Analysis of a nonstandard computer method to simulate a nonlinear stochastic epidemiological model of coronavirus-like diseases

Fractional epidemic model of coronavirus disease with vaccination and crowding effects

Most of the countries in the world are affected by the coronavirus epidemic that put people in danger, with many infected cases and deaths. The crowding factor plays a significant role in the transmission of coronavirus disease. On the other hand, the vaccines of the covid-19 played a decisive role in the control of coronavirus infection. In this paper, a fractional order epidemic model (SIVR) of coronavirus disease is proposed by considering the effects of crowding and vaccination because the transmission of this infection is highly influenced by these two factors. The nonlinear incidence rate with the inclusion of these effects is a better approach to understand and analyse the dynamics of the model. The positivity and boundedness of the fractional order model is ensured by applying some standard results of Mittag Leffler function and Laplace transformation. The equilibrium points are described analytically. The existence and uniqueness of the non-integer order model is also confirmed by using results of the fixed-point theory. Stability analysis is carried out for the system at both the steady states by using Jacobian matrix theory, Routh-Hurwitz criterion and Volterra-type Lyapunov functions. Basic reproductive number is calculated by using next generation matrix. It is verified that disease-free equilibrium is locally asymptotically stable ifR 0 < 1 and endemic equilibrium is locally asymptotically stable ifR 0 > 1 . Moreover, the disease-free equilibrium is globally asymptotically stable ifR 0 < 1 and endemic equilibrium is globally asymptotically stable ifR 0 > 1 . The non-standard finite difference (NSFD) scheme is developed to approximate the solutions of the system. The simulated graphs are presented to show the key features of the NSFD approach. It is proved that non-standard finite difference approach preserves the positivity and boundedness properties of model. The simulated graphs show that the implementation of control strategies reduced the infected population and increase the recovered population. The impact of fractional order parameter α is described by the graphical templates. The future trends of the virus transmission are predicted under some control measures. The current work will be a value addition in the literature. The article is closed by some useful concluding remarks.

The Effect of Fangcang Shelter Hospitals under Resource Constraints on the Spread of Epidemics

Since the outbreak of the COVID-19 pandemic, Fangcang shelter hospitals have been built and operated in several cities, and have played a huge role in epidemic prevention and control. How to use medical resources effectively in order to maximize epidemic prevention and control is a big challenge that the government should address. In this paper, a two-stage infectious disease model was developed to analyze the role of Fangcang shelter hospitals in epidemic prevention and control, and examine the impact of medical resources allocation on epidemic prevention and control. Our model suggested that the Fangcang shelter hospital could effectively control the rapid spread of the epidemic, and for a very large city with a population of about 10 million and a relative shortage of medical resources, the model predicted that the final number of confirmed cases could be only 3.4% of the total population in the best case scenario. The paper further discusses the optimal solutions regarding medical resource allocation when medical resources are either limited or abundant. The results show that the optimal allocation ratio of resources between designated hospitals and Fangcang shelter hospitals varies with the amount of additional resources. When resources are relatively sufficient, the upper limit of the proportion of makeshift hospitals is about 91%, while the lower limit decreases with the increase in resources. Meanwhile, there is a negative correlation between the intensity of medical work and the proportion of distribution. Our work deepens our understanding of the role of Fangcang shelter hospitals in the pandemic and provides a reference for feasible strategies by which to contain the pandemic.

