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

Deciphering the enigma of Lassa virus transmission dynamics and strategies for effective epidemic control through awareness campaigns and rodenticides

This study aims to formulate a mathematical framework to examine how the Lassa virus spreads in humans of opposite genders. The stability of the model is analyzed at an equilibrium point in the absence of the Lassa fever. The model's effectiveness is evaluated using real-life data, and all the parameters needed to determine the basic reproduction number are estimated. Sensitivity analysis is performed to pinpoint the crucial parameters significantly influencing the spread of the infection. The interaction between threshold parameters and the basic reproduction number is simulated. Control theory is employed to devise and evaluate strategies, such as awareness campaigns, advocating condom usage, and deploying rodenticides to reduce the possibility of virus transmission efficiently.

A novel collocation method with a coronavirus optimization algorithm for the optimal control of COVID-19: A case study of Wuhan, China

In this study, we develop a numerical optimization approach to address the challenge of optimal control in the spread of COVID-19. We evaluate the impact of various control strategies aimed at reducing the number of exposed and infectious individuals. Our novel approach employs Legendre wavelets, their derivative operational matrix, and a collocation method to transform the COVID-19 transmission optimal control model into a nonlinear programming (NLP) problem. To solve this problem, we employ a coronavirus optimization algorithm (COVIDOA) to determine the optimal control, state variables, and objective value. We investigate three control plans for this highly contagious disease, focusing on individual protection, rapid detection and treatment, detection with delay in treatment, and environmental viral dispersion as time-based control functions. These strategies are applied within an SEIR-type control model specific to COVID-19 in China, designed to mitigate disease spread. Lastly, we analyze the effects of various parameters within the COVID-19 spread model. Our numerical results highlight the significant impact of strategies that minimize the number of exposed and infectious individuals, particularly those related to rapid detection, detection delay, and environmental viral dispersion, in controlling and preventing the transmission of the COVID-19 virus.

Optimal control strategies for toxoplasmosis disease transmission dynamics via harmonic mean-type incident rate

Toxoplasma infection in humans is considered due to direct contact with infected cats. Toxoplasma infection (an endemic disease) has the potential to affect various organs and systems (brain, eyes, heart, lungs, liver, and lymph nodes). Bilinear incidence rate and constant population (birth rate is equal to death rate) are used in the literature to explain the dynamics of Toxoplasmosis disease transmission in humans and cats. The goal of this study is to consider the mathematical model of Toxoplasma disease with harmonic mean type incident rate and also consider that the population of humans and cats is not equal (birth rate and the death rate are not equal). In examining Toxoplasma transmission dynamics in humans and cats, harmonic mean incidence rates are better than bilinear incidence rates. The disease dynamics are first schematically illustrated, and then the law of mass action is applied to obtain nonlinear ordinary differential equations (ODEs). Analysis of the boundedness, positivity, and equilibrium points of the system has been analyzed. The reproduction number is calculated using the next-generation matrix technique. The stability of disease-free and endemic equilibrium are analyzed. Sensitivity analysis is also done for reproduction number. Numerical simulation shows that the infection is spread in the population when the contact rate β h and β c increases while the infection is reduced when the recovery rate δ h increases. This study investigates the impact of various optimal control strategies, such as vaccinations for the control of disease and the awareness of disease awareness, on the management of disease.

Optimal control and cost-effectiveness analysis for the human melioidosis model

In this work, we formulated and investigated an optimal control problem of the melioidosis epidemic to explain the effectiveness of time-dependent control functions in controlling the spread of the epidemic. The basic reproduction number ( R 0 c ) with control measures is obtained, using the next-generation matrix approach and the impact of the controls on R 0 c is illustrated numerically. The optimal control problem is analyzed using Pontryagin's maximum principle to derive the optimality system. The optimality system is simulated using the forward-backward sweep method based on the fourth-order Runge-Kutta method in the MATLAB program to illustrate the impact of all the possible combinations of the control interventions on the transmission dynamics of the disease. The numerical results indicate that among strategies considered, strategy C is shown to be the most effective in reducing the number of infectious classes compared to both strategy A and strategy B. Furthermore, we carried out a cost-effectiveness analysis to determine the most cost-effective strategy and the result indicated that the strategy B (treatment control strategy) should be recommended to mitigate the spread and impact of the disease regarding the costs of the strategies.

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.

A mathematical model for the impact of disinfectants on the control of bacterial diseases

Here, we investigate a mathematical model to assess the impact of disinfectants in controlling diseases that spread in the population via direct contacts with the infected persons and also due to bacteria present in the environment. We find that the disease-free and endemic equilibria of the system are related via a transcritical bifurcation whose direction is forward. Our numerical results show that controlling the transmissions of disease through direct contacts and bacteria present in the environment can help in reducing the disease prevalence. Moreover, fostering the recovery rate and the death rate of bacteria play significant roles in disease eradication. Our numerical observations convey that reducing the bacterial density at the source discharged by the infected population through the use of chemicals has prominent effect in disease control. Overall, our findings manifest that the disinfectants of high quality can completely control the bacterial density and the disease outbreak.

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.

The stability analysis of a co-circulation model for COVID-19, dengue, and zika with nonlinear incidence rates and vaccination strategies

This paper aims to study the impacts of COVID-19 and dengue vaccinations on the dynamics of zika transmission by developing a vaccination model with the incorporation of saturated incidence rates. Analyses are performed to assess the qualitative behavior of the model. Carrying out bifurcation analysis of the model, it was concluded that co-infection, super-infection and also re-infection with same or different disease could trigger backward bifurcation. Employing well-formulated Lyapunov functions, the model's equilibria are shown to be globally stable for a certain scenario. Moreover, global sensitivity analyses are performed out to assess the impact of dominant parameters that drive each disease's dynamics and its co-infection. Model fitting is performed on the actual data for the state of Amazonas in Brazil. The fittings reveal that our model behaves very well with the data. The significance of saturated incidence rates on the dynamics of three diseases is also highlighted. Based on the numerical investigation of the model, it was observed that increased vaccination efforts against COVID-19 and dengue could positively impact zika dynamics and the co-spread of triple infections.

