Analysis of COVID-19 and comorbidity co-infection model with optimal control

Mathematical assessment of the roles of age heterogeneity and vaccination on the dynamics and control of SARS-CoV-2

The COVID-19 pandemic, caused by SARS-CoV-2, disproportionately affected certain segments of society, particularly the elderly population (which suffered the brunt of the burden of the pandemic in terms of severity of the disease, hospitalization, and death). This study presents a generalized multigroup model, with m heterogeneous sub-populations, to assess the population-level impact of age heterogeneity and vaccination on the transmission dynamics and control of the SARS-CoV-2 pandemic in the United States. Rigorous analysis of the model for the homogeneous case (i.e., the model with m = 1) reveal that its disease-free equilibrium is globally-asymptotically stable for two special cases (with perfect vaccine efficacy or negligible disease-induced mortality) whenever the associated reproduction number is less than one. The model has a unique and globally-asymptotically stable endemic equilibrium, for special a case, when the associated reproduction threshold exceeds one. The homogeneous model was fitted using the observed cumulative mortality data for the United States during three distinct waves (Waves A (October 17, 2020 to April 5, 2021), B (July 9, 2021 to November 7, 2021) and C (January 1, 2022 to May 7, 2022)) chosen to align with time periods when the Alpha, Delta and Omicron were, respectively, the predominant variants in the United States. The calibrated model was used to derive a theoretical expression for achieving vaccine-derived herd immunity (needed to eliminate the disease in the United States). It was shown that, using the one-group homogeneous model, vaccine-derived herd immunity is not attainable during Wave C of the pandemic in the United States, regardless of the coverage level of the fully-vaccinated individuals. Global sensitivity analysis was carried out to determine the parameters of the model that have the most influence on the disease dynamics and burden. These analyses reveal that control and mitigation strategies that may be very effective during one wave may not be so very effective during the other wave or waves. However, strategies that target asymptomatic and pre-symptomatic infectious individuals are shown to be consistently effective across all waves. To study the impact of the disproportionate effect of COVID-19 on the elderly population, we considered the heterogeneous model for the case where the total population is subdivided into the sub-populations of individuals under 65 years of age and those that are 65 and older. The resulting two-group heterogeneous model, which was also fitted using the cumulative mortality data for wave C, was also rigorously analysed. Unlike for the case of the one-group model, it was shown, for the two-group model, that vaccine-derived herd immunity can indeed be achieved during Wave C of the pandemic if at least 61% of the populace is fully vaccinated. Thus, this study shows that adding age heterogeneity into a SARS-CoV-2 vaccination model with homogeneous mixing significantly reduces the level of vaccination coverage needed to achieve vaccine-derived herd immunity (specifically, for the heterogeneous model, herd-immunity can be attained during Wave C if a moderate proportion of susceptible individuals are fully vaccinated). The consequence of this result is that vaccination models for SARS-CoV-2 that do not explicitly account for age heterogeneity may be overestimating the level of vaccine-derived herd immunity threshold needed to eliminate the SARS-CoV-2 pandemic.

Analyzing the worldwide progression of COVID-19 cases and deaths using nonlinear mixed-effects model

COVID-19 is an infectious disease that continues to spread worldwide. A precise estimation of the cases and deaths due to COVID-19 would allow for appropriate consideration of healthcare resource allocation, public health response, and vaccination and economic planning, to minimize social damage. In this study, we analyzed the progression of COVID-19 cases and deaths until January 2022 in 156 countries using a nonlinear mixed-effect model based on the SIR framework. Given the major changes in mortality from infection, risk of re-infection and social responses, the analysis was limited to the period before the emergence of the Omicron variant. The impact of infection prevention measures in various countries was assessed, with a specific focus on estimating the effectiveness of lockdowns, where the effect was assumed to change over time. By accounting for excess mortality, our analysis allowed the estimation of unreported cases and deaths, and thus providing a more comprehensive understanding of the impact of pandemic. In the analysis, we identified gross domestic product (GDP), proportion of people aged 65 years or older, latitude of the capital city on transmissibility of infection, and city population and cardiovascular death rate on mortality rate as significant influencing factors. Furthermore, the differences in transmissibility and mortality rates by variants and the effect of vaccination on the mortality rate were assessed. The transmissibility has increased by odds ratios of 1.2 to 1.4 in Beta, Gamma, and Delta variants; mortality rate has increased by odds ratios of 1.7, 2.2, and 1.4 in Beta, Gamma, and Delta variants, respectively; and vaccination decreased the mortality rate by odds ratios of 0.4 and 0.1 in Delta and other variants, respectively.

