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The Ebola virus disease (EVD) has been endemic since 1976, and the case fatality rate is extremely high. EVD is spread by infected animals, symptomatic individuals, dead bodies, and contaminated environment. In this paper, we formulate an EVD model with four transmission modes and a time delay describing the incubation period. Through dynamical analysis, we verify the importance of blocking the infection source of infected animals. We get the basic reproduction number without considering the infection source of infected animals. And, it is proven that the model has a globally attractive disease-free equilibrium when the basic reproduction number is less than unity; the disease eventually becomes endemic when the basic reproduction number is greater than unity. Taking the EVD epidemic in Sierra Leone in 2014-2016 as an example, we complete the data fitting by combining the effect of the media to obtain the unknown parameters, the basic reproduction number and its time-varying reproduction number. It is shown by parameter sensitivity analysis that the contact rate and the removal rate of infected group have the greatest influence on the prevalence of the disease. And, the disease-controlling thresholds of these two parameters are obtained. In addition, according to the existing vaccination strategy, only the inoculation ratio in high-risk areas is greater than 0.4, the effective reproduction number can be less than unity. And, the earlier the vaccination time, the greater the inoculation ratio, and the faster the disease can be controlled.

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The serial interval distribution is used to approximate the generation time distribution, an essential parameter to infer the transmissibility (${R}_t$) of an epidemic. However, serial interval distributions may change as an epidemic progresses. We examined detailed contact tracing data on laboratory-confirmed cases of COVID-19 in Hong Kong during the five waves from January 2020 to July 2022. We reconstructed the transmission pairs and estimated time-varying effective serial interval distributions and factors associated with longer or shorter intervals. Finally, we assessed the biases in estimating transmissibility using constant serial interval distributions. We found clear temporal changes in mean serial interval estimates within each epidemic wave studied and across waves, with mean serial intervals ranged from 5.5 days (95% CrI: 4.4, 6.6) to 2.7 (95% CrI: 2.2, 3.2) days. The mean serial intervals shortened or lengthened over time, which were found to be closely associated with the temporal variation in COVID-19 case profiles and public health and social measures and could lead to the biases in predicting ${R}_t$. Accounting for the impact of these factors, the time-varying quantification of serial interval distributions could lead to improved estimation of ${R}_t$, and provide additional insights into the impact of public health measures on transmission.

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Background: Countries across Europe have faced similar evolutions of SARS-CoV-2 variants of concern, including the Alpha, Delta, and Omicron variants. Materials and methods: We used data from GISAID and applied a robust, automated mathematical substitution model to study the dynamics of COVID-19 variants in Europe over a period of more than 2 years, from late 2020 to early 2023. This model identifies variant substitution patterns and distinguishes between residual and dominant behavior. We used weekly sequencing data from 19 European countries to estimate the increase in transmissibility ( Δ ß ) between consecutive SARS-CoV-2 variants. In addition, we focused on large countries with separate regional outbreaks and complex scenarios of multiple competing variants. Results: Our model accurately reproduced the observed substitution patterns between the Alpha, Delta, and Omicron major variants. We estimated the daily variant prevalence and calculated Δ ß between variants, revealing that: ( i ) Δ ß increased progressively from the Alpha to the Omicron variant; ( i i ) Δ ß showed a high degree of variability within Omicron variants; ( i i i ) a higher Δ ß was associated with a later emergence of the variant within a country; ( i v ) a higher degree of immunization of the population against previous variants was associated with a higher Δ ß for the Delta variant; ( v ) larger countries exhibited smaller Δ ß , suggesting regionally diverse outbreaks within the same country; and finally ( v i ) the model reliably captures the dynamics of competing variants, even in complex scenarios. Conclusion: The use of mathematical models allows for precise and reliable estimation of daily cases of each variant. By quantifying Δ ß , we have tracked the spread of the different variants across Europe, highlighting a robust increase in transmissibility trend from Alpha to Omicron. Additionally, we have shown that the geographical characteristics of a country, as well as the timing of new variant entrances, can explain some of the observed differences in variant substitution dynamics across countries.

