Optimizing COVID-19 vaccination programs during vaccine shortages: A review of mathematical models

Impact assessment of self-medication on COVID-19 prevalence in Gauteng, South Africa, using an age-structured disease transmission modelling framework

OBJECTIVE

To assess the impact of self-medication on the transmission dynamics of COVID-19 across different age groups, examine the interplay of vaccination and self-medication in disease spread, and identify the age group most prone to self-medication.

METHODS

We developed an age-structured compartmentalized epidemiological model to track the early dynamics of COVID-19. Age-structured data from the Government of Gauteng, encompassing the reported cumulative number of cases and daily confirmed cases, were used to calibrate the model through a Markov Chain Monte Carlo (MCMC) framework. Subsequently, uncertainty and sensitivity analyses were conducted on the model parameters.

RESULTS

We found that self-medication is predominant among the age group 15-64 (74.52%), followed by the age group 0-14 (34.02%), and then the age group 65+ (11.41%). The mean values of the basic reproduction number, the size of the first epidemic peak (the highest magnitude of the disease), and the time of the first epidemic peak (when the first highest magnitude occurs) are 4.16499, 241,715 cases, and 190.376 days, respectively. Moreover, we observed that self-medication among individuals aged 15-64 results in the highest spreading rate of COVID-19 at the onset of the outbreak and has the greatest impact on the first epidemic peak and its timing.

CONCLUSION

Studies aiming to understand the dynamics of diseases in areas prone to self-medication should account for this practice. There is a need for a campaign against COVID-19-related self-medication, specifically targeting the active population (ages 15-64).

Learning from the COVID-19 pandemic: a systematic review of mathematical vaccine prioritization models

As the world becomes ever more connected, the chance of pandemics increases as well. The recent COVID-19 pandemic and the concurrent global mass vaccine roll-out provides an ideal setting to learn from and refine our understanding of infectious disease models for better future preparedness. In this review, we systematically analyze and categorize mathematical models that have been developed to design optimal vaccine prioritization strategies of an initially limited vaccine. As older individuals are disproportionately affected by COVID-19, the focus is on models that take age explicitly into account. The lower mobility and activity level of older individuals gives rise to non-trivial trade-offs. Secondary research questions concern the optimal time interval between vaccine doses and spatial vaccine distribution. This review showcases the effect of various modeling assumptions on model outcomes. A solid understanding of these relationships yields better infectious disease models and thus public health decisions during the next pandemic.

Perspectives on the COVID-19 Vaccination Rollout in 17 Countries: Reflexive Thematic and Frequency Analysis Based on the Strengths, Weaknesses, Opportunities, and Threats (SWOT) Framework

BACKGROUND

As the SARS-CoV-2 virus created a global pandemic and rapidly became an imminent threat to the health and lives of people worldwide, the need for a vaccine and its quick distribution among the population was evident. Due to the urgency, and on the back of international collaboration, vaccines were developed rapidly. However, vaccination rollouts showed different success rates in different countries and some also led to increased vaccine hesitancy.

OBJECTIVE

The aim of this study was to identify the role of information sharing and context sensitivity in various vaccination programs throughout the initial COVID-19 vaccination rollout in different countries. Moreover, we aimed to identify factors in national vaccination programs related to COVID-19 vaccine hesitancy, safety, and effectiveness. Toward this end, multidisciplinary and multinational opinions from members of the Navigating Knowledge Landscape (NKL) network were analyzed.

METHODS

From May to July 2021, 25 completed questionnaires from 27 NKL network members were collected. These contributors were from 17 different countries. The responses reflected the contributors' subjective viewpoints on the status and details of the COVID-19 vaccination rollout in their countries. Contributors were asked to identify strengths, weaknesses, opportunities, and threats (ie, SWOT) of the respective vaccination programs. The responses were analyzed using reflexive thematic analysis, followed by frequency analysis of identified themes according to the represented countries.