Impacts of optimal control strategies on the HBV and COVID-19 co-epidemic spreading dynamics

Different cross-sectional and clinical research studies investigated that chronic HBV infected individuals' co-epidemic with COVID-19 infection will have more complicated liver infection than HBV infected individuals in the absence of COVID-19 infection. The main objective of this study is to investigate the optimal impacts of four time dependent control strategies on the HBV and COVID-19 co-epidemic transmission using compartmental modeling approach. The qualitative analyses of the model investigated the model solutions non-negativity and boundedness, calculated all the models effective reproduction numbers by applying the next generation operator approach, computed all the models disease-free equilibrium point (s) and endemic equilibrium point (s) and proved their local stability, shown the phenomenon of backward bifurcation by applying the Center Manifold criteria. By applied the Pontryagin's Maximum principle, the study re-formulated and analyzed the co-epidemic model optimal control problem by incorporating four time dependent controlling variables. The study also carried out numerical simulations to verify the model qualitative results and to investigate the optimal impacts of the proposed optimal control strategies. The main finding of the study reveals that implementation of protections, COVID-19 vaccine, and treatment strategies simultaneously is the most effective optimal control strategy to tackle the HBV and COVID-19 co-epidemic spreading in the community.

A dynamical analysis and numerical simulation of COVID-19 and HIV/AIDS co-infection with intervention strategies

HIV/AIDS-COVID-19 co-infection is a major public health concern especially in developing countries of the world. This paper presents HIV/AIDS-COVID-19 co-infection to investigate the impact of interventions on its transmission using ordinary differential equation. In the analysis of the model, the solutions are shown to be non-negative and bounded, using next-generation matrix approach the basic reproduction numbers are computed, sufficient conditions for stabilities of equilibrium points are established. The sensitivity analysis showed that transmission rates are the most sensitive parameters that have direct impact on the basic reproduction numbers and protection and treatment rates are more sensitive and have indirect impact to the basic reproduction numbers. Numerical simulations shown that some parameter effects on the transmission of single infections as well as co-infection, and applying the protection rates and treatment rates have effective roles to minimize and also to eradicate the HIV/AIDS-COVID-19 co-infection spreading in the community.

Co-infection dynamics of COVID-19 and HIV/AIDS

Although there are many results that can be used to treat and prevent Coronavirus Disease 2019 (COVID-19) and Human Immunodeficiency Virus (HIV), these diseases continue to be public health concerns and cause socioeconomic consequences. Following compromised immunity, COVID-19 is considered to be a challenge for people with HIV. People with advanced HIV are considered a vulnerable population at high risk in several case studies that discuss COVID-19 and HIV co-infection. As there is no cure for HIV and there is a chance of contracting COVID-19 again, co-infection continues to pose a problem. The purpose of this study is to investigate the impact of intervention strategies and identify the role of different parameters in risking people living with HIV to death when they get infected with COVID-19. This is achieved through the development and rigorous analysis of a mathematical model that considers a population at risk of death due to COVID-19 and HIV. The model formulation provides a detailed explanation of the transmission dynamics of COVID-19 and HIV co-infection. The solution's invariant region, positivity, and boundedness were established. The reproduction numbers of the sub-models and the co-infection model were determined. The existence and stability of equilibria, including backward bifurcation for the COVID-19 sub-model, were examined. The epidemiological significance of backward bifurcation is that the condition [Formula: see text] less than 1 for eliminating COVID-19, though necessary, is no longer sufficient. Parametric estimation and curve fitting were performed based on data from Ethiopia. Numerical simulations were employed to support and clarify the analytical findings and to show some parameter effects on COVID-19 and HIV co-infection. Accordingly, the simulations indicated that parameters [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], related to HIV patients' exposure to other diseases and the increase in infectiousness, have a positive role in increasing the number of co-infections. On the other hand, an increase in COVID-19 vaccination ([Formula: see text]) shows the suppression of co-infection cases. In addition, treating co-infected individuals for COVID-19, increasing treatment rates [Formula: see text] and [Formula: see text], reduces the death risk of HIV-infected individuals due to the co-infection burden. It was implied that improving vaccine delivery programs and other medical interventions have important contributions to lowering the risk of COVID-19 infection-related fatalities in HIV patients.

