A multi-source global-local model for epidemic management

The Effective Reproduction Number Rt provides essential information for the management of an epidemic/pandemic. Projecting Rt into the future could further assist in the management process. This article proposes a methodology based on exposure scenarios to perform such a procedure. The method utilizes a compartmental model and its adequate parametrization; a way to determine suitable parameters for this model in México’s case is detailed. In conjunction with the compartmental model, the projection of Rt permits estimating unobserved variables, such as the size of the asymptomatic population, and projecting into the future other relevant variables, like the active hospitalizations, using scenarios. The uses of the proposed methodologies are exemplified by analyzing the pandemic in a Mexican state; the main quantities derived from the compartmental model, such as the active and total cases, are included in the analysis. This article also presents a national summary based on the methodologies to illustrate how these procedures could be further exploited. The supporting information includes an application of the proposed methods to a metropolitan area to show that it also works well at other demographic disaggregation levels. The procedures developed in this article shed light on how to develop an effective surveillance system when information is incomplete and can be applied in cases other than México’s.

Mathematical Model and Analysis of Corruption Dynamics with Optimal Control

In this study, a deterministic mathematical model that explains the transmission dynamics of corruption is proposed and analyzed by considering social influence on honest individuals. Positivity and boundedness of solution of the model are proved and basic reproduction number R 0 is computed using the next-generation matrix method. The analysis shows that corruption-free equilibrium is locally and globally asymptotically stable whenever R 0 < 1 . Also, the endemic equilibrium point is locally and globally asymptotically stable whenever R 0 > 1 . Then, the model was extended to optimal control, and some numerical simulations with and without optimal control are also performed to verify the theoretical analysis using MATLAB. Numerical simulation of optimal control model shows that the prevention and punishment strategy is the most effective strategy to reduce the dynamic transmission of corruption.

Omicron Impact in India: An Early Analysis of the Ongoing COVID-19 Third Wave

India is currently experiencing the third wave of COVID-19, which began on around 28 Dec. 2021. Although genome sequencing data of a sufficiently large sample is not yet available, the rapid growth in the daily number of cases, comparable to South Africa, United Kingdom, suggests that the current wave is primarily driven by the Omicron variant. The logarithmic regression suggests the growth rate of the infections during the early days in this wave is nearly four times than that in the second wave. Another notable difference in this wave is the relatively concurrent arrival of outbreaks in all the states; the effective reproduction number (Rt) although has significant variations among them. The test positivity rate (TPR) also displays a rapid growth in the last 10 days in several states. Preliminary estimates with the SIR model suggest that the peak to occur in late January 2022 with peak caseload exceeding that in the second wave. Although the Omicron trends in several countries suggest a decline in case fatality rate and hospitalizations compared to Delta, a sudden surge in active caseload can temporarily choke the already stressed healthcare India is currently experiencing the third wave of COVID-19, which began on around 28 Dec. 2021. Although genome sequencing data of a sufficiently large sample is not yet available, the rapid growth in the daily number of cases, comparable to South Africa, United Kingdom, suggests that the current wave is primarily driven by the Omicron variant. The logarithmic regression suggests the growth rate of the infections during the early days in this wave is nearly four times than that in the second wave. Another notable difference in this wave is the relatively concurrent arrival of outbreaks in all the states; the effective reproduction number (Rt) although has significant variations among them. The test positivity rate (TPR) also displays a rapid growth in the last 10 days in several states. Preliminary estimates with the SIR model suggest that the peak to occur in late January 2022 with peak caseload exceeding that in the second wave. Although the Omicron trends in several countries suggest a decline in case fatality rate and hospitalizations compared to Delta, a sudden surge in active caseload can temporarily choke the already stressed healthcare infrastructure. Therefore, it is advisable to strictly adhere to COVID-19 appropriate behavior for the next few weeks to mitigate an explosion in the number of infections.

Country-specific optimization strategy for testing through contact tracing can help maintain a low reproduction number ($$R_{0}$$) during unlock

In response to the COVID19 pandemic, many countries have implemented lockdowns in multiple phases to ensure social distancing and quarantining of the infected subjects. Subsequent unlocks to reopen the economies started next waves of infection and imposed an extra burden on quarantine to keep the reproduction number ($$R_{0}$$ R 0 ) < 1. However, most countries could not effectively contain the infection spread, suggesting identification of the potential sources weakening the effect of lockdowns could help design better informed lockdown-unlock cycles in the future. Here, through building quantitative epidemic models and analyzing the metadata of 50 countries from across the continents we first found that the estimated value of $$R_{0}$$ R 0 , adjusted w.r.t the distribution of medical facilities and virus clades correlates strongly with the testing rates in a country. Since the testing capacity of a country is limited by its medical resources, we investigated if a cost–benefit trade-off can be designed connecting testing rate and extent of unlocking. We present a strategy to optimize this trade-off in a country specific manner by providing a quantitative estimate of testing and quarantine rates required to allow different extents of unlocks while aiming to maintain $$R_{0} < 1$$ R 0 < 1 . We further show that a small fraction of superspreaders can dramatically increase the number of infected individuals even during strict lockdowns by strengthening the positive feedback loop driving infection spread. Harnessing the benefit of optimized country-specific testing rates would critically require minimizing the movement of these superspreaders via strict social distancing norms, such that the positive feedback driven switch-like exponential spread phase of infection can be avoided/delayed.

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.