RESULTS

The perspectives of NKL network members showed a link between organizational elements of the vaccination rollout and the accompanying societal response, both of which were related to strengths and weaknesses of the process. External sociocultural variables, improved public communication around vaccination-related issues, ethical controversies, and the spread of disinformation were the dominant themes related to opportunities and challenges. In the SWOT 2×2 matrix, Availability and Barriers emerged as internal categories, whereas Transparent communication and promotion and Societal divide emerged as key external categories.

CONCLUSIONS

Inventory of themes and categories inspired by elements of the SWOT framework provides an informative multidisciplinary perspective for effective implementation of public health strategies in the battle against COVID-19 or any future pandemics of a similar nature.

Analysis of the yearly transition function in measles disease modeling

Globally, there were an estimated 9.8 million measles cases and 207 500 measles deaths in 2019. As the effort to eliminate measles around the world continues, modeling remains a valuable tool for public health decision-makers and program implementers. This study presents a novel approach to the use of a yearly transition function that formulates mathematically the vaccine schedules for different age groups while accounting for the effects of the age of vaccination, the timing of vaccination, and disease seasonality on the yearly number of measles cases in a country. The methodology presented adds to an existing modeling framework and expands its analysis, making its utilization more adjustable for the user and contributing to its conceptual clarity. This article also adjusts for the temporal interaction between vaccination and exposure to disease, applying adjustments to estimated yearly counts of cases and the number of vaccines administered that increase population immunity. These new model features provide the ability to forecast and compare the effects of different vaccination timing scenarios and seasonality of transmission on the expected disease incidence. Although the work presented is applied to the example of measles, it has potential relevance to modeling other vaccine-preventable diseases.

Optimal vaccination ages for emerging infectious diseases under limited vaccine supply

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.

Incidence rate drive the multiple wave in the COVID-19 pandemic

The last three years have been the most challenging for humanity due to the COVID-19 pandemic. The novel viral infection has eventually been able to infect most of the human population. It is now considered to be in the endemic stage, meaning it will remain in our world throughout our lifetime. There will be an intermittent outbreak of the COVID infection from time to time. Therefore, it is necessary to formulate a robust Mathematical model to study the dynamics of disease to have a control mechanism in place. In this article, we suggest a modified MSEIR model to explain the dynamics of COVID-19 infection. We assume that a susceptible person contracting the coronavirus develops a transient immunity to the illness. Further, infectives comprise asymptomatic, symptomatic, hospitalized and quarantined individuals. We assume that the incidence rate is of standard type, and susceptible can only become infective if they come in contact with either asymptomatic or symptomatic individuals. This basic and simple model effectively models the various waves every country has seen during the Pandemic. The simple analysis shows that the model could suggest various waves in future if we carefully select the incidence rate for the infection. In summary, we have discussed the following major points in this article. •We have analysed for local behavior infection-free equilibrium solution. Further, a thorough numerical exploration with various parameter settings has been performed to obtain the different cases of infection dynamics of the coronavirus epidemic.•We have found some interesting scenarios which explain the emergence of multiple waves observed in many countries.

Minimizing outbreak through targeted blocking for disease control: a community-based approach using super-spreader node identification

The COVID-19 pandemic has caused significant disruptions to the daily lives of individuals worldwide, with many losing their lives to the virus. Vaccination has been identified as a crucial strategy to combat the spread of a disease, but with a limited supply of vaccines, targeted blocking is becoming increasingly necessary. One such approach is to block a select group of individuals in the community to control the spread of the disease in its early stages. Therefore, in this paper, a method is proposed for solving this problem, based on the similarity between this issue and the problem of identifying super-spreader nodes. The proposed method attempts to select the minimum set of network nodes that, when removed, no large component remains in the network. To this end, the network is partitioned into various communities, and a method for limiting the spread of the disease to communities is proposed by blocking connecting nodes. Four real networks and four synthetics networks created using the LFR algorithm were used to evaluate the control of the disease by the selected set of nodes using each method, and the results obtained indicate better performance of the proposed method compared to other methods.

