A dynamic model for the COVID-19 with direct and indirect transmission pathways.

Two common transmission pathways for the spread of COVID-19 virus are direct and indirect. The direct pathway refers to the person-to-person transmission between susceptibles and infectious individuals. Infected individuals shed virus on the objects, and new infections arise through touching a contaminated surface; this refers to the indirect transmission pathway. We model the direct and indirect transmission pathways with a S A D O I R ode model. Our proposal explicitly includes compartments for the contaminated objects, susceptible individuals, asymptomatic infectious, detected infectious, and recovered individuals. We compute the basic reproduction number and epidemic growth rate of the model and determine how these fundamental quantities relate to the transmission rate of the pathways. We further study the relationship between the rate of loss of immunity and the occurrence of backward bifurcation. An efficient statistical framework is introduced to estimate the parameters of the model. We show the performance of the model in the simulation scenarios and the real data from the COVID-19 daily cases in South Korea.

Impact of spasticity on functioning in spinal cord injury: an application of graphical modelling.

OBJECTIVE: To identify the impact of moderate-to-severe spasticity on functioning in people living with spinal cord injury. DESIGN: Secondary analysis of cross-sectional survey data using graphical modelling. SUBJECTS: Individuals (n = 1,436) with spinal cord injury aged over 16 years with reported spasticity problems. METHODS: Spasticity and 13 other impairments in body functions were assessed using the spinal cord injury Secondary Conditions Scale. Impairments in mental functions were assessed using the Mental Health subscale of the 36-item Short Form (SF-36). Independence in activities was measured with the Spinal Cord Injury Independence Measure Self-Report. Restrictions in participation were measured with the Utrecht Scale for Evaluation Rehabilitation - Participation. RESULTS: Fifty-one percent of participants reported moderate-to-severe spasticity. Graphical modelling showed that Chronic pain, Contractures, Tiredness, Doing housework, and Respiratory functions were associated with spasticity and were the top 5 potential targets for interventions to improve the experience of spasticity. The associations and intervention targets were dependent on the level and completeness of the lesion. CONCLUSION: This is the first application of graphical modelling in studying spasticity in people living with spinal cord injury. The results can be used as a basis for studies aiming to optimize rehabilitation interventions in people with moderate-to-severe spasticity.

Reconstruction of Networks with Direct and Indirect Genetic Effects.

Genetic variance of a phenotypic trait can originate from direct genetic effects, or from indirect effects, i.e., through genetic effects on other traits, affecting the trait of interest. This distinction is often of great importance, for example, when trying to improve crop yield and simultaneously control plant height. As suggested by Sewall Wright, assessing contributions of direct and indirect effects requires knowledge of (1) the presence or absence of direct genetic effects on each trait, and (2) the functional relationships between the traits. Because experimental validation of such relationships is often unfeasible, it is increasingly common to reconstruct them using causal inference methods. However, most current methods require all genetic variance to be explained by a small number of quantitative trait loci (QTL) with fixed effects. Only a few authors have considered the "missing heritability" case, where contributions of many undetectable QTL are modeled with random effects. Usually, these are treated as nuisance terms that need to be eliminated by taking residuals from a multi-trait mixed model (MTM). But fitting such an MTM is challenging, and it is impossible to infer the presence of direct genetic effects. Here, we propose an alternative strategy, where genetic effects are formally included in the graph. This has important advantages: (1) genetic effects can be directly incorporated in causal inference, implemented via our PCgen algorithm, which can analyze many more traits; and (2) we can test the existence of direct genetic effects, and improve the orientation of edges between traits. Finally, we show that reconstruction is much more accurate if individual plant or plot data are used, instead of genotypic means. We have implemented the PCgen-algorithm in the R-package pcgen.