A non-linear mathematical model for analysing the impact of COVID-19 disease on higher education in developing countries

This study proposes a non-linear mathematical model for analysing the effect of COVID-19 dynamics on the student population in higher education institutions. The theory of positivity and boundedness of solution is used to investigate the well-posedness of the model. The disease-free equilibrium solution is examined analytically. The next-generation operator method calculates the basic reproduction number ( R 0 ) . Sensitivity analyses are carried out to determine the relative importance of the model parameters in spreading COVID-19. In light of the sensitivity analysis results, the model is further extended to an optimal control problem by introducing four time-dependent control variables: personal protective measures, quarantine (or self-isolation), treatment, and management measures to mitigate the community spread of COVID-19 in the population. Simulations evaluate the effects of different combinations of the control variables in minimizing COVID-19 infection. Moreover, a cost-effectiveness analysis is conducted to ascertain the most effective and least expensive strategy for preventing and controlling the spread of COVID-19 with limited resources in the student population.

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.

A national risk analysis model (NRAM) for the assessment of COVID-19 epidemic

COVID-19 has caused a critical health concern and severe economic crisis worldwide. With multiple variants, the epidemic has triggered waves of mass transmission for nearly 3 years. In order to coordinate epidemic control and economic development, it is important to support decision-making on precautions or prevention measures based on the risk analysis for different countries. This study proposes a national risk analysis model (NRAM) combining Bayesian network (BN) with other methods. The model is built and applied through three steps. (1) The key factors affecting the epidemic spreading are identified to form the nodes of BN. Then, each node can be assigned state values after data collection and analysis. (2) The model (NRAM) will be built through the determination of the structure and parameters of the network based on some integrated methods. (3) The model will be applied to scenario deduction and sensitivity analysis to support decision-making in the context of COVID-19. Through the comparison with other models, NRAM shows better performance in the assessment of spreading risk at different countries. Moreover, the model reveals that the higher education level and stricter government measures can achieve better epidemic prevention and control effects. This study provides a new insight into the prevention and control of COVID-19 at the national level.

Measuring the clustering effect of the SARS-CoV-2 transmission in a school population: a cross-sectional study in a high incidence region

Since the beginning of the pandemic, there has been a great deal of controversy regarding the role of schools in the spread of SARS-CoV-2 infection, and the relative contribution of students, teachers, and others. To quantify the clustering effect of SARS-CoV-2 infection within classes and schools considering the seroprevalence of specific antibodies among students and school staff (teachers and non-teachers) evaluated in schools located in the Northern region of Portugal. 1517 individuals (1307 students and 210 school staff) from 4 public and 2 private schools, comprising daycare to secondary levels, were evaluated. A rapid point-of-care test for SARS-CoV-2 specific IgM and IgG antibodies was performed and a questionnaire was completed providing sociodemographic and clinical information. We calculated the seroprevalence of IgM and IgG antibodies and estimated the Median Odds Ratio (OR) and 95% confidence interval (CI) to assess the clustering effect, using a multilevel (school and class) logistic regression. SARS-CoV-2 seroprevalence (IgM or IgG) was 21.8% and 23.8% (p = 0.575) in students and school staff, respectively. A total of 84 (8.6%) students and 35 (16.7%) school staff reported a previous molecular diagnosis. Among students, those who reported high-risk contacts only at school (OR = 1.13; 95% CI 0.72-1.78) had a seroprevalence similar to those without high-risk contacts; however, seroprevalence was significantly higher among those who only reported a high-risk contact outside the school (OR = 6.56; 95% CI 3.68-11.72), or in both places (OR = 7.83; 95% CI 5.14-11.93). Similar associations were found for school staff. The median OR was 1.00 (95% CI 1.00, 1.38) at the school-level and 1.78 (95% CI 1.40, 2.06) at the class-level. SARS-CoV-2 seroprevalence was similar between students and staff, without a clustering effect observed at the school level, and only a moderate clustering effect documented within classes. These results indicate that the mitigation measures in the school environment can prevent the spread of class outbreaks to the remaining school community.

A hierarchical intervention scheme based on epidemic severity in a community network

As there are no targeted medicines or vaccines for newly emerging infectious diseases, isolation among communities (villages, cities, or countries) is one of the most effective intervention measures. As such, the number of intercommunity edges ([Formula: see text]) becomes one of the most important factor in isolating a place since it is closely related to normal life. Unfortunately, how [Formula: see text] affects epidemic spread is still poorly understood. In this paper, we quantitatively analyzed the impact of [Formula: see text] on infectious disease transmission by establishing a four-dimensional [Formula: see text] edge-based compartmental model with two communities. The basic reproduction number [Formula: see text] is explicitly obtained subject to [Formula: see text] [Formula: see text]. Furthermore, according to [Formula: see text] with zero [Formula: see text], epidemics spread could be classified into two cases. When [Formula: see text] for the case 2, epidemics occur with at least one of the reproduction numbers within communities greater than one, and otherwise when [Formula: see text] for case 1, both reproduction numbers within communities are less than one. Remarkably, in case 1, whether epidemics break out strongly depends on intercommunity edges. Then, the outbreak threshold in regard to [Formula: see text] is also explicitly obtained, below which epidemics vanish, and otherwise break out. The above two cases form a severity-based hierarchical intervention scheme for epidemics. It is then applied to the SARS outbreak in Singapore, verifying the validity of our scheme. In addition, the final size of the system is gained by demonstrating the existence of positive equilibrium in a four-dimensional coupled system. Theoretical results are also validated through numerical simulation in networks with the Poisson and Power law distributions, respectively. Our results provide a new insight into controlling epidemics.

A simulation of undiagnosed population and excess mortality during the COVID-19 pandemic

Whereas the extent of outbreak of COVID-19 is usually accessed via the number of reported cases and the number of patients succumbed to the disease, the officially recorded overall excess mortality numbers during the pandemic waves, which are significant and often followed the rise and fall of the pandemic waves, put a question mark on the above methodology. Gradually it has been recognized that estimating the size of the undiagnosed population (which includes asymptomatic cases and symptomatic cases but not reported) is also crucial. Here we used the classical mathematical SEIR model having an additional compartment, that is the undiagnosed group in addition to the susceptible, exposed, diagnosed, recovered and deceased groups, to link the undiagnosed COVID-19 cases to the reported excess mortality numbers and thereby try to know the actual size of the disease outbreak. The developed model wase successfully applied to relevant COVID-19 waves in USA (initial months of 2020), South Africa (mid of 2021) and Russia (2020–21) when a large discrepancy between the reported COVID-19 mortality and the overall excess mortality had been noticed.