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BACKGROUND: During the COVID-19 pandemic, analytics and predictive models built on regional data provided timely, accurate monitoring of epidemiological behavior, informing critical planning and decision-making for health system leaders. At Atrium Health, a large, integrated healthcare system in the southeastern United States, a team of statisticians and physicians created a comprehensive forecast and monitoring program that leveraged an array of statistical methods. METHODS: The program utilized the following methodological approaches: (i) exploratory graphics, including time plots of epidemiological metrics with smoothers; (ii) infection prevalence forecasting using a Bayesian epidemiological model with time-varying infection rate; (iii) doubling and halving times computed using changepoints in local linear trend; (iv) death monitoring using combination forecasting with an ensemble of models; (v) effective reproduction number estimation with a Bayesian approach; (vi) COVID-19 patients hospital census monitored via time series models; and (vii) quantified forecast performance. RESULTS: A consolidated forecast and monitoring report was produced weekly and proved to be an effective, vital source of information and guidance as the healthcare system navigated the inherent uncertainty of the pandemic. Forecasts provided accurate and precise information that informed critical decisions on resource planning, bed capacity and staffing management, and infection prevention strategies. CONCLUSIONS: In this paper, we have presented the framework used in our epidemiological forecast and monitoring program at Atrium Health, as well as provided recommendations for implementation by other healthcare systems and institutions to facilitate use in future pandemics.

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Wastewater surveillance has been increasingly acknowledged as a useful tool for monitoring transmission dynamics of infections of public health concern, including the coronavirus disease (COVID-19). While a range of models have been proposed to estimate the time-varying effective reproduction number (Rt) utilizing clinical data, few have harnessed the viral concentration in wastewater samples to do so, leaving uncertainties about the potential precision gains with its use. In this study, we developed a Bayesian hierarchical model which simultaneously reconstructed the latent infection trajectory and estimated Rt. Focusing on the 2022 and early 2023 COVID-19 transmission trends in Singapore, where mass community wastewater surveillance has become routine, we performed estimations using a spectrum of data sources, including reported case counts, hospital admissions, deaths, and wastewater viral loads. We further explored the performance of our wastewater model across various scenarios with different sampling strategies. The results showed consistent estimates derived from models employing diverse data streams, while models incorporating more wastewater samples exhibited greater uncertainty and variation in the inferred Rts. Additionally, our analysis revealed prominent day-of-the-week effect in reported case counts and substantial temporal variations in ascertainment rates. In response to these findings, we advocate for a hybrid approach leveraging both clinical and wastewater surveillance data to account for changes in case-ascertainment rates. Furthermore, our study demonstrates the possibility of reducing sampling frequency or sample size without compromising estimation accuracy for Rt, highlighting the potential for optimizing resource allocation in surveillance efforts while maintaining robust insights into the transmission dynamics of infectious diseases.

