Mathematical analysis of a COVID-19 model with double dose vaccination in Bangladesh

Insights from qualitative and bifurcation analysis of COVID-19 vaccination model in Bangladesh

The unprecedented global impact of the 2019 coronavirus disease (COVID-19) has necessitated a comprehensive understanding of its transmission dynamics and control measures. In this study, we present a detailed analysis of a COVID-19 vaccination model tailored to the context of Bangladesh, incorporating dual-dose vaccination strategies. By employing qualitative and bifurcation analysis techniques, we investigate the equilibrium points, effective reproduction number (R0), and critical thresholds that influence the prevalence and control of COVID-19 in the region. Our findings reveal insights into the effectiveness of vaccination programs and provide a framework for developing targeted control plans. Through a rigorous examination of model parameters and sensitivity analysis, we identify key factors driving COVID-19 transmission dynamics, emphasizing the significance of vaccination rates and other critical parameters. The validation of our model against real-world data underscores its utility in informing evidence-based decision-making for managing the COVID-19 pandemic in Bangladesh and beyond.

A deterministic transmission model for analytics-driven optimization of COVID-19 post-pandemic vaccination and quarantine strategies

This study developed a deterministic transmission model for the coronavirus disease of 2019 (COVID-19), considering various factors such as vaccination, awareness, quarantine, and treatment resource limitations for infected individuals in quarantine facilities. The proposed model comprised five compartments: susceptible, vaccinated, quarantined, infected, and recovery. It also considered awareness and limited resources by using a saturated function. Dynamic analyses, including equilibrium points, control reproduction numbers, and bifurcation analyses, were conducted in this research, employing analytics to derive insights. Our results indicated the possibility of an endemic equilibrium even if the reproduction number for control was less than one. Using incidence data from West Java, Indonesia, we estimated our model parameter values to calibrate them with the real situation in the field. Elasticity analysis highlighted the crucial role of contact restrictions in reducing the spread of COVID-19, especially when combined with community awareness. This emphasized the analytics-driven nature of our approach. We transformed our model into an optimal control framework due to budget constraints. Leveraging Pontriagin's maximum principle, we meticulously formulated and solved our optimal control problem using the forward-backward sweep method. Our experiments underscored the pivotal role of vaccination in infection containment. Vaccination effectively reduces the risk of infection among vaccinated individuals, leading to a lower overall infection rate. However, combining vaccination and quarantine measures yields even more promising results than vaccination alone. A second crucial finding emphasized the need for early intervention during outbreaks rather than delayed responses. Early interventions significantly reduce the number of preventable infections, underscoring their importance.

The impact of triple doses vaccination and other interventions for controlling the outbreak of COVID-19 cases and mortality in Australia: A modelling study

COVID-19 is a significant public health problem around the globe, including in Australia. Despite this, Australia's Ministry of Health has expanded COVID-19 control measures widely, logistical trials exist, and the disease burden still needs more clarity. One of the best methods to comprehend the dynamics of disease transmission is by mathematical modeling of COVID-19, which also makes it possible to quantify factors in many places, including Australia. In order to understand the dynamics of COVID-19 in Australia, we examine a mathematical modeling framework for the virus in this study. Australian COVID-19 actual incidence data from January to December 2021 was used to calibrate the model. We also performed a sensitivity analysis of the model parameters and found that the COVID-19 transmission rate was the primary factor in determining the basic reproduction number (R0). Gradually influential intervention policies were established, with accurate effect and coverage regulated with the help of COVID-19 experts in Australia. We simulated data for the period from April 2022 to August 2023. To ascertain which of these outcomes is most effective in lowering the COVID-19 burden, we here assessed the COVID-19 burden (as shown by the number of incident cases and mortality) under a range of intervention scenarios. Regarding the policy of single intervention, the fastest and most efficient way to lower the incidence of COVID-19 is via increasing the first-dose immunization rate, while an improved treatment rate for the afflicted population is also helps to lower mortality in Australia. Furthermore, our results imply that integrating more therapies at the same time increases their efficacy, particularly for mortality, which significantly reduced with a moderate effort, while lowering the number of COVID-19 instances necessitates a major and ongoing commitment.

Cost-effectiveness analysis of COVID-19 intervention policies using a mathematical model: an optimal control approach

COVID-19 is an infectious disease that causes millions of deaths worldwide, and it is the principal leading cause of morbidity and mortality in all nations. Although the governments of developed and developing countries are enforcing their universal control strategies, more precise and cost-effective single or combination interventions are required to control COVID-19 outbreaks. Using proper optimal control strategies with appropriate cost-effectiveness analysis is important to simulate, examine, and forecast the COVID-19 transmission phase. In this study, we developed a COVID-19 mathematical model and considered two important features including direct link between vaccination and latently population, and practical healthcare cost by separation of infections into Mild and Critical cases. We derived basic reproduction numbers and performed mesh and contour plots to explore the impact of different parameters on COVID-19 dynamics. Our model fitted and calibrated with number of cases of the COVID-19 data in Bangladesh as a case study to determine the optimal combinations of interventions for particular scenarios. We evaluated the cost-effectiveness of varying single and combinations of three intervention strategies, including transmission control, treatment, and vaccination, all within the optimal control framework of the single-intervention policies; enhanced transmission control is the most cost-effective and prompt in declining the COVID-19 cases in Bangladesh. Our finding recommends that a three-intervention strategy that integrates transmission control, treatment, and vaccination is the most cost-effective compared to single and double intervention techniques and potentially reduce the overall infections. Other policies can be implemented to control COVID-19 depending on the accessibility of funds and policymakers' judgments.