Optimal control dynamics of Gonorrhea in a structured population

Gonorrhea is a serious global health problem due to its high incidence, with approximately 82.4 million new cases in 2020. To evaluate the consequences of targeted dynamic control of gonorrhea infection transmission, a model for gonorrhea with optimal control analysis is proposed for a structured population. The study looked at the model's positively invariant and bounded regions. The gonorrhea secondary infection expression, R 0 for the structured population is computed. The maximum principle of Pontryagin is utilised to construct the optimal system for the formulated mathematical model. To reduce the continuous propagation of gonorrhea, we incorporated education, condoms usage, vaccinations, and treatment as control strategies. The numerical simulations show that the number of infections decreases when the controls are implemented. The effectiveness of the controls is shown using the efficacy plots.

Analysis of HBV and COVID-19 Coinfection Model with Intervention Strategies

Coinfection of hepatitis B virus (HBV) and COVID-19 is a common public health problem throughout some nations in the world. In this study, a mathematical model for hepatitis B virus (HBV) and COVID-19 coinfection is constructed to investigate the effect of protection and treatment mechanisms on its spread in the community. Necessary conditions of the proposed model nonnegativity and boundedness of solutions are analyzed. We calculated the model reproduction numbers and carried out the local stabilities of disease-free equilibrium points whenever the associated reproduction number is less than unity. Using the well-known Castillo-Chavez criteria, the disease-free equilibrium points are shown to be globally asymptotically stable whenever the associated reproduction number is less than unity. Sensitivity analysis proved that the most influential parameters are transmission rates. Moreover, we carried out numerical simulation and shown results: some parameters have high spreading effect on the disease transmission, single infections have great impact on the coinfection transmission, and using protections and treatments simultaneously is the most effective strategy to minimize and also to eradicate the HBV and COVID-19 coinfection spreading in the community. It is concluded that to control the transmission of both diseases in a population, efforts must be geared towards preventing incident infection with either or both diseases.

A nonlinear mathematical model on the Covid-19 transmission pattern among diabetic and non-diabetic population

In this paper, a three tier mathematical model describing the interactions between susceptible population, Covid-19 infected, diabetic population and Covid-19 infected, non diabetic population is proposed. Basic properties of such a dynamic model, namely, non negativity, boundedness of solutions, existence of disease-free and disease equilibria are studied and sufficient conditions are obtained. Basic reproduction number for the system is derived. Sufficient conditions on functionals and parameters of the system are obtained for the local as well as global stability of equilibria, thus, establishing the conditions for eventual prevalence of disease free or disease environment, as the case may be. The stability aspects are discussed in the context of basic reproduction number and vice versa. An important contribution of this article is that a novel technique is presented to estimate some key, influencing parameters of the system so that a pre-specified, assumed equilibrium state is approached eventually. This enables the society to prepare itself with the help of these key, influencing parameters so estimated. Several examples are provided to illustrate the results established and simulations are provided to visualize the examples.

Mathematical modeling and analysis of COVID-19 and TB co-dynamics

This study proposes a mathematical model for examining the COVID-19 and tuberculosis (TB) co-dynamics thoroughly. First, the single infection dynamics: COVID-19 infection and TB infection models are taken into consideration and examined. Following that, the co-dynamics with TB and COVID-19 is also investigated. In order to comprehend the developed model dynamics, the basic system attributes including the region of definition, theory of nonnegativity and boundedness of solution are investigated. Further, a qualitative analysis of the equilibria of the formulated model equations is performed. The equilibria of both infection models are globally asymptotically stable if their respective basic reproductive number is smaller than one. As the associated reproductive number reaches unity, they experience the forward bifurcation phenomenon. Additionally, it is demonstrated that the formulated co-dynamics model would not experience backward bifurcation by applying the center manifold theory. Moreover, model fitting is done by using daily reported COVID-19 cumulative data in Ethiopia between March 13, 2020, and May 31, 2022. For instance, the non-linear least squares approach of fitting a function to data was performed in the fitting process using s c i p y . o p t i m i z e . c u r v e _ f i t from the Python. Finally, to corroborate the analytical findings of the model equation, numerical simulations were conducted.