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BACKGROUND: In Japan, long-distance domestic travel was banned while the ancestral SARS-CoV-2 strain was dominant under the first declared state of emergency from March 2020 until the end of May 2020. Subsequently, the "Go To Travel" campaign travel subsidy policy was activated, allowing long-distance domestic travel, until the second state of emergency as of January 7, 2021. The effects of this long-distance domestic travel ban on SARS-CoV-2 infectivity have not been adequately evaluated. OBJECTIVE: We evaluated the effects of the long-distance domestic travel ban in Japan on SARS-CoV-2 infectivity, considering climate conditions, mobility, and countermeasures such as the "Go To Travel" campaign and emergency status. METHODS: We calculated the effective reproduction number R(t), representing infectivity, using the epidemic curve in Kagoshima prefecture based on the empirical distribution of the incubation period and procedurally delayed reporting from an earlier study. Kagoshima prefecture, in southern Japan, has several resorts, with an airport commonly used for transportation to Tokyo or Osaka. We regressed R(t) on the number of long-distance domestic travelers (based on the number of airport limousine bus users provided by the operating company), temperature, humidity, mobility, and countermeasures such as state of emergency declarations and the "Go To Travel" campaign in Kagoshima. The study period was June 20, 2020, through February 2021, before variant strains became dominant. A second state of emergency was not declared in Kagoshima prefecture but was declared in major cities such as Tokyo and Osaka. RESULTS: Estimation results indicated a pattern of declining infectivity with reduced long-distance domestic travel volumes as measured by the number of airport limousine bus users. Moreover, infectivity was lower during the "Go To Travel" campaign and the second state of emergency. Regarding mobility, going to restaurants, shopping malls, and amusement venues was associated with increased infectivity. However, going to grocery stores and pharmacies was associated with decreased infectivity. Climate conditions showed no significant association with infectivity patterns. CONCLUSIONS: The results of this retrospective analysis suggest that the volume of long-distance domestic travel might reduce SARS-CoV-2 infectivity. Infectivity was lower during the "Go To Travel" campaign period, during which long-distance domestic travel was promoted, compared to that outside this campaign period. These findings suggest that policies banning long-distance domestic travel had little legitimacy or rationale. Long-distance domestic travel with appropriate infection control measures might not increase SARS-CoV-2 infectivity in tourist areas. Even though this analysis was performed much later than the study period, if we had performed this study focusing on the period of April or May 2021, it would likely yield the same results. These findings might be helpful for government decision-making in considering restarting a "Go To Travel" campaign in light of evidence-based policy.

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Key epidemiological parameters, including the effective reproduction number, R(t), and the instantaneous growth rate, r(t), generated from an ensemble of models, have been informing public health policy throughout the COVID-19 pandemic in the four nations of the United Kingdom of Great Britain and Northern Ireland (UK). However, estimation of these quantities became challenging with the scaling down of surveillance systems as part of the transition from the "emergency" to "endemic" phase of the pandemic. The Office for National Statistics (ONS) COVID-19 Infection Survey (CIS) provided an opportunity to continue estimating these parameters in the absence of other data streams. We used a penalised spline model fitted to the publicly-available ONS CIS test positivity estimates to produce a smoothed estimate of the prevalence of SARS-CoV-2 positivity over time. The resulting fitted curve was used to estimate the "ONS-based" R(t) and r(t) across the four nations of the UK. Estimates produced under this model are compared to government-published estimates with particular consideration given to the contribution that this single data stream can offer in the estimation of these parameters. Depending on the nation and parameter, we found that up to 77% of the variance in the government-published estimates can be explained by the ONS-based estimates, demonstrating the value of this singular data stream to track the epidemic in each of the four nations. We additionally find that the ONS-based estimates uncover epidemic trends earlier than the corresponding government-published estimates. Our work shows that the ONS CIS can be used to generate key COVID-19 epidemiological parameters across the four UK nations, further underlining the enormous value of such population-level studies of infection. This is not intended as an alternative to ensemble modelling, rather it is intended as a potential solution to the aforementioned challenge faced by public health officials in the UK in early 2022.

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We develop a mathematical model to investigate the effect of contact tracing on containing epidemic outbreaks and slowing down the spread of transmissible diseases. We propose a discrete-time epidemic model structured by disease-age which includes general features of contact tracing. The model is fitted to data reported for the early spread of COVID-19 in South Korea, Brazil, and Venezuela. The calibrated values for the contact tracing parameters reflect the order pattern observed in its performance intensity within the three countries. Using the fitted values, we estimate the effective reproduction number Re and investigate its responses to varied control scenarios of contact tracing. Alongside the positivity of solutions, and a stability analysis of the disease-free equilibrium are provided.