Quantitative evaluation of the role of Fangcang shelter hospitals in the control of Omicron transmission: A case study of the outbreak in Shanghai, China in 2022

Since Omicron began to spread in China, Shanghai has become one of the cities with more severe outbreaks. Under the comprehensive consideration of the vaccine coverage rate, the number of Fangcang shelter hospital beds and the number of designated hospital beds in Shanghai, this paper established a deterministic compartmental model and used the Nelder-Mead Simplex Direct Search Algorithm and chi-square values to estimate the model parameters. we calculate ℛ0 = 3.6429 when the number of beds in the Fangcang shelter hospital is relatively tight in the second stage and ℛ0 = 0.4974 in the fifth stage when there are enough beds in both Fangcang shelter hospital and designated hospital. Then we perform a sensitivity analysis on ℛ0 by using perturbation of fixed point estimation of model parameters in the fifth stage, and obtain three parameters that are more sensitive to ℛ0, which are transmission rate (β 1d ), proportion of the infectious (η) and the hospitalization rate of asymptomatic infected cases (δ 1). Through simulation, we obtain that if the hospitalization rate of asymptomatic infections δ 2 > 0.9373 or the transmission rate β 1b  < 0.0467, the second stage of Omicron transmission in Shanghai can be well controlled. Finally, we find the measure that converting the National Convention and Exhibition Center (NECC) into a Fangcang shelter hospital has played an important role in curbing the epidemic. Whether this temporary Fangcang shelter hospital is not built or delayed, the cumulative number of confirmed cases will both exceed 100,000, and the cumulative asymptomatic infections will both exceed 1 million. In addition, for a city of 10 million people, we obtain that if a permanent Fangcang shelter hospital with 17,784 beds is built ahead of epidemic, there will be no shortage of beds during the outbreak of Omicron. Our findings enrich the content of the impact of Fangcang shelter hospital beds on the spread of Omicron and confirm the correct policy adopted by the Chinese government.

Forecast for peak infections in the second wave of the Omicron after the adjustment of zero-COVID policy in the mainland of China

On December 7, 2022, the Chinese government optimized the current epidemic prevention and control policy, and no longer adopted the zero-COVID policy and mandatory quarantine measures. Based on the above policy changes, this paper establishes a compartment dynamics model considering age distribution, home isolation and vaccinations. Parameter estimation was performed using improved least squares and Nelder-Mead simplex algorithms combined with modified case data. Then, using the estimated parameter values to predict a second wave of the outbreak, the peak of severe cases will reach on 8 May 2023, the number of severe cases will reach 206,000. Next, it is proposed that with the extension of the effective time of antibodies obtained after infection, the peak of severe cases in the second wave of the epidemic will be delayed, and the final scale of the disease will be reduced. When the effectiveness of antibodies is 6 months, the severe cases of the second wave will peak on July 5, 2023, the number of severe cases is 194,000. Finally, the importance of vaccination rates is demonstrated, when the vaccination rate of susceptible people under 60 years old reaches 98%, and the vaccination rate of susceptible people over 60 years old reaches 96%, the peak of severe cases in the second wave of the epidemic will be reached on 13 July 2023, when the number of severe cases is 166,000.

Studying of COVID-19 fractional model: Stability analysis

This article focuses on the recent epidemic caused by COVID-19 and takes into account several measures that have been taken by governments, including complete closure, media coverage, and attention to public hygiene. It is well known that mathematical models in epidemiology have helped determine the best strategies for disease control. This motivates us to construct a fractional mathematical model that includes quarantine categories as well as government sanctions. In this article, we prove the existence and uniqueness of positive bounded solutions for the suggested model. Also, we investigate the stability of the disease-free and endemic equilibriums by using the basic reproduction number (BRN). Moreover, we investigate the stability of the considering model in the sense of Ulam-Hyers criteria. To underpin and demonstrate this study, we provide a numerical simulation, whose results are consistent with the analysis presented in this article.

A stochastic agent-based model to evaluate COVID-19 transmission influenced by human mobility

The COVID-19 pandemic has created an urgent need for mathematical models that can project epidemic trends and evaluate the effectiveness of mitigation strategies. A major challenge in forecasting the transmission of COVID-19 is the accurate assessment of the multiscale human mobility and how it impacts infection through close contacts. By combining the stochastic agent-based modeling strategy and hierarchical structures of spatial containers corresponding to the notion of geographical places, this study proposes a novel model, Mob-Cov, to study the impact of human traveling behavior and individual health conditions on the disease outbreak and the probability of zero-COVID in the population. Specifically, individuals perform power law-type local movements within a container and global transport between different-level containers. It is revealed that frequent long-distance movements inside a small-level container (e.g., a road or a county) and a small population size reduce both the local crowdedness and disease transmission. It takes only half of the time to induce global disease outbreaks when the population increases from 150 to 500 (normalized unit). When the exponent c 1 of the long-tail distribution of distance k moved in the same-level container, p ( k ) ∼ k - c 1 · level , increases, the outbreak time decreases rapidly from 75 to 25 (normalized unit). In contrast, travel between large-level containers (e.g., cities and nations) facilitates global spread of the disease and outbreak. When the mean traveling distance across containers 1 d increases from 0.5 to 1 (normalized unit), the outbreak occurs almost twice as fast. Moreover, dynamic infection and recovery in the population are able to drive the bifurcation of the system to a "zero-COVID" state or to a "live with COVID" state, depending on the mobility patterns, population number and health conditions. Reducing population size and restricting global travel help achieve zero-COVID-19. Specifically, when c 1 is smaller than 0.2, the ratio of people with low levels of mobility is larger than 80% and the population size is smaller than 400, zero-COVID can be achieved within fewer than 1000 time steps. In summary, the Mob-Cov model considers more realistic human mobility at a wide range of spatial scales, and has been designed with equal emphasis on performance, low simulation cost, accuracy, ease of use and flexibility. It is a useful tool for researchers and politicians to apply when investigating pandemic dynamics and when planning actions against disease.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11071-023-08489-5.

Policy Disparities Between Singapore and Israel in Response to the First Omicron Wave

Purpose

The purpose of this study is to evaluate public health measures during the first Omicron wave in Singapore and Israel to inform other countries confronted by COVID-19 outbreaks.

Methods

A comparative analysis was conducted using epidemiological data from Singapore and Israel between November 25th, 2021 and May 2nd, 2022 and policy information to examine the effects of public health measures in the two countries during the COVID-19 pandemic.