A dynamical study on stochastic reaction diffusion epidemic model with nonlinear incidence rate

The current study deals with the stochastic reaction-diffusion epidemic model numerically with two proposed schemes. Such models have many applications in the disease dynamics of wildlife, human life, and others. During the last decade, it is observed that the epidemic models cannot predict the accurate behavior of infectious diseases. The empirical data gained about the spread of the disease shows non-deterministic behavior. It is a strong challenge for researchers to consider stochastic epidemic models. The effect of the stochastic process is analyzed. So, the SIR epidemic model is considered under the influence of the stochastic process. The time noise term is taken as the stochastic source. The coefficient of the stochastic term is a Borel function, and it is used to control the random behavior in the solutions. The proposed stochastic backward Euler scheme and the proposed stochastic implicit finite difference scheme (IFDS) are used for the numerical solution of the underlying model. Both schemes are consistent in the mean square sense. The stability of the schemes is proven with Von-Neumann criteria and schemes are unconditionally stable. The proposed stochastic backward Euler scheme converges toward a disease-free equilibrium and does not converge toward an endemic equilibrium but also possesses negative behavior. The proposed stochastic IFD scheme converges toward disease-free equilibrium and endemic equilibrium. This scheme also preserves positivity. The graphical behavior of the stochastic SIR model is much similar to the classical SIR epidemic model when noise strength approaches zero. The three-dimensional plots of the susceptible and infected individuals are drawn for two cases of endemic equilibrium and disease-free equilibriums. The efficacy of the proposed scheme is shown in the graphical behavior of the test problem for the various values of the parameters.

Vaccine Coverage and Effectiveness in a School-Based Varicella Outbreak in Jinan Prefecture, Shandong Province

Background: Licheng District of Jinan Prefecture reported a school-based varicella outbreak. We conducted an investigation to analyze the epidemiology and scope of the outbreak, determine varicella vaccine coverage on the school campus, and estimate varicella vaccine effectiveness (VE). Methods: In the epidemiological investigation, we determined the attack rate, the clinical manifestations of varicella cases, and histories of prior varicella disease and varicella vaccination. We tested students for presence of serum IgM antibodies, and we attempted to isolate the varicella virus from vesicular fluid samples. We used chi-square to compare incidences between classes and floors. VE was estimated using a retrospective cohort study. Results: There were 13 varicella cases in the outbreak. All were among fourth grade students - twelve in Class 7 and one in Class 6. The attack rate in the two classrooms was 14.3% (13/91). Clinical symptoms were rash (100%) and fever (46.15%). All cases were reported within one average incubation period, and the epidemic curve suggested common exposure. Six of the 13 cases previously received one dose of varicella vaccine with a median time between vaccination and infection of 9 years; the other seven cases had not been vaccinated. Varicella vaccine coverage with one or more doses was 81.31%; 2-dose coverage was 38.15%. The median age of receipt of dose 1 was 1.18 years, and median age for receiving dose 2 was 5.12 years. One-dose varicella VE was 73.2% (95% confidence interval: 37.0%, 88.6%), and two-dose VE was 100%. Conclusions: Varicella vaccine coverage has been gradually increasing in recent years, as ≥1-dose and 2-dose coverage rates are higher in younger children than older children. High one-dose vaccination coverage limited the outbreak scope and led to the breakthrough cases being mild. Mild cases were difficult to detect in a timely manner. Varicella vaccine was highly effective, with 1-dose VE of 73% nine years after vaccination and 2-dose VE of 100%. We strongly recommended that all school students receive two doses of varicella vaccine.

Dynamical analysis of coronavirus disease with crowding effect, and vaccination: a study of third strain

Countries affected by the coronavirus epidemic have reported many infected cases and deaths based on world health statistics. The crowding factor, which we named "crowding effects," plays a significant role in spreading the diseases. However, the introduction of vaccines marks a turning point in the rate of spread of coronavirus infections. Modeling both effects is vastly essential as it directly impacts the overall population of the studied region. To determine the peak of the infection curve by considering the third strain, we develop a mathematical model (susceptible-infected-vaccinated-recovered) with reported cases from August 01, 2021, till August 29, 2021. The nonlinear incidence rate with the inclusion of both effects is the best approach to analyze the dynamics. The model's positivity, boundedness, existence, uniqueness, and stability (local and global) are addressed with the help of a reproduction number. In addition, the strength number and second derivative Lyapunov analysis are examined, and the model was found to be asymptotically stable. The suggested parameters efficiently control the active cases of the third strain in Pakistan. It was shown that a systematic vaccination program regulates the infection rate. However, the crowding effect reduces the impact of vaccination. The present results show that the model can be applied to other countries' data to predict the infection rate.