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OBJECTIVES: Although the role of specific holidays in modifying transmission dynamics of infectious diseases has received some research attention, the epidemiological impact of public holidays on the transmission of coronavirus disease 2019 (COVID-19) remains unclear. METHODS: To assess the extent of increased transmission frequency during public holidays, we collected COVID-19 incidence and mobility data in Hokkaido, Tokyo, Aichi, and Osaka from February 15, 2020 to September 30, 2021. Models linking the estimated effective reproduction number (Rt) with raw or adjusted mobility, public holidays, and the state of emergency declaration were developed. The best-fit model included public holidays as an essential input variable, and was used to calculate counterfactuals of Rt in the absence of holidays. RESULTS: During public holidays, on average, Rt increased by 5.71%, 3.19%, 4.84%, and 24.82% in Hokkaido, Tokyo, Aichi, and Osaka, respectively, resulting in a total increase of 580 (95% confidence interval [CI], 213 to 954), 2,209 (95% CI, 1,230 to 3,201), 1,086 (95% CI, 478 to 1,686), and 5,211 (95% CI, 4,554 to 5,867) cases that were attributable to the impact of public holidays. CONCLUSIONS: Public holidays intensified the transmission of COVID-19, highlighting the importance of considering public holidays in designing appropriate public health and social measures in the future.

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The effective reproduction number (Rt) is one of the most important epidemiological parameters, providing suggestions for monitoring the development trend of diseases and also for adjusting the prevention and control policies. However, a few studies have focused on the performance of some common computational methods for Rt. The purpose of this article is to compare the performance of three computational methods for Rt: the time-dependent (TD) method, the new time-varying (NT) method, and the sequential Bayesian (SB) method. Four evaluation methods-accuracy, correlation coefficient, similarity based on trend, and dynamic time warping distance-were used to compare the effectiveness of three computational methods for Rt under different time lags and time windows. The results showed that the NT method was a better choice for real-time monitoring and analysis of the epidemic in the middle and late stages of the infectious disease. The TD method could reflect the change of the number of cases stably and accurately, and was more suitable for monitoring the change of Rt during the whole process of the epidemic outbreak. When the data were relatively stable, the SB method could also provide a reliable estimate for Rt, while the error would increase when the fluctuation in the number of cases increased. The results would provide suggestions for selecting appropriate Rt estimation methods and making policy adjustments more timely and effectively according to the change of Rt.

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Starting from May 31, 2023, the local transmission of monkeypox (Mpox) in mainland China began in Beijing. Till now, the transmission characteristics have not been explored. Based on the daily Mpox incidence data in the first 3 weeks of Beijing (from May 31 to June 21, 2023), we employed the instant-individual heterogeneity transmission model to simultaneously calculate the effective reproduction number (Re ) and the degree of heterogeneity (k) of the Beijing epidemic. We additionally simulated the monthly infection size in Beijing from July to November and compared with the reported data to project subsequent transmission dynamics. We estimated Re to be 1.68 (95% highest posterior density [HPD]: 1.12-2.41), and k to be 2.57 [95% HPD: 0.54-83.88], suggesting the transmission of Mpox in Beijing was supercritical and didn't have considerable transmission heterogeneity. We projected that Re fell in the range of 0.95-1.0 from July to November, highlighting more efforts needed to further reduce the Mpox transmissibility. Our findings revealed supercritical and homogeneous transmission of the Mpox epidemic in Beijing. Our results could serve as a reference for understanding and predicting the ongoing Mpox transmission in other regions of China and evaluating the effect of control measures.

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A compartmental model with a time-varying contact rate, the seasonality effect, and its corresponding nonautonomous model are investigated. The model is developed based on the six compartments: susceptible, latent, infected, asymptomatic, treated, and recovered individuals. We determine the effective reproduction number for this nonautonomous system, and analytic discussion shows that at least one positive periodic solution exists for R0>1. The model is simulated using the RK-45 numerical method, and the parameter values for the model are taken from the available literature. From the numerical results, we observe that the degree of seasonality and vaccine efficacy significantly impact the amplitude of the epidemic curve. The latent-infected phase plane shows that periodic solutions exhibit a period-doubling bifurcation as the amplitude of seasonality increases. Finally, the model outcome was compared with the actual field data and found to be consistent.