Results

Public health measures implemented by Singapore and Israel in response to the first Omicron wave were primarily intended to mitigate the effects of the COVID-19 pandemic. In Singapore, the pandemic led to more than 910,000 confirmed cases, a mortality rate of approximately 0.047%, a hospitalization rate of approximately 10.95%, and a severe illness rate of approximately 0.48%, without a second peak. In Israel, the pandemic not only resulted in over 2.74 million confirmed cases, a mortality rate of 0.095%, a hospitalization rate of about 7.39%, and a severe illness rate of approximately 2.30% but also returned after the significant relaxation of prevention regulations from March 1st, 2022.

Conclusion

Early and strict border control measures and surveillance measures are more effective in preventing and controlling the rapid spread of new strains of COVID-19 in the early stage. Furthermore, to prevent and control this highly infectious disease, COVID-19 vaccinations and booster shots must be promoted as soon as possible, medical service capacity must be enhanced, the hierarchical medical system must be improved, and non-pharmacological interventions must be implemented.

Modeling SARS-CoV-2 and HBV co-dynamics with optimal control

Clinical reports have shown that chronic hepatitis B virus (HBV) patients co-infected with SARS-CoV-2 have a higher risk of complications with liver disease than patients without SARS-CoV-2. In this work, a co-dynamical model is designed for SARS-CoV-2 and HBV which incorporates incident infection with the dual diseases. Existence of boundary and co-existence endemic equilibria are proved. The occurrence of backward bifurcation, in the absence and presence of incident co-infection, is investigated through the proposed model. It is noted that in the absence of incident co-infection, backward bifurcation is not observed in the model. However, incident co-infection triggers this phenomenon. For a special case of the study, the disease free and endemic equilibria are shown to be globally asymptotically stable. To contain the spread of both infections in case of an endemic situation, the time dependent controls are incorporated in the model. Also, global sensitivity analysis is carried out by using appropriate ranges of the parameter values which helps to assess their level of sensitivity with reference to the reproduction numbers and the infected components of the model. Finally, numerical assessment of the control system using various intervention strategies is performed, and reached at the conclusion that enhanced preventive efforts against incident co-infection could remarkably control the co-circulation of both SARS-CoV-2 and HBV.

Predicting COVID-19 positivity and hospitalization with multi-scale graph neural networks

The pandemic of COVID-19 is undoubtedly one of the biggest challenges for modern healthcare. In order to analyze the spatio-temporal aspects of the spread of COVID-19, technology has helped us to track, identify and store information regarding positivity and hospitalization, across different levels of municipal entities. In this work, we present a method for predicting the number of positive and hospitalized cases via a novel multi-scale graph neural network, integrating information from fine-scale geographical zones of a few thousand inhabitants. By leveraging population mobility data and other features, the model utilizes message passing to model interaction between areas. Our proposed model manages to outperform baselines and deep learning models, presenting low errors in both prediction tasks. We specifically point out the importance of our contribution in predicting hospitalization since hospitals became critical infrastructure during the pandemic. To the best of our knowledge, this is the first work to exploit high-resolution spatio-temporal data in a multi-scale manner, incorporating additional knowledge, such as vaccination rates and population mobility data. We believe that our method may improve future estimations of positivity and hospitalization, which is crucial for healthcare planning.

A dynamic model for elevator operation-induced spread of a respiratory infectious disease in an apartment building

Residents have to use elevators to leave and enter their high-rise apartments frequently. An elevator car can easily spread respiratory infectious diseases, as it has a confined and small space. Therefore, studying how elevator operations promote epidemic transmission is of importance to public health. We developed an infectious disease dynamics model. First, we used homemade codes to simulate the operating state of an elevator and the dynamic process of infectious disease transmission in an apartment building due to elevator operations. Second, we analysed the temporal distribution patterns of infected individuals and patients. Finally, we validated the reliability of the model by performing continuous-time sensitivity analysis on important model parameters. We found that elevator operations can cause rapid spread of infectious diseases within an apartment building. Therefore, it is necessary to enhance elevator ventilation and disinfection mechanisms to prevent the outbreak of respiratory infections. Moreover, residents should reduce elevator use and wear masks.

Global asymptotic stability, extinction and ergodic stationary distribution in a stochastic model for dual variants of SARS-CoV-2

Several mathematical models have been developed to investigate the dynamics SARS-CoV-2 and its different variants. Most of the multi-strain SARS-CoV-2 models do not capture an important and more realistic feature of such models known as randomness. As the dynamical behavior of most epidemics, especially SARS-CoV-2, is unarguably influenced by several random factors, it is appropriate to consider a stochastic vaccination co-infection model for two strains of SARS-CoV-2. In this work, a new stochastic model for two variants of SARS-CoV-2 is presented. The conditions of existence and the uniqueness of a unique global solution of the stochastic model are derived. Constructing an appropriate Lyapunov function, the conditions for the stochastic system to fluctuate around endemic equilibrium of the deterministic system are derived. Stationary distribution and ergodicity for the new co-infection model are also studied. Numerical simulations are carried out to validate theoretical results. It is observed that when the white noise intensities are larger than certain thresholds and the associated stochastic reproduction numbers are less than unity, both strains die out and go into extinction with unit probability. More-over, it is observed that, for weak white noise intensities, the solution of the stochastic system fluctuates around the endemic equilibrium (EE) of the deterministic model. Frequency distributions are also studied to show random fluctuations due to stochastic white noise intensities. The results presented herein also reveal the impact of vaccination in reducing the co-circulation of SARS-CoV-2 variants within a given population.

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.

Estimating the time-dependent effective reproduction number and vaccination rate for COVID-19 in the USA and India

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

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.

Transmission characteristic and dynamic analysis of COVID-19 on contact network with Tianjin city in China

The outbreak of 2019 novel coronavirus pneumonia (COVID-19) has had a profound impact on people's lives around the world, and the spread of COVID-19 between individuals were mainly caused by contact transmission of the social networks. In order to analyze the network transmission of COVID-19, we constructed a case contact network using available contact data of 136 early diagnosed cases in Tianjin. Based on the constructed case contact network, the structural characteristics of the network were first analyzed, and then the centrality of the nodes was analyzed to find the key nodes. In addition, since the constructed network may contain missing edges and false edges, link prediction algorithms were used to reconstruct the network. Finally, to understand the spread of COVID-19 in the network, an individual-based susceptible-latent-exposed-infected-recover (SLEIR) model is established and simulated in the network. The results showed that the disease peak scale caused by the node with the highest centrality is larger, and reducing the contact infection rate of the infected person during the incubation period has a greater impact on the peak disease scale.