A model based on cellular automata for investigating the impact of lockdown, migration and vaccination on COVID-19 dynamics

BACKGROUND AND OBJECTIVE

COVID-19 pandemic continues unabated due to the rapid spread of new mutant strains of the virus. Decentralized cluster containment is an efficient approach to manage the pandemic in the long term, without straining the healthcare system and economy. In this study, the objective is to forecast the peak and duration of COVID-19 spread in a cluster under different conditions, using a probabilistic cellular automata configuration designed to include the observed characteristics of the pandemic with appropriate neighbourhood schemes and transition rules.

METHODS

The cellular automata, initially configured to have only susceptible and exposed states, enlarges and evolves in discrete time steps to different infection states of the COVID-19 pandemic. The transition rules take into account the probability and proximity of contact between infected hosts and susceptible individuals. A transmittable and transition neighbourhoods are defined to identify the most probable individuals infected from a single host in a time step.

RESULTS

The model with novel neighbourhood schemes and transition rules reproduce the macroscopic behaviour of infection and recovery observed in pandemics. The temporal evolution of the pandemic trajectory is sensitive to lattice size, range, latent and recovery periods but has constraints in capturing the changes in the infectious period. A study of lockdown and migration scenarios shows strict social isolation is crucial in controlling the pandemic. The simulations also indicate that earlier vaccination with a higher capacity and rate is essential to mitigate the pandemic. A comparison of simulated and actual data shows a good match.

CONCLUSIONS

The study concludes that social isolation during movement and interaction of people can limit the spread of new infections. Vaccinating a large proportion of the population reduces new cases in subsequent waves of the pandemic. The model and algorithm with real-world data as input can quickly forecast the trajectory of the pandemic, for effective response in cluster containment.

Modeling the transmission dynamics of delayed pneumonia-like diseases with a sensitivity of parameters

Pneumonia is a highly transmitted disease in children. According to the World Health Organization (WHO), the most affected regions include South Asia and sub-Saharan Africa. 15% deaths of children are due to pneumonia. In 2017, 0.88 million children were killed under the age of five years. An analysis of pneumonia disease is performed with the help of a delayed mathematical modelling technique. The epidemiological system contemplates subpopulations of susceptible, carriers, infected and recovered individuals, along with nonlinear interactions between the members of those subpopulations. The positivity and the boundedness of the ongoing problem for nonnegative initial data are thoroughly proved. The system possesses pneumonia-free and pneumonia existing equilibrium points, whose stability is studied rigorously. Moreover, the numerical simulations confirm the validity of these theoretical results.

Complex T-spherical fuzzy Dombi aggregation operators and their applications in multiple-criteria decision-making

Complex fuzzy (CF) sets (CFSs) have a significant role in modelling the problems involving two-dimensional information. Recently, the extensions of CFSs have gained the attention of researchers studying decision-making methods. The complex T-spherical fuzzy set (CTSFS) is an extension of the CFSs introduced in the last times. In this paper, we introduce the Dombi operations on CTSFSs. Based on Dombi operators, we define some aggregation operators, including complex T-spherical Dombi fuzzy weighted arithmetic averaging (CTSDFWAA) operator, complex T-spherical Dombi fuzzy weighted geometric averaging (CTSDFWGA) operator, complex T-spherical Dombi fuzzy ordered weighted arithmetic averaging (CTSDFOWAA) operator, complex T-spherical Dombi fuzzy ordered weighted geometric averaging (CTSDFOWGA) operator, and we obtain some of their properties. In addition, we develop a multi-criteria decision-making (MCDM) method under the CTSF environment and present an algorithm for the proposed method. To show the process of the proposed method, we present an example related to diagnosing the COVID-19. Besides this, we present a sensitivity analysis to reveal the advantages and restrictions of our method.