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Rational allocation of limited vaccine resources is one of the key issues in the prevention and control of emerging infectious diseases. An age-structured infectious disease model with limited vaccine resources is proposed to explore the optimal vaccination ages. The effective reproduction number [Formula: see text] of the epidemic disease is computed. It is shown that the reproduction number is the threshold value for eradicating disease in the sense that the disease-free steady state is globally stable if [Formula: see text] and there exists a unique endemic equilibrium if [Formula: see text]. The effective reproduction number is used as an objective to minimize the disease spread risk. Using the epidemic data from the early spread of Wuhan, China and demographic data of Wuhan, we figure out the strategies to distribute the vaccine to the age groups to achieve the optimal vaccination effects. These analyses are helpful to the design of vaccination schedules for emerging infectious diseases.

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Accurately estimating the effective reproduction number is crucial for characterizing the transmissibility of infectious diseases to optimize interventions and responses during epidemic outbreaks. In this study, we improve the estimation of the effective reproduction number through two main approaches. First, we derive a discrete model to represent a time series of case counts and propose an estimation method based on this framework. We also conduct numerical experiments to demonstrate the effectiveness of the proposed discretization scheme. By doing so, we enhance the accuracy of approximating the underlying epidemic process compared to previous methods, even when the counting period is similar to the mean generation time of an infectious disease. Second, we employ a negative binomial distribution to model the variability of count data to accommodate overdispersion. Specifically, given that observed incidence counts follow a negative binomial distribution, the posterior distribution of secondary infections is obtained as a Dirichlet multinomial distribution. With this formulation, we establish posterior uncertainty bounds for the effective reproduction number. Finally, we demonstrate the effectiveness of the proposed method using incidence data from the COVID-19 pandemic.

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Background: Severe acute respiratory syndrome (SARS) is a form of atypical pneumonia which took hundreds of lives when it swept the world two decades ago. The pathogen of SARS was identified as SARS-coronavirus (SARS-CoV) and it was mainly transmitted in China during the SARS epidemic in 2002-2003. SARS-CoV and SARS-CoV-2 have emerged from the SARS metapopulation of viruses. However, they gave rise to two different disease dynamics, a limited epidemic, and an uncontrolled pandemic, respectively. The characteristics of its spread in China are particularly noteworthy. In this paper, the unique characteristics of time, space, population distribution and transmissibility of SARS for the epidemic were discussed in detail. Methods: We adopted sliding average method to process the number of reported cases per day. An SEIAR transmission dynamics model, which was the first to take asymptomatic group into consideration and applied indicators of R 0, Reff, Rt to evaluate the transmissibility of SARS, and further illustrated the control effectiveness of interventions for SARS in 8 Chinese cities. Results: The R 0 for SARS in descending order was: Tianjin city (R 0 = 8.249), Inner Mongolia Autonomous Region, Shanxi Province, Hebei Province, Beijing City, Guangdong Province, Taiwan Province, and Hong Kong. R 0 of the SARS epidemic was generally higher in Mainland China than in Hong Kong and Taiwan Province (Mainland China: R 0 = 6.058 ± 1.703, Hong Kong: R 0 = 2.159, Taiwan: R 0 = 3.223). All cities included in this study controlled the epidemic successfully (Reff<1) with differences in duration. Rt in all regions showed a downward trend, but there were significant fluctuations in Guangdong Province, Hong Kong and Taiwan Province compared to other areas. Conclusion: The SARS epidemic in China showed a trend of spreading from south to north, i.e., Guangdong Province and Beijing City being the central regions, respectively, and from there to the surrounding areas. In contrast, the SARS epidemic in the central region did not stir a large-scale transmission. There were also significant differences in transmissibility among eight regions, with R0 significantly higher in the northern region than that in the southern region. Different regions were able to control the outbreak successfully in differences time.

