General Transmission Model Research Articles

Modeling and Analyzing Transmission of Infectious Diseases Using Generalized Stochastic Petri Nets

Some infectious diseases such as COVID-19 have the characteristics of long incubation period, high infectivity during the incubation period, and carriers with mild or no symptoms which are more likely to cause negligence. Global researchers are working to find out more about the transmission of infectious diseases. Modeling plays a crucial role in understanding the transmission of the new virus and helps show the evolution of the epidemic in stages. In this paper, we propose a new general transmission model of infectious diseases based on the generalized stochastic Petri net (GSPN). First, we qualitatively analyze the transmission mode of each stage of infectious diseases such as COVID-19 and explain the factors that affect the spread of the epidemic. Second, the GSPN model is built to simulate the evolution of the epidemic. Based on this model’s isomorphic Markov chain, the equilibrium state of the system and its changing laws under different influencing factors are analyzed. Our paper demonstrates that the proposed GSPN model is a compelling tool for representing and analyzing the transmission of infectious diseases from system-level understanding, and thus contributes to providing decision support for effective surveillance and response to epidemic development.

A theoretical framework to identify invariant thresholds in infectious disease epidemiology

Setting global strategies and targets for disease prevention and control often involves mathematical models. Model structure is typically subject to intense scrutiny, such as confrontation with empirical data and alternative formulations, while a less frequently challenged aspect is the widely adopted reduction of parameters to their average values. Focusing on endemic diseases, we use a general transmission model to explain how mean field approximations decrease the estimated R0 from prevalence data, while threshold phenomena – such as the epidemic and reinfection thresholds – remain invariant. This results in an underestimation of the effort required to control disease, which may be particularly severe when the approximation inappropriately places transmission estimates below important thresholds. These concepts are widely applicable across endemic pathogen systems.

Analysis of the Impact of Nonlinearity on the Capacity of Communication Channels

We study the impact of nonlinearities on the transmission rate of a communication system by establishing lower and upper bounds on the channel capacity. Our analysis is based on a general transmission model that includes transmitter and receiver nonlinearities, environmental thermal noise, and receiver chain noise. Using this model, we derive lower and upper bounds for the channel capacity of additive white Gaussian noise channels, fading channels, and multiple input multiple output channels in various thermal noise and receiver noise regimes.

Evidence for a major gene influence on persistent developmental stuttering.

Stuttering is a complex developmental speech disorder of unknown etiology. There is a substantial aggregation of stuttering in families, suggesting a genetic component to the disorder. However, the exact mode of transmission is still unknown. An earlier study of 56 multigenerational pedigrees ascertained through single adult probands (38 males and 18 females) found that biological relatives of persistent developmental stutterers have an approximately 10-fold higher risk than in the general population; risk is higher for male relatives, and proband's sex does not affect recurrence and relative risks. In the present paper we conduct a complex segregation analysis of the same data, using the logistic regression model of the SAGE software. Based on the comparisons of model likelihoods, the Mendelian model was selected over all other nongenetic models and the general transmission model. This model was further refined into the most parsimonious model, which shows an autosomal dominant major gene effect influenced by two covariates: sex and affection status of parents. With this model applied to 47 informative multiplex pedigrees, a power calculation based on linkage simulation produced an average lod score of 6.8 for 10-cM density genome scan markers. These results give impetus for a genomewide linkage analysis of susceptibility to persistent developmental stuttering.

Segregation analysis of esophageal cancer in 221 high-risk Chinese families.

Until recently, environmental factors were considered of greatest importance in the etiology of esophageal cancer. Recent studies, however, have suggested that genetic factors also have a role. Since no formal genetic study of this cancer has been previously reported, we carried out a statistical analysis to determine how important genetic factors are in the etiology of esophageal cancer in high-incidence areas of North China. Using a logistic regressive model, we performed a segregation analysis on 221 high-risk nuclear families from the Yaocun Commune, Linxian, Henan Province of China, with at least one affected family member and with all offspring aged 40 years or older. Three models, the mendelian, the environmental, and the no-transmission models, were each compared with the general-transmission model that incorporated both genetic and environmental factors. According to Akaike's Information Criterion, the mendelian model provided the best fit for the data. By the chi-square test, the mendelian inheritance model was not rejected, but the environmental and the no-transmission models were both rejected. The segregation analysis indicated an autosomal recessive mendelian inheritance, with the alleged mendelian gene present at a frequency of 19%, causing 4% of this population to be predisposed to develop esophageal cancer. Large, unmeasured, residual familial factors, however, were also significant. Both an autosomal recessive gene and unexplained environmental factors appear to be important in the etiology of esophageal cancer in the subpopulation studied.

Search for faster methods of fitting the regressive models to quantitative traits

The regressive models describe familial patterns of dependence of quantitative measures by specifying regression relationships among a person's phenotype and genotype and the phenotypes and genotypes of antecedents. When the number of sibs in the pattern of dependence increases, as in the class D regressive model, computation of the likelihood becomes time consuming, since the Elston-Stewart algorithm cannot be used generally. On the other hand, the simpler class A regressive model, which imposes a restriction on the sib-sib correlation, may lead to inference of a spurious major gene, as already observed in some instances. A simulation study is performed to explore the robustness of class A model with respect to false inference of a major gene and to search for faster methods of computing the likelihood under class D model. The class A model is not robust against the presence of a sib-sib correlation exceeding that specified by the model, unless tests on transmission probabilities are performed carefully: false detection of a major gene is reduced from a number of 26-30 to between 0 and 4 data sets out of 30 replicates after testing both the Mendelian transmission and the absence of transmission of a major effect against the general transmission model. Among various approximations of the likelihood formulation of the class D model, approximations 6 and 8 are found to work appropriately in terms of both the estimation of all parameters and hypothesis testing, for each generating model. These approximations lessen the computer time by allowing use of the Elston-Stewart algorithm.

The familial transmission of bipolar illness.

As part of the National Institute of Mental Health Collaborative Program on the Psychobiology of Depression study, data were collected on 2225 first-degree relatives of 612 probands. We analyzed 187 families of bipolar patients (149 probands with a diagnosis of bipolar I disorder and 38 with a diagnosis of schizoaffective, manic subtype). Using traditional genetic methods, the morbid risk of bipolar illness in relatives was found to be 5.7% in the relatives of bipolar probands as contrasted with 1.1% in the relatives of probands with major depression. These values compared closely with those obtained using survival analysis. Relatives of probands with early onset were found to have a greater risk than relatives of probands with late onset. The sex of the relative, the sex of the proband, or the subtype of the proband (bipolar I or schizoaffective bipolar) did not influence the risk in the relative. The age at onset was found to be accelerated with birth cohort, with individuals born in more recent cohorts having an earlier onset. Multifactorial analysis found significant heterogeneity for sex-specific sibling correlations (with the brother-sister correlation smaller than the same-sexed correlations), and path analysis estimated transmissibility of liability to be 71%. The mixed model, which allows for a single major locus with a multifactorial background, gave evidence for the presence of a major locus when controlling for the effects of birth cohort and age at onset. However, this evidence is tempered when comparing the mixed model with a more general transmission model.