Modeling COVID-19 Transmission Dynamics With Self-Learning Population Behavioral Change

Bridging the gap between models based on ordinary, delayed, and fractional differentials equations through integral kernels

Evolution equations with convolution-type integral operators have a history of study, yet a gap exists in the literature regarding the link between certain convolution kernels and new models, including delayed and fractional differential equations. We demonstrate, starting from the logistic model structure, that classical, delayed, and fractional models are special cases of a framework using a gamma Mittag-Leffler memory kernel. We discuss and classify different types of this general kernel, analyze the asymptotic behavior of the general model, and provide numerical simulations. A detailed classification of the memory kernels is presented through parameter analysis. The fractional models we constructed possess distinctive features as they maintain dimensional balance and explicitly relate fractional orders to past data points. Additionally, we illustrate how our models can reproduce the dynamics of COVID-19 infections in Australia, Brazil, and Peru. Our research expands mathematical modeling by presenting a unified framework that facilitates the incorporation of historical data through the utilization of integro-differential equations, fractional or delayed differential equations, as well as classical systems of ordinary differential equations.

A memory effect model to predict COVID-19: analysis and simulation

On 19 September 2020, the Centers for Disease Control and Prevention (CDC) recommended that asymptomatic individuals, those who have close contact with infected person, be tested. Also, American society for biological clinical comments on testing of asymptomatic individuals. So, we proposed a new mathematical model for evaluating the population-level impact of contact rates (social-distancing) and the rate at which asymptomatic people are hospitalized (isolated) following testing due to close contact with documented infected people. The model is a deterministic system of nonlinear differential equations that is fitted and parameterized by least square curve fitting using COVID-19 pandemic data of Pakistan from 1 October 2020 to 30 April 2021. The fractional derivative is used to understand the biological process with crossover behavior and memory effect. The reproduction number and conditions for asymptotic stability are derived diligently. The most common non-integer Caputo derivative is used for deeper analysis and transmission dynamics of COVID-19 infection. The fractional-order Adams-Bashforth method is used for the solution of the model. In light of the dynamics of the COVID-19 outbreak in Pakistan, non-pharmaceutical interventions (NPIs) in terms of social distancing and isolation are being investigated. The reduction in the baseline value of contact rates and enhancement in hospitalization rate of symptomatic can lead the elimination of the pandemic.

Modelling the Future Clinical and Economic Burden of Antimicrobial Resistance: The Feasibility and Value of Models to Inform Policy

Due to the increasing threat to public health and the economy, governments internationally are interested in models to estimate the future clinical and economic burden of antimicrobial resistance (AMR) and to evaluate the cost-effectiveness of interventions to prevent or control resistance and to inform resource-allocation decision making. A widely cited UK report estimated that 10 million additional deaths will occur globally per annum due to AMR by 2050; however, the utility and accuracy of this prediction has been challenged. The precision of models predicting the future economic burden of AMR is dependent upon the accuracy of predicting future resistance rates. This paper reviews the feasibility and value of modelling to inform policy and resource allocation to manage and curb AMR. Here we describe methods used to estimate future resistance in published burden-of-disease models; the sources of uncertainty are highlighted, which could potentially mislead policy decision-making. While broad assumptions can be made regarding some predictable factors contributing to future resistance rates, the unexpected emergence, establishment and spread of new resistance genes introduces substantial uncertainty into estimates of future economic burden, and in models evaluating the effectiveness of interventions or policies to address AMR. Existing reporting standards for best practice in modelling should be adapted to guide the reporting of AMR economic models, to ensure model transparency and validation for interpretation by policymakers.