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Background: Monitoring the transmission of coronavirus disease 2019 (COVID-19) requires accurate estimation of the effective reproduction number (Rt). However, existing methods for calculating Rt may yield biased estimates if important real-world factors, such as delays in confirmation, pre-symptomatic transmissions, or imperfect data observation, are not considered. Method: To include real-world factors, we expanded the susceptible-exposed-infectious-recovered (SEIR) model by incorporating pre-symptomatic (P) and asymptomatic (A) states, creating the SEPIAR model. By utilizing both stochastic and deterministic versions of the model, and incorporating predetermined time series of Rt, we generated simulated datasets that simulate real-world challenges in estimating Rt. We then compared the performance of our proposed particle filtering method for estimating Rt with the existing EpiEstim approach based on renewal equations. Results: The particle filtering method accurately estimated Rt even in the presence of data with delays, pre-symptomatic transmission, and imperfect observation. When evaluating via the root mean square error (RMSE) metric, the performance of the particle filtering method was better in general and was comparable to the EpiEstim approach if perfectly deconvolved infection time series were provided, and substantially better when Rt exhibited short-term fluctuations and the data was right truncated. Conclusions: The SEPIAR model, in conjunction with the particle filtering method, offers a reliable tool for predicting the transmission trend of COVID-19 and assessing the impact of intervention strategies. This approach enables enhanced monitoring of COVID-19 transmission and can inform public health policies aimed at controlling the spread of the disease.

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Background: On September 28, 2022, the first case of Omicron subvariant BF.7 was discovered among coronavirus disease 2019 (COVID-19) infections in Hohhot, China, and then the epidemic broke out on a large scale during the National Day holiday. It is imminently necessary to construct a mathematical model to investigate the transmission dynamics of COVID-19 in Hohhot. Methods: In this study, we first investigated the epidemiological characteristics of COVID-19 cases in Hohhot, including the spatiotemporal distribution and sociodemographic distribution. Then, we proposed a time-varying Susceptible-Quarantined Susceptible-Exposed-Quarantined Exposed-Infected-Asymptomatic-Hospitalized-Removed (SQEIAHR) model to derive the epidemic curves. The next-generation matrix method was used to calculate the effective reproduction number (Re). Finally, we explored the effects of higher stringency measures on the development of the epidemic through scenario analysis. Results: Of the 4,889 positive infected cases, the vast majority were asymptomatic and mild, mainly concentrated in central areas such as Xincheng District. People in the 30-59 age group primarily were affected by the current outbreak, accounting for 53.74%, but females and males were almost equally affected (1.03:1). Community screening (35.70%) and centralized isolation screening (26.28%) were the main ways to identify positive infected cases. Our model predicted the peak of the epidemic on October 6, 2022, the dynamic zero-COVID date on October 15, 2022, a number of peak cases of 629, and a cumulative number of infections of 4,963 (95% confidential interval (95%CI): 4,692 ~ 5,267), all four of which were highly consistent with the actual situation in Hohhot. Early in the outbreak, the basic reproduction number (R0) was approximately 7.01 (95%CI: 6.93 ~ 7.09), and then Re declined sharply to below 1.0 on October 6, 2022. Scenario analysis of higher stringency measures showed the importance of decreasing the transmission rate and increasing the quarantine rate to shorten the time to peak, dynamic zero-COVID and an Re below 1.0, as well as to reduce the number of peak cases and final affected population. Conclusion: Our model was effective in predicting the epidemic trends of COVID-19, and the implementation of a more stringent combination of measures was indispensable in containing the spread of the virus.