Co-dynamics of COVID-19 and TB with COVID-19 vaccination and exogenous reinfection for TB: An optimal control application

COVID-19 and Tuberculosis (TB) are among the major global public health problems and diseases with major socioeconomic impacts. The dynamics of these diseases are spread throughout the world with clinical similarities which makes them difficult to be mitigated. In this study, we formulate and analyze a mathematical model containing several epidemiological characteristics of the co-dynamics of COVID-19 and TB. Sufficient conditions are derived for the stability of both COVID-19 and TB sub-models equilibria. Under certain conditions, the TB sub-model could undergo the phenomenon of backward bifurcation whenever its associated reproduction number is less than one. The equilibria of the full TB-COVID-19 model are locally asymptotically stable, but not globally, due to the possible occurrence of backward bifurcation. The incorporation of exogenous reinfection into our model causes effects by allowing the occurrence of backward bifurcation for the basic reproduction number R₀ < 1 and the exogenous reinfection rate greater than a threshold (η > η∗). The analytical results show that reducing R₀ < 1 may not be sufficient to eliminate the disease from the community. The optimal control strategies were proposed to minimize the disease burden and related costs. The existence of optimal controls and their characterization are established using Pontryagin's Minimum Principle. Moreover, different numerical simulations of the control induced model are carried out to observe the effects of the control strategies. It reveals the usefulness of the optimization strategies in reducing COVID-19 infection and the co-infection of both diseases in the community.

Sliding dynamics and bifurcations of a human influenza system under logistic source and broken line control strategy

This paper proposes a non-smooth human influenza model with logistic source to describe the impact on media coverage and quarantine of susceptible populations of the human influenza transmission process. First, we choose two thresholds $ I_{T} $ and $ S_{T} $ as a broken line control strategy: Once the number of infected people exceeds $ I_{T} $, the media influence comes into play, and when the number of susceptible individuals is greater than $ S_{T} $, the control by quarantine of susceptible individuals is open. Furthermore, by choosing different thresholds $ I_{T} $ and $ S_{T} $ and using Filippov theory, we study the dynamic behavior of the Filippov model with respect to all possible equilibria. It is shown that the Filippov system tends to the pseudo-equilibrium on sliding mode domain or one endemic equilibrium or bistability endemic equilibria under some conditions. The regular/virtulal equilibrium bifurcations are also given. Lastly, numerical simulation results show that choosing appropriate threshold values can prevent the outbreak of influenza, which implies media coverage and quarantine of susceptible individuals can effectively restrain the transmission of influenza. The non-smooth system with logistic source can provide some new insights for the prevention and control of human influenza.

A fractal-fractional COVID-19 model with a negative impact of quarantine on the diabetic patients

In this article, we consider a Covid-19 model for a population involving diabetics as a subclass in the fractal-fractional (FF) sense of derivative. The study includes: existence results, uniqueness, stability and numerical simulations. Existence results are studied with the help of fixed-point theory and applications. The numerical scheme of this paper is based upon the Lagrange’s interpolation polynomial and is tested for a particular case with numerical values from available open sources. The results are getting closer to the classical case for the orders reaching to 1 while all other solutions are different with the same behavior. As a result, the fractional order model gives more significant information about the case study.

Bifurcation and optimal control analysis of HIV/AIDS and COVID-19 co-infection model with numerical simulation

HIV/AIDS and COVID-19 co-infection is a common global health and socio-economic problem. In this paper, a mathematical model for the transmission dynamics of HIV/AIDS and COVID-19 co-infection that incorporates protection and treatment for the infected (and infectious) groups is formulated and analyzed. Firstly, we proved the non-negativity and boundedness of the co-infection model solutions, analyzed the single infection models steady states, calculated the basic reproduction numbers using next generation matrix approach and then investigated the existence and local stabilities of equilibriums using Routh-Hurwiz stability criteria. Then using the Center Manifold criteria to investigate the proposed model exhibited the phenomenon of backward bifurcation whenever its effective reproduction number is less than unity. Secondly, we incorporate time dependent optimal control strategies, using Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. Finally, we carried out numerical simulations for both the deterministic model and the model incorporating optimal controls and we found the results that the model solutions are converging to the model endemic equilibrium point whenever the model effective reproduction number is greater than unity, and also from numerical simulations of the optimal control problem applying the combinations of all the possible protection and treatment strategies together is the most effective strategy to drastically minimizing the transmission of the HIV/AIDS and COVID-19 co-infection in the community under consideration of the study.