Estimation the state of the Covid-19 epidemic curve in Mayotte

We study in this work some statistical methods to estimate the parameters resulting from the use of an age-structured contact mathematical epidemic model in order to analyze the evolution of the epidemic curve of Covid-19 in the French overseas department Mayotte from march 13, 2020 to february 26,2021. Using several statistic methods based on time dependent method, maximum likelihood, mixture method, we fit the probability distribution which underlines the serial interval distribution and we give an adapted version of the generation time distribution from Package R0. The best-fit model of the serial interval was given by a mixture of Weibull distribution. Furthermore this estimation allows to obtain the evolution of the time varying effective reproduction number and hence the temporal transmission rates. Finally based on others known estimates parameters we incorporate the estimated parameters in the model in order to give an approximation of the epidemic curve in Mayotte under the conditions of the model. We also discuss the limit of our study and the conclusion concerned a probable impact of non pharmacological interventions of the Covid-19 in Mayotte such us the re-infection cases and the introduction of the variants which probably affect the estimates.

Shielding individuals at high risk of COVID-19: a micro-simulation study

Background One of the proposed interventions for mitigating COVID-19 epidemics, particularly in low-income and crisis-affected settings, is to physically isolate individuals known to be at high risk of severe disease and death due to age or co-morbidities. This intervention, known as 'shielding', could be implemented in various ways. If shielded people are grouped together in residences and isolation is imperfect, any introduction of infections within the shielding group could cause substantial mortality and thus negate the intervention's benefits. We explored the effectiveness of shielding under various modalities of implementation and considered mitigation measures to reduce its possible harms. Methods We used an individual-based mathematical model to simulate the evolution of a COVID-19 epidemic in a population of which a fraction above a given age cut-off are relocated to shielding residences, in which they have variable levels of contacts with their original household, the outside world and fellow shielding residents. We set our simulation with the context of an internally displaced persons' camp in Somaliland, for which we had recently collected data on household demographics and social mixing patterns. We compared an unmitigated epidemic with a shielding intervention accompanied by various measures to reduce the risk of virus introduction and spread within the shielding residences. We did sensitivity analyses to explore parameters such as residence size, reduction in contacts, basic reproduction number, and prior immunity in the population. Results Shielded residences are likely to be breached with infection during the outbreak. Nonetheless, shielding can be effective in preventing COVID-19 infections in the shielded population. The effectiveness of shielding is mostly affected by the size of the shielded residence, and by the degree by which contacts between shielded and unshielded individuals are reduced. Reductions in contacts between shielded individuals could further increase the effectiveness of shielding, but is only effective in larger shielded residences. Large shielded residences increase the risk of infection, unless very large reductions in contacts can be achieved. In epidemics with a lower reproduction number, the effectiveness of shielding could be negative effectiveness. Discussion Shielding could be an effective method to protect the most at-risk individuals. It should be considered where other measures cannot easily be implemented, but with attention to the epidemiological situation. Shielding should only be implemented through small to medium-sized shielding residences, with appropriate mitigation measures such as reduced contact intensity between shielded individuals and self-isolation of cases to prevent subsequent spread.

A Theoretical Linguistic Fuzzy Rule-Based Compartmental Modeling for the COVID-19 Pandemic

Recently COVID-19 pandemic has affected the whole world quite seriously. The number of new infectious cases and death cases are rapidly increasing over time. In this study, a theoretical linguistic fuzzy rule-based Susceptible-Exposed-Infectious-Isolated-Recovered (SEIIsR) compartmental model has been proposed to predict the dynamics of the transmission of COVID-19 over time considering population immunity and infectiousness heterogeneity based on viral load in the model. The model’s equilibrium points have been calculated and stability analysis of the model’s equilibrium points has been conducted. Consequently, the fuzzy basic reproduction number, R0f of the fuzzy model has been formulated. Finally, the temporal dynamics of different compartmental populations with immunity and infectiousness heterogeneity using the fuzzy Mamdani model are delineated and some disease control policies have been suggested to get over the infection in no time.

Dynamical analysis, optimal control and spatial pattern in an influenza model with adaptive immunity in two stratified population

<abstract><p>Consistently, influenza has become a major cause of illness and mortality worldwide and it has posed a serious threat to global public health particularly among the immuno-compromised people all around the world. The development of medication to control influenza has become a major challenge now. This work proposes and analyzes a structured model based on two geographical areas, in order to study the spread of influenza. The overall underlying population is separated into two sub populations: urban and rural. This geographical distinction is required as the immunity levels are significantly higher in rural areas as compared to urban areas. Hence, this paper is a novel attempt to proposes a linear and non-linear mathematical model with adaptive immunity and compare the host immune response to disease. For both the models, disease-free equilibrium points are obtained which are locally as well as globally stable if the reproduction number is less than 1 (<italic>R</italic>₀₁ &lt; 1 &amp; <italic>R</italic>₀₂ &lt; 1) and the endemic point is stable if the reproduction number is greater then 1 (<italic>R</italic>₀₁ &gt; 1 &amp; <italic>R</italic>₀₂ &gt; 1). Next, we have incorporated two treatments in the model that constitute the effectiveness of antidots and vaccination in restraining viral creation and slow down the production of new infections and analyzed an optimal control problem. Further, we have also proposed a spatial model involving diffusion and obtained the local stability for both the models. By the use of local stability, we have derived the Turing instability condition. Finally, all the theoretical results are verified with numerical simulation using MATLAB.</p></abstract>