A two-strain model of infectious disease spread with asymmetric temporary immunity periods and partial cross-immunity

We introduce a two-strain model with asymmetric temporary immunity periods and partial cross-immunity. We derive explicit conditions for competitive exclusion and coexistence of the strains depending on the strain-specific basic reproduction numbers, temporary immunity periods, and degree of cross-immunity. The results of our bifurcation analysis suggest that, even when two strains share similar basic reproduction numbers and other epidemiological parameters, a disparity in temporary immunity periods and partial or complete cross-immunity can provide a significant competitive advantage. To analyze the dynamics, we introduce a quasi-steady state reduced model which assumes the original strain remains at its endemic steady state. We completely analyze the resulting reduced planar hybrid switching system using linear stability analysis, planar phase-plane analysis, and the Bendixson-Dulac criterion. We validate both the full and reduced models with COVID-19 incidence data, focusing on the Delta (B.1.617.2), Omicron (B.1.1.529), and Kraken (XBB.1.5) variants. These numerical studies suggest that, while early novel strains of COVID-19 had a tendency toward dramatic takeovers and extinction of ancestral strains, more recent strains have the capacity for co-existence.

Modeling the effects of Prophylactic behaviors on the spread of SARS-CoV-2 in West Africa

Various general and individual measures have been implemented to limit the spread of SARS-CoV-2 since its emergence in China. Several phenomenological and mechanistic models have been developed to inform and guide health policy. Many of these models ignore opinions about certain control measures, although various opinions and attitudes can influence individual actions. To account for the effects of prophylactic opinions on disease dynamics and to avoid identifiability problems, we expand the SIR-Opinion model of Tyson et al. (2020) to take into account the partial detection of infected individuals in order to provide robust modeling of COVID-19 as well as degrees of adherence to prophylactic treatments, taking into account a hybrid modeling technique using Richard's model and the logistic model. Applying the approach to COVID-19 data from West Africa demonstrates that the more people with a strong prophylactic opinion, the smaller the final COVID-19 pandemic size. The influence of individuals on each other and from the media significantly influences the susceptible population and, thus, the dynamics of the disease. Thus, when considering the opinion of susceptible individuals to the disease, the view of the population at baseline influences its dynamics. The results are expected to inform public policy in the context of emerging and re-emerging infectious diseases.

Study of optimal vaccination strategies for early COVID-19 pandemic using an age-structured mathematical model: A case study of the USA

In this paper we study different vaccination strategies that could have been implemented for the early COVID-19 pandemic. We use a demographic epidemiological mathematical model based on differential equations in order to investigate the efficacy of a variety of vaccination strategies under limited vaccine supply. We use the number of deaths as the metric to measure the efficacy of each of these strategies. Finding the optimal strategy for the vaccination programs is a complex problem due to the large number of variables that affect the outcomes. The constructed mathematical model takes into account demographic risk factors such as age, comorbidity status and social contacts of the population. We perform simulations to assess the performance of more than three million vaccination strategies which vary depending on the vaccine priority of each group. This study focuses on the scenario corresponding to the early vaccination period in the USA, but can be extended to other countries. The results of this study show the importance of designing an optimal vaccination strategy in order to save human lives. The problem is extremely complex due to the large amount of factors, high dimensionality and nonlinearities. We found that for low/moderate transmission rates the optimal strategy prioritizes high transmission groups, but for high transmission rates, the optimal strategy focuses on groups with high CFRs. The results provide valuable information for the design of optimal vaccination programs. Moreover, the results help to design scientific vaccination guidelines for future pandemics.

Modeling and analysis of novel COVID-19 outbreak under fractal-fractional derivative in Caputo sense with power-law: a case study of Pakistan

In this paper, a five-compartment model is used to explore the dynamics of the COVID-19 pandemic, taking the vaccination campaign into account. The present model consists of five components that lead to a system of five ordinary differential equations. In this paper, we examined the disease from the perspective of a fractal fractional derivative in the Caputo sense with a power law type kernal. The model is also fitted with real data for Pakistan between June 1, 2020, and March 8, 2021. The fundamental mathematical characteristics of the model have been investigated thoroughly. We have calculated the equilibrium points and the reproduction number for the model and obtained the feasible region for the system. The existence and stability criteria of the model have been validated using the Banach fixed point theory and the Picard successive approximation technique. Furthermore, we have conducted stability analysis for both the disease-free and endemic equilibrium states. On the basis of sensitivity analysis and the dynamics of the threshold parameter, we have estimated the effectiveness of vaccination and identified potential control strategies for the disease using the proposed model outbreaks. The stability of the concerned solution in Ulam-Hyers and Ulam-Hyers-Rassias sense is also investigated. For the proposed problem, some results regarding basic reproduction numbers and stability analysis for various parameters are represented graphically. Matlab software is used for numerical illustrations. Graphical representations are given for different fractional orders and for various parametric values.