Mathematical analysis and optimal control of an epidemic model with vaccination and different infectivity

This paper aims to explore the complex dynamics and impact of vaccinations on controlling epidemic outbreaks. An epidemic transmission model which considers vaccinations and two different infection statuses with different infectivity is developed. In terms of a dynamic analysis, we calculate the basic reproduction number and control reproduction number and discuss the stability of the disease-free equilibrium. Additionally, a numerical simulation is performed to explore the effects of vaccination rate, immune waning rate and vaccine ineffective rate on the epidemic transmission. Finally, a sensitivity analysis revealed three factors that can influence the threshold: transmission rate, vaccination rate, and the hospitalized rate. In terms of optimal control, the following three time-related control variables are introduced to reconstruct the corresponding control problem: reducing social distance, enhancing vaccination rates, and enhancing the hospitalized rates. Moreover, the characteristic expression of optimal control problem. Four different control combinations are designed, and comparative studies on control effectiveness and cost effectiveness are conducted by numerical simulations. The results showed that Strategy C (including all the three controls) is the most effective strategy to reduce the number of symptomatic infections and Strategy A (including reducing social distance and enhancing vaccination rate) is the most cost-effective among the three strategies.

Global stability of latency-age/stage-structured epidemic models with differential infectivity

In this paper, we first formulate a system of ODEs-PDE to model diseases with latency-age and differential infectivity. Then, based on the ways how latent individuals leave the latent stage, one ODE and two DDE models are derived. We only focus on the global stability of the models. All the models have some similarities in the existence of equilibria. Each model has a threshold dynamics for global stability, which is completely characterized by the basic reproduction number. The approach is the Lyapunov direct method. We propose an idea on constructing Lyapunov functionals for the two DDE and the original ODEs-PDE models. During verifying the negative (semi-)definiteness of derivatives of the Lyapunov functionals along solutions, a novel positive definite function and a new inequality are used. The idea here is also helpful in applying the Lyapunov direct method to prove the global stability of some epidemic models with age structure or delays.

Modeling the Spread of COVID-19 with the Control of Mixed Vaccine Types during the Pandemic in Thailand

COVID-19 is a respiratory disease that can spread rapidly. Controlling the spread through vaccination is one of the measures for activating immunization that helps to reduce the number of infected people. Different types of vaccines are effective in preventing and alleviating the symptoms of the disease in different ways. In this study, a mathematical model, SVIHR, was developed to assess the behavior of disease transmission in Thailand by considering the vaccine efficacy of different vaccine types and the vaccination rate. The equilibrium points were investigated and the basic reproduction number R0 was calculated using a next-generation matrix to determine the stability of the equilibrium. We found that the disease-free equilibrium point was asymptotically stable if, and only if, R0<1, and the endemic equilibrium was asymptotically stable if, and only if, R0>1. The simulation results and the estimation of the parameters applied to the actual data in Thailand are reported. The sensitivity of parameters related to the basic reproduction number was compared with estimates of the effectiveness of pandemic controls. The simulations of different vaccine efficacies for different vaccine types were compared and the average mixing of vaccine types was reported to assess the vaccination policies. Finally, the trade-off between the vaccine efficacy and the vaccination rate was investigated, resulting in the essentiality of vaccine efficacy to restrict the spread of COVID-19.

Mathematical Model of COVID-19 Pandemic with Double Dose Vaccination

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.

Booster Dose Vaccination and Dynamics of COVID-19 Pandemic in the Fifth Wave: An Efficient and Simple Mathematical Model for Disease Progression

Background: Mathematical studies exploring the impact of booster vaccine doses on the recent COVID-19 waves are scarce, leading to ambiguity regarding the significance of booster doses. Methods: A mathematical model with seven compartments was used to determine the basic and effective reproduction numbers and the proportion of infected people during the fifth wave of COVID-19. Using the next-generation matrix, we computed the effective reproduction parameter, Rt. Results: During the fifth COVID-19 wave, the basic reproductive number in Thailand was calculated to be R0= 1.018691. Analytical analysis of the model revealed both local and global stability of the disease-free equilibrium and the presence of an endemic equilibrium. A dose-dependent decrease in the percentage of infected individuals was observed in the vaccinated population. The simulation results matched the real-world data of the infected patients, establishing the suitability of the model. Furthermore, our analysis suggested that people who had received vaccinations had a better recovery rate and that the death rate was the lowest among those who received the booster dose. The booster dose reduced the effective reproduction number over time, suggesting a vaccine efficacy rate of 0.92. Conclusion: Our study employed a rigorous analytical approach to accurately describe the dynamics of the COVID-19 fifth wave in Thailand. Our findings demonstrated that administering a booster dose can significantly increase the vaccine efficacy rate, resulting in a lower effective reproduction number and a reduction in the number of infected individuals. These results have important implications for public health policymaking, as they provide useful information for the more effective forecasting of the pandemic and improving the efficiency of public health interventions. Moreover, our study contributes to the ongoing discourse on the effectiveness of booster doses in mitigating the impact of the COVID-19 pandemic. Essentially, our study suggests that administering a booster dose can substantially reduce the spread of the virus, supporting the case for widespread booster dose campaigns.