Fractal-fractional age-structure study of omicron SARS-CoV-2 variant transmission dynamics

This paper proposes a new fractal-fractional age-structure model for the omicron SARS-CoV-2 variant under the Caputo-Fabrizio fractional order derivative. Caputo-Fabrizio fractal-fractional order is particularly successful in modelling real-world phenomena due to its repeated memory effect and ability to capture the exponentially decreasing impact of disease transmission dynamics. We consider two age groups, the first of which has a population under 50 and the second of a population beyond 50. Our results show that at a population dynamics level, there is a high infection and recovery of omicron SARS-CoV-2 variant infection among the population under 50 (Group-1), while a high infection rate and low recovery of omicron SARS-CoV-2 variant infection among the population beyond 50 (Group-2) when the fractal-fractional order is varied.

A Stochastic Mathematical Model for Understanding the COVID-19 Infection Using Real Data

Natural symmetry exists in several phenomena in physics, chemistry, and biology. Incorporating these symmetries in the differential equations used to characterize these processes is thus a valid modeling assumption. The present study investigates COVID-19 infection through the stochastic model. We consider the real infection data of COVID-19 in Saudi Arabia and present its detailed mathematical results. We first present the existence and uniqueness of the deterministic model and later study the dynamical properties of the deterministic model and determine the global asymptotic stability of the system for R0≤1. We then study the dynamic properties of the stochastic model and present its global unique solution for the model. We further study the extinction of the stochastic model. Further, we use the nonlinear least-square fitting technique to fit the data to the model for the deterministic and stochastic case and the estimated basic reproduction number is R0≈1.1367. We show that the stochastic model provides a good fitting to the real data. We use the numerical approach to solve the stochastic system by presenting the results graphically. The sensitive parameters that significantly impact the model dynamics and reduce the number of infected cases in the future are shown graphically.

What is the role of aerosol transmission in SARS-Cov-2 Omicron spread in Shanghai?

The Omicron transmission has infected nearly 600,000 people in Shanghai from March 26 to May 31, 2022. Combined with different control measures taken by the government in different periods, a dynamic model was constructed to investigate the impact of medical resources, shelter hospitals and aerosol transmission generated by clustered nucleic acid testing on the spread of Omicron. The parameters of the model were estimated by least square method and MCMC method, and the accuracy of the model was verified by the cumulative number of asymptomatic infected persons and confirmed cases in Shanghai from March 26 to May 31, 2022. The result of numerical simulation demonstrated that the aerosol transmission figured prominently in the transmission of Omicron in Shanghai from March 28 to April 30. Without aerosol transmission, the number of asymptomatic subjects and symptomatic cases would be reduced to 130,000 and 11,730 by May 31, respectively. Without the expansion of shelter hospitals in the second phase, the final size of asymptomatic subjects and symptomatic cases might reach 23.2 million and 4.88 million by May 31, respectively. Our results also revealed that expanded vaccination played a vital role in controlling the spread of Omicron. However, even if the vaccination rate were 100%, the transmission of Omicron should not be completely blocked. Therefore, other control measures should be taken to curb the spread of Omicron, such as widespread antiviral therapies, enhanced testing and strict tracking quarantine measures. This perspective could be utilized as a reference for the transmission and prevention of Omicron in other large cities with a population of 10 million like Shanghai.

A Mathematical Model of Vaccinations Using New Fractional Order Derivative

Purpose: This paper studies a simple SVIR (susceptible, vaccinated, infected, recovered) type of model to investigate the coronavirus’s dynamics in Saudi Arabia with the recent cases of the coronavirus. Our purpose is to investigate coronavirus cases in Saudi Arabia and to predict the early eliminations as well as future case predictions. The impact of vaccinations on COVID-19 is also analyzed. Methods: We consider the recently introduced fractional derivative known as the generalized Hattaf fractional derivative to extend our COVID-19 model. To obtain the fitted and estimated values of the parameters, we consider the nonlinear least square fitting method. We present the numerical scheme using the newly introduced fractional operator for the graphical solution of the generalized fractional differential equation in the sense of the Hattaf fractional derivative. Mathematical as well as numerical aspects of the model are investigated. Results: The local stability of the model at disease-free equilibrium is shown. Further, we consider real cases from Saudi Arabia since 1 May−4 August 2022, to parameterize the model and obtain the basic reproduction number R0v≈2.92. Further, we find the equilibrium point of the endemic state and observe the possibility of the backward bifurcation for the model and present their results. We present the global stability of the model at the endemic case, which we found to be globally asymptotically stable when R0v>1. Conclusion: The simulation results using the recently introduced scheme are obtained and discussed in detail. We present graphical results with different fractional orders and found that when the order is decreased, the number of cases decreases. The sensitive parameters indicate that future infected cases decrease faster if face masks, social distancing, vaccination, etc., are effective.

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.

Biruni Index as a Novel Diagnostic Tool for the Early Prediction of Mortality in Critical Patients With COVID-19: A Cohort Study

BACKGROUND

The aim of this study was to find out the potential risk factors associated with mortality in severe coronavirus disease 2019 (COVID-19) patients hospitalized due to viral bronchopneumonia, and to establish a novel COVID-19 mortality index for daily use.

METHODS

The study included 431 quantitative real-time polymerase chain reaction (qRT-PCR)-confirmed COVID-19-positive patients admitted to the intensive care unit in a tertiary care hospital. Patients were divided into training and validation cohorts at random (n= 285 and n= 130, respectively). Biruni Index was developed by multivariate logistic regression analysis for predicting COVID-19-related mortality.

RESULTS

In univariate logistic regression analysis, age, systolic and diastolic blood pressures, respiratory and pulse rates per minute, D-dimer, pH, urea, ferritin, and lactate dehydrogenase levels at first admission were statistically significant factors for the prediction of mortality in the training cohort. By using multivariate logistic regression analysis, all of these statistically significant parameters were used to produce Biruni Index. Statistically significant differences in Biruni Index were observed between ex and non-ex groups in both training and validation cohorts (P < 0.001 for both comparisons). Areas under receiver operating characteristic (ROC) curve for Biruni Index were 0.901 (95CI%: 0.864-0.938, P < 0.001) and 0.860 (95CI%: 0.795-0.926, P < 0.001) in training and validation cohorts, respectively.

