatic infectious subjects. The results confirm the hypothesis that the implementation of early control measures significantly reduces the number of symptomatic infected subjects, which is a key aspect for the resilience of the healthcare system. The sensitivity analysis of the solutions to the weighting parameters of the objective functional reveals that it is possible to obtain a vaccination strategy that allows vaccination supplies to be saved while keeping the same number of symptomatic infected subjects. Furthermore, it indicates that if the vaccination plan is not supported by a sufficient rate of testing, the number of symptomatic infected subjects could increase. Finally, the sensitivity analysis shows that a significant reduction in the efficacy of the vaccines could also lead to a relevant increase in the number of symptomatic infected subjects.
Conclusions:
The numerical experiments show that the proposed approach, which is based on optimal control of compartmental epidemic models, provides healthcare systems with a suitable method for scheduling vaccination plans and testing policies to control the spread of the SARS-CoV-2 virus.
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