Mathematical analysis of the transmission dynamics of COVID-19 infection in the presence of intervention strategies

The novel Coronavirus (COVID-19) infection has become a global public health issue, and it has been a cause for morbidity and mortality of more people throughout the world. In this paper, we investigated the impacts of vaccination, other protection measures, home quarantine with treatment, and hospital quarantine with treatment strategies simultaneously using a deterministic mathematical modelling approach. No one has considered these intervention strategies simultaneously in his/her modelling approach. We examined all the qualitative properties of the model such as the positivity and boundedness of the model solutions, the disease-free and endemic equilibrium points, the effective reproduction number using next-generation matrix method, local stabilities of equilibrium points using the Routh-Hurwitz method. Using the Centre Manifold criteria, we have shown the existence of backward bifurcation whenever the COVID-19 effective reproduction number is less than unity. Moreover, we have analysed both sensitivity and numerical simulation using parameter values taken from published literature. The numerical results show that the transmission rate is the most sensitive parameter we have to control. Also vaccination, other protection measures, home quarantine with treatment, and hospital quarantine with treatment have great effects to minimize the COVID-19 transmission in the community.

Optimal control and cost-effectiveness analysis for a COVID-19 model with individual protection awareness

This paper is focused on the design of optimal control strategies for COVID-19 and the model containing susceptible individuals with awareness of protection and susceptible individuals without awareness of protection is established. The goal of this paper is to minimize the number of infected people and susceptible individuals without protection awareness, and to increase the willingness of susceptible individuals to take protection measures. We conduct a qualitative analysis of this mathematical model. Based on the sensitivity analysis, the optimal control method is proposed, namely personal protective measures, vaccination and awareness raising programs. It is found that combining the three methods can minimize the number of infected people. Moreover, the introduction of awareness raising program in society will greatly reduce the existence of susceptible individuals without protection awareness. To evaluate the most cost-effective strategy we performed a cost-effectiveness analysis using the ICER method.

A fractional order control model for Diabetes and COVID-19 co-dynamics with Mittag-Leffler function☆

The aim of this paper is to present and analyze the fractional optimal control model for COVID-19 and diabetes co-dynamics, using the Atangana-Baleanu derivative. The positivity and boundedness of the solutions was shown by the method of Laplace transform. The existence and uniqueness of the solutions of the proposed model were established using Banach fixed point Theorem and Leray–Schauder alternative Theorem. The fractional model was also shown to be Hyers-Ulam stable. The model was fitted to the cumulative confirmed daily COVID-19 cases for Indonesia. The simulations of the total number of hospitalized individuals co-infected with COVID-19 and diabetes, at different face-mask compliance levels, when vaccination strategy is maintained reveals that the total number of hospitalized co-infection cases decreases with increase in face-mask compliance levels, while maintaining COVID-19 vaccination. The simulation results show that to curtail COVID-19 and diabetes co-infections, policies and measures to enforce mass COVID-19 vaccination and strict face-mask usage in the public must be put in place. To further cut down the spread of COVID-19 and diabetes co-infection, time dependent controls are added into the fractional model, and the obtained optimal control problem investigated via the Pontryagin’s Maximum Principle.

A stochastically perturbed co-infection epidemic model for COVID-19 and hepatitis B virus

A new co-infection model for the transmission dynamics of two virus hepatitis B (HBV) and coronavirus (COVID-19) is formulated to study the effect of white noise intensities. First, we present the model equilibria and basic reproduction number. The local stability of the equilibria points is proved. Moreover, the proposed stochastic model has been investigated for a non-negative solution and positively invariant region. With the help of Lyapunov function, analysis was performed and conditions for extinction and persistence of the disease based on the stochastic co-infection model were derived. Particularly, we discuss the dynamics of the stochastic model around the disease-free state. Similarly, we obtain the conditions that fluctuate at the disease endemic state holds if min ( R H s , R C s , R HC s ) > 1 . Based on extinction as well as persistence some conditions are established in form of expression containing white noise intensities as well as model parameters. The numerical results have also been used to illustrate our analytical results.