CONCLUSION

As a pioneering clinical study, Biruni Index may be a useful diagnostic tool for clinicians to predict the mortality in critically ill patients with COVID-19 hospitalized due to severe viral bronchopneumonia. However, Biruni Index should be validated with larger series of multicenter prospective clinical studies.

An optimal control model for COVID-19, zika, dengue, and chikungunya co-dynamics with reinfection

The co-circulation of different emerging viral diseases is a big challenge from an epidemiological point of view. The similarity of symptoms, cases of virus co-infection, and cross-reaction can mislead in the diagnosis of the disease. In this article, a new mathematical model for COVID-19, zika, chikungunya, and dengue co-dynamics is developed and studied to assess the impact of COVID-19 on zika, dengue, and chikungunya dynamics and vice-versa. The local and global stability analyses are carried out. The model is shown to undergo a backward bifurcation under a certain condition. Global sensitivity analysis is also performed on the parameters of the model to determine the most dominant parameters. If the zika-related reproduction numberℛ 0Z is used as the response function, then important parameters are: the effective contact rate for vector-to-human transmission of zika (β 2 h , which is positively correlated), the human natural death rate (ϑ h , positively correlated), and the vector recruitment rate (Ψ v , also positively correlated). In addition, using the class of individuals co-infected with COVID-19 and zika (ℐ CZ h ) as response function, the most dominant parameters are: the effective contact rate for COVID-19 transmission (β 1 , positively correlated), the effective contact rate for vector-to-human transmission of zika (β 2 h , positively correlated). To control the co-circulation of all the diseases adequately under an endemic setting, time dependent controls in the form of COVID-19, zika, dengue, and chikungunya preventions are incorporated into the model and analyzed using the Pontryagin's principle. The model is fitted to real COVID-19, zika, dengue, and chikungunya datasets for Espirito Santo (a city with the co-circulation of all the diseases), in Brazil and projections made for the cumulative cases of each of the diseases. Through simulations, it is shown that COVID-19 prevention could greatly reduce the burden of co-infections with zika, dengue, and chikungunya. The negative impact of the COVID-19 pandemic on the control of the arbovirus diseases is also highlighted. Furthermore, it is observed that prevention controls for zika, dengue, and chikungunya can significantly reduce the burden of co-infections with COVID-19.

Mathematical modeling for COVID-19 with focus on intervention strategies and cost-effectiveness analysis

The realistic assessments of public health intervention strategies are of great significance to effectively combat the COVID-19 epidemic and the formation of intervention policy. In this paper, an extended COVID-19 epidemic model is devised to assess the severity of the pandemic and explore effective control strategies. The model is characterized by ordinary differential equations with seven-state variables, and it incorporates some parameters associated with the interventions (i.e., media publicity, home isolation, vaccination and face-mask wearing) to investigate the impacts of these interventions on the spread of the COVID-19 epidemic. Some dynamic behaviors of the model, such as forward and backward bifurcation, are analyzed. Specifically, we calibrate the model parameters using actual COVID-19 infected data in Brazil by Markov Chain Monte Carlo algorithm such that we can study the effects of interventions on a practical case. Through a comprehensive exploration of model design and analysis, model calibration, sensitivity analysis, implementation of optimal control problems and cost-effectiveness analysis, the rationality of our model is verified, and the effective strategies to combat the epidemic in Brazil are revealed. The results show that the asymptomatic infected individuals are the main drivers of COVID-19 transmission, and rapid detection of asymptomatic infections is critical to combat the COVID-19 epidemic in Brazil. Interestingly, the effect of the vaccination rate associated with pharmaceutical intervention on the basic reproduction number is much lower than that of non-pharmaceutical interventions (NPIs). Our study also highlights the importance of media publicity. To reduce the infected individuals, the multi-pronged NPIs have considerable positive effects on controlling the outbreak of COVID-19. The infections are significantly decreased by the early implementation of media publicity complemented with home isolation and face-mask wearing strategy. When the cost of implementation is taken into account, the early implementation of media publicity complemented with a face-mask wearing strategy can significantly mitigate the second wave of the epidemic in Brazil. These results provide some management implications for controlling COVID-19.

Turing pattern induced by the directed ER network and delay

Infectious diseases generally spread along with the asymmetry of social network propagation because the asymmetry of urban development and the prevention strategies often affect the direction of the movement. But the spreading mechanism of the epidemic remains to explore in the directed network. In this paper, the main effect of the directed network and delay on the dynamic behaviors of the epidemic is investigated. The algebraic expressions of Turing instability are given to show the role of the directed network in the spread of the epidemic, which overcomes the drawback that undirected networks cannot lead to the outbreaks of infectious diseases. Then, Hopf bifurcation is analyzed to illustrate the dynamic mechanism of the periodic outbreak, which is consistent with the transmission of COVID-19. Also, the discrepancy ratio between the imported and the exported is proposed to explain the importance of quarantine policies and the spread mechanism. Finally, the theoretical results are verified by numerical simulation.

The impact of lockdown in Wuhan on residents confidence in controlling COVID-19 outbreak at the destination cities

Objective

From January 23rd, 2020, lock-down measures were adopted in Wuhan, China to stop the spread of COVID-19. However, due to the approach of the Spring Festival and the nature of COVID-19, more than 6 million permanent and temporary residents of Wuhan (who were potential carriers or spreaders of the virus), left the city before the lock-down measures were implemented. This study aims to explore whether and how the population inflow from Wuhan city impacted residents' confidence in controlling COVID-19 outbreaks at the destination cities.

Study design and setting

Based on questionnaire data and migration big data, a multiple regression model was developed to quantify the impact of the population inflow from Wuhan city on the sense of confidence of residents in controlling the COVID-19 outbreak at the destination cities. Scenarios were considered that varied residents' expected month for controlling COVID-19 outbreak at the destination cities, residents' confidence in controlling COVID-19 outbreak at the destination cities, and the overall indicators for the sense of confidence of residents in controlling COVID-19. A marginal effect analysis was also conducted to calculate the probability of change in residents' confidence in controlling the COVID-19 outbreak with per unit change in the population inflow from Wuhan city.

