Fraction Of Susceptible Individuals Research Articles

Reproduction Factor Based Latent Epidemic Model Inference: A Data-Driven Approach Using COVID-19 Datasets.

The mathematical modeling of infectious diseases aims to evaluate the transmissibility of the on-going spread of disease and guide the government's control strategies and interventions. In this paper, we propose a novel transmissibility indicator, reproduction factor, which evaluates the number of secondary infections from a single nonisolated infectious individual. In contrast to classic reproduction numbers, the reproduction factor explicitly considers the fraction of susceptible individuals (who are not immune to disease naturally or through vaccination) and the nonisolated population to evaluate near real-time transmissibility. Thus, it can be an effective indicator when the spread of disease has progressed and control strategies have been implemented. Other merits of the proposed reproduction factor include data-driven inference based on a Markov chain, which enables the inference of latent information, such as the number of nondetected infectious individuals and the number of daily new infections. We performed an extensive simulation using the COVID-19 datasets of Germany, Italy, South Korea, and California (the U.S.) to verify our model. We further compared the results with other transmissibility measures, including reproduction numbers, and the results of state-of-the-art epidemic models. Through the results, we confirmed that the proposed reproduction factor and corresponding inference model explained the COVID-19 datasets.

ARE THE BEGINNING AND ENDING PHASES OF EPIDEMICS CHARACTERIZED BY THE NEXT GENERATION MATRICES? – A CASE STUDY OF DRUG-SENSITIVE AND RESISTANT TUBERCULOSIS MODEL

In epidemiological modeling, the basic reproduction number is usually defined as being the spectral radius of the next-generation matrix evaluated at the trivial equilibrium. The global stability of the trivial equilibrium point was determined by the left eigenvector associated with that next-generation matrix. More recently, the fraction of susceptible individuals was also obtained from the next generation matrix. The gross reproduction number and the fraction of susceptible individuals were calculated by revisiting the drug-sensitive and resistant tuberculosis model. Hence, the next-generation matrices shed light on the evolution of the dynamics: the beginning of the epidemic via the basic reproduction number and approaching the epidemic’s steady-state via the susceptible individuals’ asymptotic fraction.

The Effect of State-Dependent Control for an SIRS Epidemic Model with Varying Total Population

Based on the mechanism of prevention and control of infectious disease, we propose, in this paper, an SIRS epidemic model with varying total population size and state-dependent control, where the fraction of susceptible individuals in population is as the detection threshold value. By the Poincaré map, theory of differential inequalities and differential equation geometry, the existence and orbital stability of the disease-free periodic solution are discussed. Theoretical results show that by state-dependent pulse vaccination we can make the proportion of infected individuals tend to zero, and control the transmission of disease in population.

Modeling of space–time infectious disease spread under conditions of uncertainty

A theoretical model for the spread of infectious diseases in a composite space–time domain is developed. The model has a general form that enables it to account for the basic mechanisms of disease distribution and to incorporate the considerable multisourced uncertainty (caused by physiographic features, disease variability, meteorological conditions, etc.). Starting from the general model formulation regarding the specification of transmission and recovery rates, as well as the population migration dynamics, several subsequent assumptions are introduced that simplify analytical tractability and practical implementation. In particular, linearization involving a deterministic functional representation for the average evolution of the fraction of susceptible individuals allows the formulation of an extended Kalman filter approach for estimation based on the time series observed at a finite set of locations. Different aspects of interest derived from the epidemic space–time model proposed, as well as the performance of the extended Kalman filter procedure, are illustrated through simulations.

The genetic base and phenotypic manifestations of Colorado potato beetle resistance to organophosphorus insecticides

A high level of resistance to organophosphorus insecticides was recorded in a local population of the Colorado potato beetle (Ufa raion, Bashkortostan). Toxicological analysis demonstrated that the fraction of susceptible individuals did not exceed 0.025. DNA analysis of the polymorphism of acetylcholinesterase gene (AChE) according to the presence of mutation 989>AG in the sample of Colorado potato beetle imagoes demonstrated the absence of wild-type (sensitive, SS) homozygotes and prevalence (0.79) of the homozygotes with mutant resistant type (RR). The phenetic analysis of the variation of the integument pattern phenes demonstrated statistically significant differences between the imago phenotypes in the ratio of SS and RR genotypes.

A Measles Epidemic Threshold in a Highly Vaccinated Population

BackgroundMass vaccination against measles has successfully lowered the incidence of the disease and has changed the epidemic pattern from a roughly biennial cycle to an irregular sequence of outbreaks. A possible explanation for this sequence of outbreaks is that the vaccinated population is protected by solid herd immunity. If so, we would expect to see the fraction of susceptible individuals remaining below an epidemic threshold. An alternative explanation is the occurrence of occasional localised lapses in herd immunity that allow for major outbreaks in areas with a low vaccine coverage. In that case, we would expect the fraction of susceptible individuals to exceed an epidemic threshold before outbreaks occur. These two explanations for the irregular sequence of measles outbreaks can be tested against observations of both the fraction of susceptible individuals and infection attack rates.Methods and FindingsWe have estimated both the fraction of susceptible individuals at the start of each epidemic year and the infection attack rates for each epidemic year in the Netherlands over a 28-y period. During this period the vaccine coverage averaged 93%, and there was no sustained measles transmission. Several measles outbreaks occurred in communities with low vaccine coverage, and these ended without intervention. We show that there is a clear threshold value for the fraction of susceptible individuals, below which only minor outbreaks occurred, and above which both minor and major outbreaks occurred. A precise, quantitative relationship exists between the fraction of susceptible individuals in excess of this threshold and the infection attack rate during the major outbreaks.ConclusionIn populations with a high but heterogeneous vaccine coverage, measles transmission can be interrupted without establishing solid herd immunity. When infection is reintroduced, a major outbreak can occur in the communities with low vaccine coverage. During such a major outbreak, each additional susceptible individual in excess of the threshold is associated with almost two additional infections. This quantitative relationship offers potential for anticipating both the likelihood and size of future major outbreaks when measles transmission has been interrupted.