A fractional-order multi-vaccination model for COVID-19 with non-singular kernel

This work examines the impact of multiple vaccination strategies on the dynamics of COVID-19 in a population using the Atangana-Baleanu derivative. The existence and uniqueness of solution of the model is proven using Banach’s fixed point theorem. Local and global asymptotic stability of the equilibria of the model is also proven (under some conditions). Conditions for the existence of a unique or multiple equilibria are also derived and the model is shown to undergo backward bifurcation under certain scenarios. Using available data for the Pfizer, Moderna and Janssen vaccination programme for the city of Texas, United States of America from March 13, 2021 to June 29, 2021, the model is fitted using the three data sets. The three vaccination rates ν1,ν2 and ν3 corresponding to each vaccine as well as the effective contact rate for COVID-19 transmission, β, are estimated. Simulations of the model under different vaccination strategies are carried out. The results show that the three vaccination strategies not only cause significant reduction in the new asymptomatic and vaccinated symptomatic cases but also cause great decrease in the total number of vaccinated symptomatic individuals with severe COVID-19 illness.

A Systematic Review of Economic Evaluations of COVID-19 Interventions: Considerations of Non-Health Impacts and Distributional Issues

OBJECTIVES

This study aims to conduct a systematic review of economic evaluations of COVID-19 interventions and to examine whether and how these studies incorporate non-health impacts and distributional concerns.

METHODS

We searched the National Institutes of Health's COVID-19 Portfolio as of May 20, 2021, and supplemented our search with additional sources. We included original articles, including preprints, evaluating both the health and economic effects of a COVID-19-related intervention. Using a pre-specified data collection form, 2 reviewers independently screened, reviewed, and extracted information about the study characteristics, intervention types, and incremental cost-effectiveness ratios (ICERs). We used an Impact Inventory to catalog the types of non-health impacts considered.

RESULTS

We included 70 articles, almost half of which were preprints. Most articles (56%) included at least one non-health impact, but fewer (21%) incorporated non-economic consequences. Few articles (17%) examined subgroups of interest. After excluding negative ICERs, the median ICER for the entire sample (n = 243 ratios) was $67,000/quality-adjusted life-year (QALY) (interquartile range [IQR] $9000-$893,000/QALY). Interventions including a pharmaceutical component yielded a median ICER of $93,000/QALY (IQR $4000-$7,809,000/QALY), whereas interventions including a non-pharmaceutical component were slightly more cost-effective overall with a median ICER of $81,000/QALY (IQR $12,000-$1,034,000/QALY). Interventions reported to be highly cost-effective were treatment, public information campaigns, quarantining identified contacts/cases, canceling public events, and social distancing.

CONCLUSIONS

Our review highlights the lack of consideration of non-health and distributional impacts among COVID-19-related economic evaluations. Accounting for non-health impacts and distributional effects is essential for comprehensive assessment of interventions' value and imperative for generating cost-effectiveness evidence for both current and future pandemics.

Optimal control model for criminal gang population in a limited-resource setting

In this present paper, the principles of optimal control theory is applied to a non-linear mathematical model for the population dynamics of criminal gangs with variability in the sub-population. To decrease (minimize) the progression rate of susceptible populations with no access to crime prevention programs from joining criminal gangs and increase (maximize) the rate of arrested and prosecution of criminals, we incorporate time-dependent control functions. These two functions represent the crime prevention strategy for the susceptible population and case finding control for the criminal gang population, in a limited-resource setting. Furthermore, we present a cost-effectiveness analysis for crime control intervention-related benefits to ascertain the most cost-effective and efficient optimal control strategy. The optimal control functions presented herein are solved by employing the Runge-Kutta Method of order four. Numerical results are demonstrated for different scenarios to exemplify the impact of the controls on the criminal gangs’ population.

Cost-effectiveness of interventions for the prevention and control of COVID-19: Systematic review of 85 modelling studies

Background

We aimed to quantitatively summarise the health economic evaluation evidence of prevention and control programs addressing COVID-19 globally.

Methods

We did a systematic review and meta-analysis to assess the economic and health benefit of interventions for COVID-19. We searched PubMed, Embase, Web of Science, and Cochrane Library of economic evaluation from December 31, 2019, to March 22, 2022, to identify relevant literature. Meta-analyses were done using random-effects models to estimate pooled incremental net benefit (INB). Heterogeneity was assessed using I2 statistics and publication bias was assessed by Egger's test. This study is registered with PROSPERO, CRD42021267475.

Results

Of 16 860 studies identified, 85 articles were included in the systematic review, and 25 articles (10 studies about non-pharmacological interventions (NPIs), five studies about vaccinations and 10 studies about treatments) were included in the meta-analysis. The pooled INB of NPIs, vaccinations, and treatments were $1378.10 (95% CI = $1079.62, $1676.59), $254.80 (95% CI = $169.84, $339.77) and $4115.11 (95% CI = $1631.09, $6599.14), respectively. Sensitivity analyses showed similar findings.