Results

The impact of population inflow from Wuhan city on residents' expected month for controlling COVID-19 outbreak at the destination cities was positive and significant at the 1% level, while that on residents' confidence in controlling COVID-19 at the destination cities was negative and significant at the 1% level. Robustness checks, which included modifying the sample range and replacing measurement indicators of the population inflow from Wuhan city, demonstrated these findings were robust and credible. When the population inflow from Wuhan city increased by one additional unit, the probabilities of the variables "February" and "March" decreased significantly by 0.1023 and 0.1602, respectively, while the probabilities of "April," "May," "June," "July," "before the end of 2020," and "unknown" significantly increased by 0.0470, 0.0856, 0.0333, 0.0080, 0.0046, and 0.0840, respectively. Similarly, when the population inflow from Wuhan city increased by one additional unit, the probability of the variable "extremely confident" decreased by 0.1973. Furthermore, the probabilities of the variables "confident," "neutral," and "unconfident" significantly increased by 0.1392, 0.0224, and 0.0320, respectively.

Conclusion

The population inflow from Wuhan city played a negative role in the sense of confidence of residents in controlling COVID-19 in the destination cities. The higher the population inflow from Wuhan city, the longer the residents' expected month for controlling COVID-19 outbreak at the destination cities became, and the weaker the residents' confidence in controlling the COVID-19 outbreak at the destination cities.

Unravelling the dynamics of the COVID-19 pandemic with the effect of vaccination, vertical transmission and hospitalization

The coronavirus disease 2019 (COVID-19) is caused by a newly emerged virus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), transmitted through air droplets from an infected person. However, other transmission routes are reported, such as vertical transmission. Here, we propose an epidemic model that considers the combined effect of vertical transmission, vaccination and hospitalization to investigate the dynamics of the virus's dissemination. Rigorous mathematical analysis of the model reveals that two equilibria exist: the disease-free equilibrium, which is locally asymptotically stable when the basic reproduction number ( R 0 ) is less than 1 (unstable otherwise), and an endemic equilibrium, which is globally asymptotically stable when R 0 > 1 under certain conditions, implying the plausibility of the disease to spread and cause large outbreaks in a community. Moreover, we fit the model using the Saudi Arabia cases scenario, which designates the incidence cases from the in-depth surveillance data as well as displays the epidemic trends in Saudi Arabia. Through Caputo fractional-order, simulation results are provided to show dynamics behaviour on the model parameters. Together with the non-integer order variant, the proposed model is considered to explain various dynamics features of the disease. Further numerical simulations are carried out using an efficient numerical technique to offer additional insight into the model's dynamics and investigate the combined effect of vaccination, vertical transmission, and hospitalization. In addition, a sensitivity analysis is conducted on the model parameters against the R 0 and infection attack rate to pinpoint the most crucial parameters that should be emphasized in controlling the pandemic effectively. Finally, the findings suggest that adequate vaccination coupled with basic non-pharmaceutical interventions are crucial in mitigating disease incidences and deaths.

A (2+1)-Dimensional Fractional-Order Epidemic Model with Pulse Jumps for Omicron COVID-19 Transmission and Its Numerical Simulation

In this paper, we would like to propose a (2+1)-dimensional fractional-order epidemic model with pulse jumps to describe the spread of the Omicron variant of COVID-19. The problem of identifying the involved parameters in the proposed model is reduced to a minimization problem of a quadratic objective function, based on the reported data. Moreover, we perform numerical simulation to study the effect of the parameters in diverse fractional-order cases. The number of undiscovered cases can be calculated precisely to assess the severity of the outbreak. The results by numerical simulation show that the degree of accuracy is higher than the classical epidemic models. The regular testing protocol is very important to find the undiscovered cases in the beginning of the outbreak.

Mathematical modeling and optimal control of SARS-CoV-2 and tuberculosis co-infection: a case study of Indonesia

A new mathematical model incorporating epidemiological features of the co-dynamics of tuberculosis (TB) and SARS-CoV-2 is analyzed. Local asymptotic stability of the disease-free and endemic equilibria are shown for the sub-models when the respective reproduction numbers are below unity. Bifurcation analysis is carried out for the TB only sub-model, where it was shown that the sub-model undergoes forward bifurcation. The model is fitted to the cumulative confirmed daily SARS-CoV-2 cases for Indonesia from February 11, 2021 to August 26, 2021. The fitting was carried out using the fmincon optimization toolbox in MATLAB. Relevant parameters in the model are estimated from the fitting. The necessary conditions for the existence of optimal control and the optimality system for the co-infection model is established through the application of Pontryagin’s Principle. Different control strategies: face-mask usage and SARS-CoV-2 vaccination, TB prevention as well as treatment controls for both diseases are considered. Simulations results show that: (1) the strategy against incident SARS-CoV-2 infection averts about 27,878,840 new TB cases; (2) also, TB prevention and treatment controls could avert 5,397,795 new SARS-CoV-2 cases. (3) In addition, either SARS-CoV-2 or TB only control strategy greatly mitigates a significant number of new co-infection cases.

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.

Computing R 0 of dynamic models by a definition-based method

Objectives

Computing the basic reproduction number (R 0) in deterministic dynamical models is a hot topic and is frequently demanded by researchers in public health. The next-generation methods (NGM) are widely used for such computation, however, the results of NGM are usually not to be the true R 0 but only a threshold quantity with little interpretation. In this paper, a definition-based method (DBM) is proposed to solve such a problem.

Methods

Start with the definition of R 0, consider different states that one infected individual may develop into, and take expectations. A comparison with NGM has proceeded. Numerical verification is performed using parameters fitted by data of COVID-19 in Hunan Province.

Results

DBM and NGM give identical expressions for single-host models with single-group and interactive R ij of single-host models with multi-groups, while difference arises for models partitioned into subgroups. Numerical verification showed the consistencies and differences between DBM and NGM, which supports the conclusion that R 0 derived by DBM with true epidemiological interpretations are better.

Conclusions

DBM is more suitable for single-host models, especially for models partitioned into subgroups. However, for multi-host dynamic models where the true R 0 is failed to define, we may turn to the NGM for the threshold R 0.

HIV and COVID-19 co-infection: A mathematical model and optimal control

A new mathematical model for COVID-19 and HIV/AIDS is considered to assess the impact of COVID-19 on HIV dynamics and vice-versa. Investigating the epidemiologic synergy between COVID-19 and HIV is important. The dynamics of the full model is driven by that of its sub-models; therefore, basic analysis of the two sub-models; HIV-only and COVID-19 only is carried out. The basic reproduction number is computed and used to prove local and global asymptotic stability of the sub-models' disease-free and endemic equilibria. Using the fmincon function in the Optimization Toolbox of MATLAB, the model is fitted to real COVID-19 data set from South Africa. The impact of intervention measures, namely, COVID-19 and HIV prevention interventions and COVID-19 treatment are incorporated into the model using time-dependent controls. It is observed that HIV prevention measures can significantly reduce the burden of co-infections with COVID-19, while effective treatment of COVID-19 could reduce co-infections with opportunistic infections such as HIV/AIDS. In particular, the COVID-19 only prevention strategy averted about 10,500 new co-infection cases, with similar number also averted by the HIV-only prevention control.