The modeling and analysis of the COVID-19 pandemic with vaccination and isolation: a case study of Italy

The global spread of COVID-19 has not been effectively controlled. It poses a significant threat to public health and global economic development. This paper uses a mathematical model with vaccination and isolation treatment to study the transmission dynamics of COVID-19. In this paper, some basic properties of the model are analyzed. The control reproduction number of the model is calculated and the stability of the disease-free and endemic equilibria is analyzed. The parameters of the model are obtained by fitting the number of cases that were detected as positive for the virus, dead, and recovered between January 20 and June 20, 2021, in Italy. We found that vaccination better controlled the number of symptomatic infections. A sensitivity analysis of the control reproduction number has been performed. Numerical simulations demonstrate that reducing the contact rate of the population and increasing the isolation rate of the population are effective non-pharmaceutical control measures. We found that if the isolation rate of the population is reduced, a short-term decrease in the number of isolated individuals can lead to the disease not being controlled at a later stage. The analysis and simulations in this paper may provide some helpful suggestions for preventing and controlling COVID-19.

Modelling and analysis of fractional-order vaccination model for control of COVID-19 outbreak using real data

In this paper, we construct the SV1V2EIR model to reveal the impact of two-dose vaccination on COVID-19 by using Caputo fractional derivative. The feasibility region of the proposed model and equilibrium points is derived. The basic reproduction number of the model is derived by using the next-generation matrix method. The local and global stability analysis is performed for both the disease-free and endemic equilibrium states. The present model is validated using real data reported for COVID-19 cumulative cases for the Republic of India from 1 January 2022 to 30 April 2022. Next, we conduct the sensitivity analysis to examine the effects of model parameters that affect the basic reproduction number. The Laplace Adomian decomposition method (LADM) is implemented to obtain an approximate solution. Finally, the graphical results are presented to examine the impact of the first dose of vaccine, the second dose of vaccine, disease transmission rate, and Caputo fractional derivatives to support our theoretical results.

Optimal COVID-19 epidemic strategy with vaccination control and infection prevention measures in Thailand

COVID-19 is a severe acute respiratory syndrome caused by the Coronavirus-2 virus (SARS-CoV-2). The virus spreads from one to another through droplets from an infected person, and sometimes these droplets can contaminate surfaces that may be another infection pathway. In this study, we developed a COVID-19 model based on data and observations in Thailand. The country has strictly distributed masks, vaccination, and social distancing measures to control the disease. Hence, we have classified the susceptible individuals into two classes: one who follows the measures and another who does not take the control guidelines seriously. We conduct epidemic and endemic analyses and represent the threshold dynamics characterized by the basic reproduction number. We have examined the parameter values used in our model using the mean general interval (GI). From the calculation, the value is 5.5 days which is the optimal value of the COVID-19 model. Besides, we have formulated an optimal control problem to seek guidelines maintaining the spread of COVID-19. Our simulations suggest that high-risk groups with no precaution to prevent the disease (maybe due to lack of budgets or equipment) are crucial to getting vaccinated to reduce the number of infections. The results also indicate that preventive measures are the keys to controlling the disease.

Mathematical model of COVID-19 transmission dynamics incorporating booster vaccine program and environmental contamination

COVID-19 is one of the greatest human global health challenges that causes economic meltdown of many nations. In this study, we develop an SIR-type model which captures both human-to-human and environment-to-human-to-environment transmissions that allows the recruitment of corona viruses in the environment in the midst of booster vaccine program. Theoretically, we prove some basic properties of the full model as well as investigate the existence of SARS-CoV-2-free and endemic equilibria. The SARS-CoV-2-free equilibrium for the special case, where the constant inflow of corona virus into the environment by any other means, Ω is suspended ( Ω = 0 ) is globally asymptotically stable when the effective reproduction numberR 0 c < 1 and unstable if otherwise. Whereas in the presence of free-living Corona viruses in the environment ( Ω > 0 ), the endemic equilibrium using the centre manifold theory is shown to be stable globally wheneverR 0 c > 1 . The model is extended into optimal control system and analyzed analytically using Pontryagin's Maximum Principle. Results from the optimal control simulations show that strategy E for implementing the public health advocacy, booster vaccine program, treatment of isolated people and disinfecting or fumigating of surfaces and dead bodies before burial is the most effective control intervention for mitigating the spread of Corona virus. Importantly, based on the available data used, the study also revealed that if at least 70% of the constituents followed the aforementioned public health policies, then herd immunity could be achieved for COVID-19 pandemic in the community.