Conclusions

NPIs, vaccinations, and treatments are all cost-effective in combating the COVID-19 pandemic. However, evidence was mostly from high-income and middle-income countries. Further studies from lower-income countries are needed.

Backward bifurcation and optimal control in a co-infection model for SARS-CoV-2 and ZIKV

In co-infection models for two diseases, it is mostly claimed that, the dynamical behavior of the sub-models usually predict or drive the behavior of the complete models. However, under a certain assumption such as, allowing incident co-infection with both diseases, we have a different observation. In this paper, a new mathematical model for SARS-CoV-2 and Zika co-dynamics is presented which incorporates incident co-infection by susceptible individuals. It is worth mentioning that the assumption is missing in many existing co-infection models. We shall discuss the impact of this assumption on the dynamics of a co-infection model. The model also captures sexual transmission of Zika virus. The positivity and boundedness of solution of the proposed model are studied, in addition to the local asymptotic stability analysis. The model is shown to exhibit backward bifurcation caused by the disease-induced death rates and parameters associated with susceptibility to a second infection by those singly infected. Using Lyapunov functions, the disease free and endemic equilibria are shown to be globally asymptotically stable for R 0 1 , respectively. To manage the co-circulation of both infections effectively, under an endemic setting, time dependent controls in the form of SARS-CoV-2, Zika and co-infection prevention strategies are incorporated into the model. The simulations show that SARS-CoV-2 prevention could greatly reduce the burden of co-infections with Zika. Furthermore, it is also shown that prevention controls for Zika can significantly decrease the burden of co-infections with SARS-CoV-2.

Global analysis of a time fractional order spatio-temporal SIR model

We deal in this paper with a diffusive SIR epidemic model described by reaction–diffusion equations involving a fractional derivative. The existence and uniqueness of the solution are shown, next to the boundedness of the solution. Further, it has been shown that the global behavior of the solution is governed by the value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document}R0, which is known in epidemiology by the basic reproduction number. Indeed, using the Lyapunov direct method it has been proved that the disease will extinct for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ R_0 <1 $$\end{document}R0<1 for any value of the diffusion constants. For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0>1$$\end{document}R0>1, the disease will persist and the unique positive equilibrium is globally stable. Some numerical illustrations have been used to confirm our theoretical results.

Optimal control and comprehensive cost-effectiveness analysis for COVID-19

Cost-effectiveness analysis is a mode of determining both the cost and economic health outcomes of one or more control interventions. In this work, we have formulated a non-autonomous nonlinear deterministic model to study the control of COVID-19 to unravel the cost and economic health outcomes for the autonomous nonlinear model proposed for the Kingdom of Saudi Arabia. We calculated the strength number and noticed the strength number is less than zero, meaning the proposed model does not capture multiple waves, hence to capture multiple wave new compartmental model may require for the Kingdom of Saudi Arabia. We proposed an optimal control problem based on a previously studied model and proved the existence of the proposed optimal control model. The optimality system associated with the non-autonomous epidemic model is derived using Pontryagin's maximum principle. The optimal control model captures four time-dependent control functions, thus,u 1 -practising physical or social distancing protocols;u 2 -practising personal hygiene by cleaning contaminated surfaces with alcohol-based detergents;u 3 -practising proper and safety measures by exposed, asymptomatic and symptomatic infected individuals;u 4 -fumigating schools in all levels of education, sports facilities, commercial areas and religious worship centres. We have performed numerical simulations to investigate extensive cost-effectiveness analysis for fourteen optimal control strategies. Comparing the control strategies, we noticed that; Strategy 1 (practising physical or social distancing protocols) is the most cost-saving and most effective control intervention in Saudi Arabia in the absence of vaccination. But, in terms of the infection averted, we saw that strategy 6, strategy 11, strategy 12, and strategy 14 are just as good in controlling COVID-19.