Global Stability of a Humoral Immunity COVID-19 Model with Logistic Growth and Delays

The mathematical modeling and analysis of within-host or between-host coronavirus disease 2019 (COVID-19) dynamics are considered robust tools to support scientific research. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the cause of COVID-19. This paper proposes and investigates a within-host COVID-19 dynamics model with latent infection, the logistic growth of healthy epithelial cells and the humoral (antibody) immune response. Time delays can affect the dynamics of SARS-CoV-2 infection predicted by mathematical models. Therefore, we incorporate four time delays into the model: (i) delay in the formation of latent infected epithelial cells, (ii) delay in the formation of active infected epithelial cells, (iii) delay in the activation of latent infected epithelial cells, and (iv) maturation delay of new SARS-CoV-2 particles. We establish that the model’s solutions are non-negative and ultimately bounded. This confirms that the concentrations of the virus and cells should not become negative or unbounded. We deduce that the model has three steady states and their existence and stability are perfectly determined by two threshold parameters. We use Lyapunov functionals to confirm the global stability of the model’s steady states. The analytical results are enhanced by numerical simulations. The effect of time delays on the SARS-CoV-2 dynamics is investigated. We observe that increasing time delay values can have the same impact as drug therapies in suppressing viral progression. This offers some insight useful to develop a new class of treatment that causes an increase in the delay periods and then may control SARS-CoV-2 replication.

Comprehensive Analysis of the COVID-19: Based on the Social-Related Indexes From NUMBEO

Background

The COVID-19 has been spreading globally since 2019 and causes serious damage to the whole society. A macro perspective study to explore the changes of some social-related indexes of different countries is meaningful.

Methods

We collected nine social-related indexes and the score of COVID-safety-assessment. Data analysis is carried out using three time series models. In particular, a prediction-correction procedure was employed to explore the impact of the pandemic on the indexes of developed and developing countries.

Results

It shows that COVID-19 epidemic has an impact on the life of residents in various aspects, specifically in quality of life, purchasing power, and safety. Cluster analysis and bivariate statistical analysis further indicate that indexes affected by the pandemic in developed and developing countries are different.

Conclusion

This pandemic has altered the lives of residents in many ways. Our further research shows that the impacts of social-related indexes in developed and developing countries are different, which is bounded up with their epidemic severity and control measures. On the other hand, the climate is crucial for the control of COVID-19. Consequently, exploring the changes of social-related indexes is significative, and it is conducive to provide targeted governance strategies for various countries. Our article will contribute to countries with different levels of development pay more attention to social changes and take timely and effective measures to adjust social changes while trying to control this pandemic.

Optimal Breeding Strategy for Livestock with a Dynamic Price

China’s livestock output has been growing, but domestic livestock products such as beef, mutton and pork have been unable to meet domestic consumers’ demands. The imbalance between supply and demand causes unstable livestock prices and affects profits on livestock. Therefore, the purpose of this paper is to provide the optimal breeding strategy for livestock farmers to maximize profits and adjust the balance between supply and demand. Firstly, when the price changes, livestock farmers will respond in two ways: by not adjusting the scale of livestock with the price or adjusting the scale with the price. Therefore, combining the model of price and the behavior of livestock farmers, two livestock breeding models were established. Secondly, we proposed four optimal breeding strategies based on the previously studied models and the main research method is Pontryagin’s Maximum Principle. Optimal breeding strategies are achieved by controlling the growth and output of livestock. Further, their existence was verified. Finally, we simulated two situations and found the most suitable strategy for both situations by comparing profits of four strategies. From that, we obtained several conclusions: The optimal strategy under constant prices is not always reasonable. The effect of price on livestock can promote a faster balance. To get more profits, the livestock farmers should adjust the farm’s productivity reasonably. It is necessary to calculate the optimal strategy results under different behaviors.

Effective mathematical modelling of health passes during a pandemic

We study the impact on the epidemiological dynamics of a class of restrictive measures that are aimed at reducing the number of contacts of individuals who have a higher risk of being infected with a transmittable disease. Such measures are currently either implemented or at least discussed in numerous countries worldwide to ward off a potential new wave of COVID-19. They come in the form of Health Passes (HP), which grant full access to public life only to individuals with a certificate that proves that they have either been fully vaccinated, have recovered from a previous infection or have recently tested negative to SARS-Cov-2. We develop both a compartmental model as well as an epidemic Renormalisation Group approach, which is capable of describing the dynamics over a longer period of time, notably an entire epidemiological wave. Introducing different versions of HPs in this model, we are capable of providing quantitative estimates on the effectiveness of the underlying measures as a function of the fraction of the population that is vaccinated and the vaccination rate. We apply our models to the latest COVID-19 wave in several European countries, notably Germany and Austria, which validate our theoretical findings.

Transmission dynamics of brucellosis with patch model: Shanxi and Hebei Provinces as cases

Brucellosis is a zoonotic disease caused by Brucella, and it is an important infectious disease all over the world. The prevalence of brucellosis in the Chinese mainland has some spatial characteristics besides the temporal trend in recent years. Due to the large-scale breeding of sheep and the frequent transportation of sheep in various regions, brucellosis spreads wantonly in pastoral areas, and human brucellosis spreads from traditional pastoral areas and semi-pastoral areas in the north to non-pastoral areas with low incidence in the south. In order to study the influence of sheep immigration on the epidemic transmission, a patch dynamics model was established. In each patch, the sub-model was composed of humans, sheep and Brucella. The basic reproduction number, disease-free equilibrium and positive equilibrium of the model were discussed. On the other hand, taking Shanxi Province and Hebei Province as examples, we carried out numerical simulations. The results show that the basic reproduction numbers of Shanxi Province and Hebei Province are 0.7497 and 0.5022, respectively, which indicates that the current brucellosis in the two regions has been effectively controlled. To reduce brucellosis faster in the two provinces, there should be a certain degree of sheep immigration from high-infection area to low-infection areas, and reduce the immigration of sheep from low-infection areas to high-infection areas.