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The currently ongoing COVID-19 outbreak remains a global health concern. Understanding the transmission modes of COVID-19 can help develop more effective prevention and control strategies. In this study, we devise a two-strain nonlinear dynamical model with the purpose to shed light on the effect of multiple factors on the outbreak of the epidemic. Our targeted model incorporates the simultaneous transmission of the mutant strain and wild strain, environmental transmission and the implementation of vaccination, in the context of shortage of essential medical resources. By using the nonlinear least-square method, the model is validated based on the daily case data of the second COVID-19 wave in India, which has triggered a heavy load of confirmed cases. We present the formula for the effective reproduction number and give an estimate of it over the time. By conducting Latin Hyperbolic Sampling (LHS), evaluating the partial rank correlation coefficients (PRCCs) and other sensitivity analysis, we have found that increasing the transmission probability in contact with the mutant strain, the proportion of infecteds with mutant strain, the ratio of probability of the vaccinated individuals being infected, or the indirect transmission rate, all could aggravate the outbreak by raising the total number of deaths. We also found that increasing the recovery rate of those infecteds with mutant strain while decreasing their disease-induced death rate, or raising the vaccination rate, both could alleviate the outbreak by reducing the deaths. Our results demonstrate that reducing the prevalence of the mutant strain, improving the clearance of the virus in the environment, and strengthening the ability to treat infected individuals are critical to mitigate and control the spread of COVID-19, especially in the resource-constrained regions.

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The effective reproduction number, $ R_t $, is a vital epidemic parameter utilized to judge whether an epidemic is shrinking, growing, or holding steady. The main goal of this paper is to estimate the combined $ R_t $ and time-dependent vaccination rate for COVID-19 in the USA and India after the vaccination campaign started. Accounting for the impact of vaccination into a discrete-time stochastic augmented SVEIR (Susceptible-Vaccinated-Exposed-Infectious-Recovered) model, we estimate the time-dependent effective reproduction number $ (R_t) $ and vaccination rate $ (\xi_t) $ for COVID-19 by using a low pass filter and the Extended Kalman Filter (EKF) approach for the period February 15, 2021 to August 22, 2022 in India and December 13, 2020 to August 16, 2022 in the USA. The estimated $ R_t $ and $ \xi_t $ show spikes and serrations with the data. Our forecasting scenario represents the situation by December 31, 2022 that the new daily cases and deaths are decreasing for the USA and India. We also noticed that for the current vaccination rate, $ R_t $ would remain greater than one by December 31, 2022. Our results are beneficial for the policymakers to track the status of the effective reproduction number, whether it is greater or less than one. As restrictions in these countries ease, it is still important to maintain safety and preventive measures.

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This paper is concerned with the formulation and analysis of an epidemic model of COVID-19 governed by an eight-dimensional system of ordinary differential equations, by taking into account the first dose and the second dose of vaccinated individuals in the population. The developed model is analyzed and the threshold quantity known as the control reproduction number [Formula: see text] is obtained. We investigate the equilibrium stability of the system, and the COVID-free equilibrium is said to be locally asymptotically stable when the control reproduction number is less than unity, and unstable otherwise. Using the least-squares method, the model is calibrated based on the cumulative number of COVID-19 reported cases and available information about the mass vaccine administration in Malaysia between the 24th of February 2021 and February 2022. Following the model fitting and estimation of the parameter values, a global sensitivity analysis was performed by using the Partial Rank Correlation Coefficient (PRCC) to determine the most influential parameters on the threshold quantities. The result shows that the effective transmission rate [Formula: see text], the rate of first vaccine dose [Formula: see text], the second dose vaccination rate [Formula: see text] and the recovery rate due to the second dose of vaccination [Formula: see text] are the most influential of all the model parameters. We further investigate the impact of these parameters by performing a numerical simulation on the developed COVID-19 model. The result of the study shows that adhering to the preventive measures has a huge impact on reducing the spread of the disease in the population. Particularly, an increase in both the first and second dose vaccination rates reduces the number of infected individuals, thus reducing the disease burden in the population.

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