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Mean Field Analysis of Hypergraph Contagion Models
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| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 6) |
| Halaman | : | 1987-2007 |
| Abstrak | : | We typically interact in groups, not just in pairs. For this reason, it has recently been proposed that the spread of information, opinion, or disease should be modeled over a hypergraph rather than a standard graph. The use of hyperedges naturally allows for a nonlinear rate of transmission, in terms of both the group size and the number of infected group members, as is the case, for example, when social distancing is encouraged. We consider a general class of individual-level, stochastic, susceptible-infected-susceptible models on a hypergraph, and focus on a mean field approximation proposed in [G. F. de Arruda, G. Petri, and Y. Moreno, Phys. Rev. Res., 2 (2020), 023032]. We derive spectral conditions under which the mean field model predicts local or global stability of the infection-free state. We also compare these results with (a) a new condition that we derive for decay to zero in mean for the exact process, (b) conditions for a different mean field approximation in [D. J. Higham and H.-L. de Kergorlay, Proc. A, 477 (2021), 20210232], and (c) numerical simulations of the microscale model. |
Stationarity and Inference in Multistate Promoter Models of Stochastic Gene Expression via Stick-Breaking Measures
| Pengarang | : | William Lippitt |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 6) |
| Halaman | : | 1953-1986 |
| Abstrak | : | In a general stochastic multistate promoter model of dynamic messenger ribonucleic acid (mRNA)/protein interactions, we identify the stationary joint distribution of the promoter state, mRNA, and protein levels through an explicit “stick-breaking" construction perhaps of interest in itself. This derivation is a constructive advance over previous work where the stationary distribution is solved only in restricted cases. Moreover, the stick-breaking construction allows us to sample directly from the stationary distribution, permitting inference procedures and model selection. In this context, we discuss numerical Bayesian experiments to illustrate the results. |
Modularity Maximization for Graphons
| Pengarang | : | Florian Klimm |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 6) |
| Halaman | : | 1930-1952 |
| Abstrak | : | Networks are a widely used tool for investigating the large-scale connectivity structure in complex systems and graphons have been proposed as an infinite-size limit of dense networks. The detection of communities or other meso-scale structures is a prominent topic in network science as it allows the identification of functional building blocks in complex systems. Similarly, we may want to simplify graphons in terms of communities, in order to gain a comprehensible description of their meso-scale structure. This raises the question of how communities in graphons can be identified. In this paper, we define a graphon modularity and demonstrate that it can be maximized to detect communities in graphons. We then investigate specific synthetic graphons and show that they may show a wide range of different community structures. We also reformulate the graphon-modularity maximization as a continuous optimization problem and so prove the optimal community structure or lack thereof for some graphons, something that is usually not possible for networks. Furthermore, we demonstrate that estimating a graphon from network data as an intermediate step can improve the detection of communities, in comparison with exclusively maximizing the modularity of the network. While the choice of graphon estimator may strongly influence the accord between the community structure of a network and its estimated graphon, we find that there is a substantial overlap if an appropriate estimator is used. Our study demonstrates that community detection for graphons is possible and may serve as a privacy-preserving way to cluster network data. |
Modeling Spatial Waves of Wolbachia Invasion for Controlling Mosquito-Borne Diseases
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 6) |
| Halaman | : | 1903-1929 |
