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Vol. 24. Issue 4.
Pages 278-290 (October - December 2023)
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Vol. 24. Issue 4.
Pages 278-290 (October - December 2023)
Original
Impact of vaccination on the entire population and dose-response relation of COVID-19
Impacto de la vacunación en toda la población y relación dosis-respuesta del COVID-19
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144
Abdul Malek
Corresponding author
malekbio@gmail.com

Corresponding author.
, Ashabul Hoque
Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh
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Tables (4)
Table 1. Average transmission rate (β) death rate (μ)and vaccination rate (ϵ) of COVID-19 per day till May 7, 2021of several countries.
Table 2. Definitions and under suitable selection of the model parameters.
Table 3. Effectivity of the several vaccines of COVID-19.
Table 4. Total population, total vaccinated and population density till May 7, 2021.
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Abstract
Objective

The objective of this study is to develop a mathematical model for the COVID-19 pandemic including vaccination, the transmissibility of the virus-pathogen dose-response relationship, vaccine efficiency, and vaccination rate.

Methods

The Runge-Kutta (RK-45) method was applied to solve the proposed model with MATLAB code and the calculated results show the dynamics of the individuals in each compartment. The data of total death due to the COVID-19 pandemic in the case of the USA were collected from GitHub and the re-use of this data needs no ethical clearance. The control reproduction number was used to assess the dose-response relationship and critical vaccination coverage.

Results

We have calculated the probability of infection and the infection risk against the different exposure doses and the virus copies, respectively. The results show that the probability of infection increases with the increasing exposure dose for certain virus copies and the risk of infection decreases with the increasing of virus copies for a certain exposure dose. The results also show that the critical vaccination coverage demands increase with an increase in transmission rate and decrease with increasing vaccine efficacy.

Conclusions

It was seen that the critical vaccination coverage corresponding to an increased transmission rate rise sharply in the beginning and then reached a threshold. Moreover, the real data of the total death cases in the USA were compared with the fitted curved of the model which validated the proposed model. Vaccination against COVID-19 is essential to control the pandemic, and achieving high vaccine uptake in the population can reduce the pandemic as fast as possible.

Keywords:
Control Reproduction Number
Vaccination
Vaccine efficacy, Exposure Dose
Virus Copies
Vaccination Coverage
Resumen
Objetivo

El objetivo de este estudio es desarrollar un modelo matemático para la pandemia de COVID-19 que incluya la vacunación, la transmisibilidad de la relación dosis-respuesta virus-patógeno, la eficacia de la vacuna y la tasa de vacunación.

Métodos

Se aplicó el método de Runge-Kutta (RK-45) para resolver el modelo propuesto con código MATLAB y los resultados calculados muestran la dinámica de los individuos en cada compartimento. Los datos de muerte total por la pandemia de COVID-19 en el caso de EE. UU. se recopilaron de GitHub y la reutilización de estos datos no necesita autorización ética. El número de reproducción de control se utilizó para evaluar la relación dosis-respuesta y la cobertura de vacunación crítica.

Resultados

Hemos calculado la probabilidad de infección y el riesgo de infección frente a las diferentes dosis de exposición y las copias del virus, respectivamente. Los resultados muestran que la probabilidad de infección aumenta con el aumento de la dosis de exposición para ciertas copias del virus y el riesgo de infección disminuye con el aumento de las copias del virus para una determinada dosis de exposición. Los resultados también muestran que las demandas críticas de cobertura de vacunación aumentan con el aumento de la tasa de transmisión y disminuyen con el aumento de la eficacia de la vacuna.

Conclusiones

Se observó que las coberturas críticas de vacunación correspondientes a una mayor tasa de transmisión aumentaron bruscamente al principio y luego alcanzaron un umbral. Además, se compararon los datos reales del total de casos de muerte en EE. UU. con la curva ajustada del modelo que validó el modelo propuesto. La vacunación contra el COVID-19 es fundamental para controlar la pandemia, y lograr una alta captación de vacunas en la población puede reducir la pandemia lo más rápido posible.

Palabras clave:
Control Número de reproducción
Vacunación
Eficacia de la vacuna, dosis de exposición
Copias de virus
Cobertura de vacunación

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