A compartmental epidemiological model with seven groups is introduced herein, to account for the dissemination of diseases similar to the Coronavirus disease 2019 (COVID-19). In its simplified version, the model contains ten parameters, four of which relate to characteristics of the virus, whereas another four are transition probabilities between the groups; the last two parameters enable the empirical modelling of the effective transmissibility, associated in this study with the cumulative number of fatalities due to the disease within each country. The application of the model to the fatality data (the main input herein) of five countries (to be specific, of those which had suffered most fatalities by April 30, 2020) enabled the extraction of an estimate for the basic reproduction number $R_0$ for the COVID-19 disease: $R_0=4.91(33)$.

To identify the exchange coefficients of a nonlinear polynomial tricompartmental general system of α+β , we follow the procedure; firstly, the recommended solution is to introduce an adequate time t*>0 in a determinable manner. That is, after injecting quantity a into the main compartment, wait a moment for the exchange in the polynomial α+β order nonlinear general system to settle, and then compare this compartment to compartment 2 at t*. Secondly, applying the Taylor formula will linearize the system and identify the exchange coefficients. Finally, we will prove that the linearization method is stable.

Fractional differential mathematical model unfolding the dynamics of the COVID-19 pandemic in India is presented and explored in this paper. The purpose of this study is to estimate the future outbreak of disease and potential control strategies using mathematical models in India as a whole country as well as in some of the states of the country. This model is calibrated based on reported cases of infections over the month of April 2020 in India. We have used iterative fractional complex transform method to find approximate solutions of the model having modified Riemann Liouville fractional differential operator. We have also carried out a comparative analysis between actual and estimated cumulative cases graphically, moreover, most sensitive parameters for basic reproduction number$(R_0)$ are computed and their effect on transmission dynamics of COVID-19 pandemic is investigated in detail.

In this study, we investigate different control scenarios through theoretical analysis and numerical simulations. To account for two important types of control for an early ascending stage of an outbreak, social distancing and treatment with antiviral medications, a compartmental model is considered with one control, $u_1(t)$, aimed to lower the disease transmission rate and the other control, $u_2(t)$, aimed to lower the period of infectiousness. In all experiments, the implementation of control strategies reduces the daily cumulative number of cases and successfully "flattens the curve". The reduction in the cumulative cases is achieved by eliminating or delaying new cases. This delay is incredibly valuable as it provides public health organizations with more time to advance antiviral treatments and devise alternative preventive measures. The main theoretical result of the paper, Theorem 3.1, concludes that the optimal control functions, $u_i(t)$, $i=1,2,$ may be increasing until some moment $\tau \in [0, T)$. However, for all $t \in [\tau, T]$, both controls, $u_i(t)$, decline as $t$ approaches $T$ (possibly causing the number of newly infected people to grow). Numerical simulations presented in Section 4 confirm theoretical findings, which indicates that, ideally, around the time $t=\tau$, the control strategy has to be upgraded and a vaccination campaign needs to start to ensure the epidemic wave does not rebound.

It is no news that the COVID–19 pandemic has affected many persons in different ways. As the number of reported cases rises across the globe, efforts are geared towards production and administration of effective vaccines for the disease. However, many developing countries are faced with the dilemma of how to slow the spread and flatten the curves of the disease as the available vaccines are not enough. Interestingly, the dynamics of the disease can be analysed to get useful insights to enhance the making of suitable preventive policies that will slow the spread, ultimately flatten the curves of the disease and also help in managing any future occurrence. In this work, the aim is to analyse the dynamics, and estimate the basic reproduction number of the second wave of the pandemic in Nigeria using a Susceptible-Infected-Recovered-Deceased (SIRD) compartmental–based model. The dynamics of the disease is described by a system of nonlinear ordinary differential equations. The model takes into consideration the current control policies in place - social distancing, mask usage, personal hygiene and quarantine. Available data provided by Nigeria Centre for Disease Control (NCDC), World Health Organization (WHO) and Wolfram Data Repository were used for the computations. The Quasi–Newton algorithm was implemented in fitting the proposed model to the available data and a sensitivity analysis was presented. Major parameters - effective contact rate, average recovery time, average mortality rate, and overall effectiveness of the control policies - influencing the dynamics of the disease, and the basic reproduction numbers were estimated. The turning points of the disease during the second wave were also obtained. The proposed model gave estimated values for the parameters influencing the spread of the disease. Also, the measure of the overall effectiveness of the current control policies gave insight into how effective the measures are.

In India the first case of coronavirus disease 2019 (COVID-19) reported on 30 January 2020, and thereafter cases were increasing daily after the last week of Feb. 2020. COVID-19 identified as family member of coronaviridae where previously Middle East Respiratory Syndrome MERS and Severe Acute Respiratory Syndrome SARS belongs to same family. The COVID-19 attacks on respiratory system signing fever, cough and breath shortness, in severe cases may cause pneumonia, SARS or some time death. The aim of this study work is to develop model which predicts the epidemic peak for COVID-19 in India by using the real-time data from 30 Jan to 10 May 2020. There are uncertainties while identifying the population information due to the incomplete and inaccurate data, we initiate the most popular model for epidemic prediction i.e Susceptible, Exposed, Infectious, & Recovered SEIR initially the compartmental model for the prediction. Based on the solution of the state estimation problem for polynomial system with Poisson noise, we estimate that the epidemic peak may reach the early-middle July 2020, initializing recovered R0 to 0 and Infected I0 to 1. The outcomes of the model will help epidemiologist to isolate the source of the disease geospatially and analyze the death. Also government authorities will be able to target their interventions for rapidly checking the spread of the epidemic.