A decision support system for scheduling a vaccination campaign during a pandemic emergency: The COVID-19 case

This paper considers the organization and scheduling of a vaccination campaign during a pandemic emergency. We describe the decision process and introduce an optimization model, which showed a powerful multi-scenario tool for scheduling a campaign in detail within a dynamic and uncertain context. The solution of the model gave the decision maker the possibility to test different settings and have a configurable solution within few seconds, compared with the man-days of effort that would have required a manual schedule. Analysis of a real case study on COVID-19 vaccination campaign in northern Italy showed that the use of such optimized solution allowed to cover the target population within a much shorter time interval, compared to a manual approach.

Mathematical modeling of vaccination as a control measure of stress to fight COVID-19 infections

The world experienced the life-threatening COVID-19 disease worldwide since its inversion. The whole world experienced difficult moments during the COVID-19 period, whereby most individual lives were affected by the disease socially and economically. The disease caused millions of illnesses and hundreds of thousands of deaths worldwide. To fight and control the COVID-19 disease intensity, mathematical modeling was an essential tool used to determine the potentiality and seriousness of the disease. Due to the effects of the COVID-19 disease, scientists observed that vaccination was the main option to fight against the disease for the betterment of human lives and the world economy. Unvaccinated individuals are more stressed with the disease, hence their body's immune system are affected by the disease. In this study, the S V E I H R deterministic model of COVID-19 with six compartments was proposed and analyzed. Analytically, the next-generation matrix method was used to determine the basic reproduction number ( R 0 ). Detailed stability analysis of the no-disease equilibrium ( E 0 ) of the proposed model to observe the dynamics of the system was carried out and the results showed that E 0 is stable if R 0 < 1 and unstable when R 0 > 1 . The Bayesian Markov Chain Monte Carlo (MCMC) method for the parameter identifiability was discussed. Moreover, the sensitivity analysis of R 0 showed that vaccination was an essential method to control the disease. With the presence of a vaccine in our S V E I H R model, the results showed that R 0 = 0 . 208 , which means COVID-19 is fading out of the community and hence minimizes the transmission. Moreover, in the absence of a vaccine in our model, R 0 = 1 . 7214 , which means the disease is in the community and spread very fast. The numerical simulations demonstrated the importance of the proposed model because the numerical results agree with the sensitivity results of the system. The numerical simulations also focused on preventing the disease to spread in the community.

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.

A Mathematical Evaluation of the Cost-Effectiveness of Self-Protection, Vaccination, and Disinfectant Spraying for COVID-19 Control

The world is on its path from the post-COVID period, but a fresh wave of the coronavirus infection engulfing most European countries makes the pandemic catastrophic. Mathematical models are of significant importance in unveiling strategies that could stem the spread of the disease. In this paper, a deterministic mathematical model of COVID-19 is studied to characterize a range of feasible control strategies to mitigate the disease. We carried out an analytical investigation of the model’s dynamic behaviour at its equilibria and observed that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number, ${\mathcal{R}}_0$ is less than unity. The endemic equilibrium is also shown to be globally asymptotically stable when ${\mathcal{R}}_0>1$ . Further, we showed that the model exhibits forward bifurcation around ${\mathcal{R}}_0=1$ . Sensitivity analysis was carried out to determine the impact of various factors on the basic reproduction number ${\mathcal{R}}_0$ and consequently, the spread of the disease. An optimal control problem was formulated from the sensitivity analysis. Cost-effectiveness analysis is conducted to determine the most cost-effective strategy that can be adopted to control the spread of COVID-19. The investigation revealed that combining self-protection and environmental control is the most cost-effective control strategy among the enlisted strategies.