A fractional-order model for COVID-19 and tuberculosis co-infection using Atangana-Baleanu derivative

This paper considers and analyzes a fractional order model for COVID-19 and tuberculosis co-infection, using the Atangana-Baleanu derivative. The existence and uniqueness of the model solutions are established by applying the fixed point theorem. It is shown that the model is locally asymptotically stable when the reproduction number is less than one. The global stability analysis of the disease free equilibrium points is also carried out. The model was simulated using data relevant to both diseases in New Delhi, India. Fitting the model to the cumulative confirmed COVID-19 cases for New Delhi from March 1, 2021 to June 26, 2021, COVID-19 and TB contact rates and some other important parameters of the model are estimated. The numerical method used combines the two-step Lagrange polynomial and the fundamental theorem of fractional calculus and has been shown to be highly accurate and efficient, user-friendly and converges quickly to the exact solution even with a large step of discretization. Simulations of the Fractional order model revealed that reducing the risk of COVID-19 infection by latently-infected TB individuals will not only bring down the burden of COVID-19, but will also reduce the co-infection of both diseases in the population. Also, the conditions for the co-existence or elimination of both diseases from the population are established.

Modeling the effects of preventive measures and vaccination on the COVID-19 spread in Benin Republic with optimal control

Coronavirus disease (COVID-19) onset in December 2019 is a contagious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Since, the spread of the virus and mortality due to COVID-19 have continued to increase daily leading to a pandemic. In absence of approved medicine and vaccines, many countries imposed policies such as social distancing, mask wearing, hand washing, airport screening, quarantine and others. But rapidly, they were confronted with the high economic and social cost resulting from those policies. Many vaccines have been proposed but their efficiency is still controversial. Now, governments and scholars search for how manage with preventives measures policies and vaccination campaigns to stop the COVID-19 spread. This work studied the effects of these different strategies as time-dependent interventions using mathematical modeling and optimal control approach to ascertain their contribution in the dynamic transmission of COVID-19. The model was proven to have an invariant region and was well-posed. The basic reproduction number was computed with and without respect of preventives measures. The optimal control analysis was carried out using the Pontryagin's maximum principle to figure out the optimal strategy necessary to curtail the disease. The findings revealed that the optimal implementation of preventive measures reduce highly the number of infected individuals but zero infection was not achieved in the population. That was obtained with the optimal implementation of vaccination campaigns which reduce the number of infected individuals. But the optimal and combined implementation of the two interventions performed better with less costs than the two singular implementations.

The Long-Term Characteristics of Immunity Conferred by COVID-19 Using Antibody Tests

Introduction

Since December 2019, more than 184 Million cases and 3.97 Million COVID-19 related deaths have been reported around the world. Since these statistics are laboratory-based confirmed cases, the true burden of disease may be underestimated. Many populations like those who are regularly visiting health care facilities and those with end-stage renal disease (ESRD) for visiting dialysis units, patients with malignancies, on regular chemo and radiotherapy, and healthcare workers (HCW) are considered high risk for nosocomial COVID-19 re-infections.

Objective

To understand the long-term behaviour and protective efficacy of already formed anti-SARS-CoV-2 antibody against spike-S protein and nucleocapsid antigen in different populations keeping in view their risk of re-exposure and re-infection is high. To delineate seropositivity with respect to age, gender, and other co-morbidities like diabetes mellitus (DM), hypertension (HTN), and chronic kidney disease (CKD)/ESRD as well as the general population.

Methodology

During the study, 480 cases of COVID-19 with a post-exposure antibody reactive were followed. These patients were followed on telemedicine for the development of reinfection symptoms and persistence of antibody response. Around 115 patients agreed for regular monitoring of their immunity against the COVID-19 virus through testing through the anti-SARS-CoV-2 antibody test. The rest of the patients were followed on telemedicine until the date of development of any re-infection, but none reported to have typical symptoms of COVID-19 along with positive polymerase chain reaction (PCR).

Results

Among 115 patients, the mean age was 42.44 + 15.755 years. 61.7% of patients were males and 66.1% were non-health workers while 26.1% of patients had DM/HTN or both. Among these patients, 76.5% had mild/no symptoms and antibodies were found present among 51.3% patients for 3-6 months. Only 2.6% of patients were re-infected. Significant association (p<0.05) of age was found with re-infection while insignificant association (p>0.05) of sex, co-morbidities, profession, symptoms, and persistence of antibodies with re-infection.

Conclusion

The study concluded that natural immune response was adequate to protect against reinfection as long as more than 9 months. It was more pronounced among patients with ESRD and those with severe disease. Surprisingly, among patients with haematological malignancies, either there was no seropositivity or a very weak positive antibody response. All other malignancies had similar seropositivity behaviour compared to the general population or other co-morbidity like DM, HTN, and coronary artery disease (CAD).