Compartmental analysis is the mathematical framework for the modelling of tracer kinetics in dynamical Positron Emission Tomography. This paper provides a review of how compartmental models are constructed and numerically optimized. Specific focus is given on the identifiability and sensitivity issues and on the impact of complex physiological conditions on the mathematical properties of the models.

Objectives: This paper presents a statistical review of modelling simulations for frequency and sensitivity of COVID-19 testing paradigms. Methods: We performed a review of preprints and published articles on PubMed from January 1, 2020 – March 1, 2021 using the search terms “COVID screening testing”, “COVID testing frequency”, “COVID testing frequency screening” and “SARS-CoV-2 testing frequency”.Results: Several authors’ conclusions support the claim that test frequency and test sensitivity both play a role in reducing SARS-CoV-2 transmission. We highlight the interplay between frequency of testing, test sensitivity and the speed at which test results are available in our review. Conclusions: Evidence suggests that sensitivity and frequency of testing both play a part in decreasing transmission of disease. We conclude that, overall, test sensitivity plays less of a role in reducing disease transmission in a population compared to the frequency of testing and how quickly test results are available.

COVID-19 transmission models have conferred great value in informing public health understanding, planning, and response. However, the pandemic also demonstrated the infeasibility of basing public health decision-making on transmission models with pre-set assumptions. No matter how favourably evidenced when built, a model with fixed assumptions is challenged by numerous factors that are difficult to predict. Ongoing planning associated with rolling back and re-instituting measures, initiating surge planning, and issuing public health advisories can benefit from approaches that allow state estimates for transmission models to be continuously updated in light of unfolding time series. A model being continuously regrounded by empirical data in this way can provide a consistent, integrated depiction of the evolving underlying epidemiology and acute care demand, offer the ability to project forward such a depiction in a fashion suitable for triggering the deployment of acute care surge capacity or public health measures, support quantative evaluation of tradeoffs associated with prospective interventions in light of the latest estimates of the underlying epidemiology. We describe here the design, implementation and multi-year daily use for public health and clinical support decision-making of a particle filtered COVID-19 compartmental model, which served Canadian federal and provincial governments via regular reporting starting in June 2020. The use of the Bayesian Sequential Monte Carlo algorithm of Particle Filtering allows the model to be re-grounded daily and adapt to new trends within daily incoming data – including test volumes and positivity rates, endogenous and travel-related cases, hospital census and admissions flows, daily counts dose-specific vaccinations administered, measured concentration of SARS-CoV-2 in wastewater, and mortality. Important model outputs include estimates (via sampling) of the count of undiagnosed infectives, the count of individuals at different stages of the natural history of frankly and pauci-symptomatic infection, the current force of infection, effective reproductive number, and current and cumulative infection prevalence. Following a brief description of model design, we describe how the machine learning algorithm of particle filtering is used to continually reground estimates of dynamic model state, support probabilistic model projection of epidemiology and health system capacity utilization and service demand and probabilistically evaluate trade-offs between potential intervention scenarios. We further note aspects of model use in practice as an effective reporting tool in a manner that is parameterized by jurisdiction, including support of a scripting pipeline that permits a fully automated reporting pipeline other than security-restricted new data retrieval, including automated model deployment, data validity checks, and automatic post-scenario scripting and reporting. As demonstrated by this multi-year deployment of Bayesian machine learning algorithm of particle filtering to provide industrial-strength reporting to inform public health decision making across Canada, such methods offer strong support for evidence-based public health decision making informed by ever-current articulated transmission models whose probabilistic state and parameter estimates are continually regrounded by diverse data streams.

Mixing is considered as a critical process parameter (CPP) during process development due to its significant influence on reaction selectivity and process safety. Nevertheless, mixing issues are difficult to identify and solve owing to their complexity and dependence on knowledge of kinetics and hydrodynamics. In this paper, we proposed an optimization methodology using Computational Fluid Dynamics (CFD) based compartmental modelling to improve mixing and reaction selectivity. More importantly, we have demonstrated that through the implementation of surrogate-based optimization, the proposed methodology can be used as a computationally non-intensive way for rapid process development of reaction unit operations. For illustration purpose, reaction selectivity of a process with Bourne competitive reaction network is discussed. Results demonstrate that we can improve reaction selectivity by dynamically controlling rates and locations of feeding in the reactor. The proposed methodology incorporates mechanistic understanding of the reaction kinetics together with an efficient optimization algorithm to determine the optimal process operation and thus can serve as a tool for quality-by-design (QbD) during product development stage.

One of the most important problems in the presence of epidemics and pandemics is an accurate prediction and preparedness. Scholars and experts argue that future pandemics and/or epidemics are almost inevitable events and is not whether next pandemics will happen, but when a new heath emergency will emerge. Epidemiologic models for prediction of Coronavirus Disease 2019 (COVID-19) have shown many limitations because of unpredictable dynamics of the new viral agent SARS-CoV-2 in environment and society. The main goals of this study are twofold: first, the analysis of anthropogenic activities and factors that may trigger pandemic threats; second, the planning of new directions for strategies to reduce risks that a pandemic threat emerges and/or in the initial phase to reduce vast diffusion and negative impact of new viral agents that can generate hazards and problems in public health, environment and socioeconomic systems. In particular, the investigation and understanding of sources and driving factors concerning the emergence and diffusion of new pandemics have critical aspects for strategic actions of forecast, prevention and preparation of effective policy responses to cope with next pandemic crises and health emergencies. Insights here endeavor, whenever possible, to clarify these problems to increase the knowledge of the sources and factor determining the emergence of new viral agents in order to design optimal response policies to face next pandemic diseases similar to COVID-19. .