Neutralizing response elicited by homologous and heterologous prime booster vaccination against ancestral SARS-CoV-2 B.1, P.1, C.37 and B.1.617.2 variants

Heterologous Covid-19 vaccination strategies arose due to interruption of vaccination programs plus delay and shortage of vaccine supplies. We analysed neutralizing response against ancestral SARS-CoV-2 B.1 and P.1, C.37 and B.1.67.2 variants elicited by 16 homologous and heterologous protocols combining Gam-COVID-Vac, ChAdOx1-S, Ad5-nCorV, BBIBP-CorV and mRNA-1273 vaccines. Homologous mRNA-1273 and heterologous schemes of a non-replicative viral vector/inactivated virus-based vaccine combined with mRNA-1273 induced significantly broader and greater neutralizing antibody-response. Moreover, serum from participants vaccinated with combinations of ChAdOx1-S/Ad5-nCorV and BBIBP-CorV/non-replicative viral vector-based vaccines showed higher or equivalent neutralizing response compared to homologous protocols, pointing them as good alternative platforms. BBIBP-CorV used as second dose exhibited significantly lower neutralizing response compared to other protocols, demonstrating that it should not be recommended as second dose. The information provided herein is valuable to redesign vaccination strategies, especially for low-income countries that still struggle with low percentages of immunized populations and vaccine supply shortage.

Incorporating mass vaccination into compartment models for infectious diseases

The standard way of incorporating mass vaccination into a compartment model for an infectious disease is as a spontaneous transition process that applies to the entire susceptible class. The large degree of COVID-19 vaccine refusal, hesitancy, and ineligibility, and initial limitations of supply and distribution require reconsideration of this standard treatment. In this paper, we address these issues for models on endemic and epidemic time scales. On an endemic time scale, we partition the susceptible class into prevaccinated and unprotected subclasses and show that vaccine refusal/hesitancy/ineligibility has a significant impact on endemic behavior, particularly for diseases where immunity is short-lived. On an epidemic time scale, we develop a supply-limited Holling type 3 vaccination model and show that it is an excellent fit to vaccination data. We then extend the Holling model to a COVID-19 scenario in which the population is divided into two risk classes, with the high-risk class being prioritized for vaccination. In both cases, with and without risk stratification, we see significant differences in epidemiological outcomes between the Holling vaccination model and naive models. Finally, we use the new model to explore implications for public health policies in future pandemics.

Prioritizing COVID-19 vaccination. Part 1: Final size comparison between a single dose and double dose

In response to the coronavirus disease 2019 (COVID-19) pandemic, Japan conducted mass vaccination. Seventy-two million doses of vaccine (i.e., for 36 million people if a double dose is planned per person) were obtained, with initial vaccination of the older population (≡ 65 years). Because of the limited number of vaccines, the government discussed shifting the plan to administering only a single dose so that younger individuals (<65 years) could also be vaccinated with one shot. This study aimed to determine the optimal vaccine distribution strategy using a simple mathematical method. After accounting for age-dependent relative susceptibility after single- and double-dose vaccination (vs and vd, respectively, compared with unvaccinated), we used the age-dependent transmission model to compute the final size for various patterns of vaccine distributions. Depending on the values of vs, the cumulative risk of death would be lower if all 72 million doses were used as a double dose for older people than if a single-dose program was conducted in which half is administered to older people and the other half is administered to adults (i.e., 1,856,000 deaths in the former program and 1,833,000-2,355,000 deaths [depending on the values of vs] in the latter). Even if 90% of older people were vaccinated twice and 100% of adults were vaccinated once, the effective reproduction number would be reduced from 2.50 to1.14. Additionally, the cumulative risk of infection would range from 12.0% to 54.6% and there would be 421,000-1,588,000deaths (depending on the values of vs). If an epidemic appears only after completing vaccination, vaccination coverage using a single-dose program with widespread vaccination among adults will not outperform a double-dose strategy.