| Abstrak | : | Wolbachia is a natural bacterium that can infect mosquitoes and reduce their ability to transmit mosquito-borne diseases, such as dengue fever, Zika, and chikungunya. Field trials and modeling studies have shown that the fraction of infection among the mosquitoes must exceed a threshold level for the infection to persist. To capture this threshold, it is critical to consider the spatial heterogeneity in the distributions of the infected and uninfected mosquitoes created by a local release of the infected mosquitoes. We develop and analyze PDE models to study the invasion dynamics of Wolbachia infection among mosquitoes in the field. Our reaction-diffusion-type models account for the complex vertical transmission and the spatial mosquito dispersion. We characterize the threshold for a successful invasion with a bubble-shaped distribution, called the “critical bubble.” The critical bubble is optimal in its release size compared to other spatial profiles in a one-dimensional landscape. The fraction of infection near the release center is higher than the threshold level for the corresponding homogeneously mixing ODE models. We show that the proposed spatial models give rise to the traveling waves of Wolbachia infection when above the threshold. We quantify how the threshold condition and traveling-wave velocity depend on the diffusion coefficients and other model parameters. Numerical studies for different scenarios are presented to inform the design of release strategies. |
Global Dynamics of a Filippov SIQR Model with Delayed Relay Control
| Pengarang | : | Jiafu Wang |
| Nama Majalah/Jurnal | : | Siam Journal On Applied Mathematics |
| Volume / Edisi | : | 82 (No. 6) |
| Halaman | : | 1879-1902 |
| Abstrak | : | Global dynamics of a Filippov susceptible, infectious, quarantine, and recovered model subject to delayed relay control are investigated in this work. The global stability of equilibria is obtained by means of the generalized Lyapunov method. In addition, combining the Poincaré maps, the displacement function, and a Melnikov-like method, we derive some sufficient conditions to ensure the existence, uniqueness, and global stability of a slowly oscillating periodic solution. Numerical simulations are performed to explore the effectiveness of the quarantine control measure and the effects of the delay. |
Peran Procalcitonin sebagai Marker Infeksi
| Pengarang | : | Juliani Dewi |
| Nama Majalah/Jurnal | : | CDK Cermin dunia kedokteran |
| Volume / Edisi | : | 45 (No. 7) |
| Halaman | : | 550-554 |
| Abstrak | : | Delayed bacterial infection diagnosis may be caused by delayed microbiology culture results. Infection markers, like leucocyte count and CRP, did not meet the expectations, even in sepsis cases. An ideal biomarker can determine bacterial or non bacterial inflammation as early as possible, and provide information on clinical conditions and prognosis. Procalcitonin can be a promising infection marker, and as a basis for evaluation of antibiotics efficacy. |
Deteksi Keterlambatan Bicara dan Bahasa pada Anak
| Pengarang | : | William Surya Hartanto |
| Nama Majalah/Jurnal | : | CDK Cermin dunia kedokteran |
| Volume / Edisi | : | 45 (No. 7) |
| Halaman | : | 545-549 |
| Abstrak | : | Speech and language delays occurred in 2.3-19% of children aged 2-7 years, mostly diagnosed at the age of less than 3 years. Comprehensive evaluation of development is important because atypical development of speech and language can be secondary characteristics of physical disorders and other development disorders. Early detection and intervention can improve emotional, social, and cognition aspects, which will also improve the outcome. |
Zika Virus and its Threads to Microcephaly
| Pengarang | : | Dias Rima Sutiono, Cintya Pradnya Pratita |
| Nama Majalah/Jurnal | : | CDK Cermin dunia kedokteran |
| Volume / Edisi | : | 45 (No. 7) |
| Halaman | : | 541-543 |
| Abstrak | : | The infection of ZIKV is through transplacental transmission. Polymerase chain reaction (PCR) detected the strains of ZIKV inside amniotic fluid only whereas in other fluids, serum and urine, revealed negative results. Microcephaly with numerous calcifications was discovered in the fetus of all cases. Ventriculomegaly and CNS structures anomalies were also discovered, though some structures such as subcortical nuclei of the brain and ascending dorsal columns of the spinal tract were well preserved. |
Pencegahan Efek Radiasi pada Pencitraan Radiologi
| Pengarang | : | Reginald Maleachi, Ricardo Tjakraatmadja |
| Nama Majalah/Jurnal | : | CDK Cermin dunia kedokteran |
| Volume / Edisi | : | 45 (No. 7) |
| Halaman | : | 537-539 |
| Abstrak | : | The effects of radiation in radiology can not be avoided. Radiologists need to be cautious of the radiation effects, know the limit of radiation dose, and minimize radiation exposure, to get the best visualization image with minimal dose. Safety of patients and medical staffs need special attention. Radiation protection is important for patients, staffs, and radiologists through proper indications, minimizing examinations, and to prioritize non-radiation imaging modalities. |
Fourniers Gangrene
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | CDK Cermin dunia kedokteran |
| Volume / Edisi | : | 45 (No. 7) |
| Halaman | : | 528-532 |
| Abstrak | : | Fourniers gangrene is a progressive and fatal necrotizing fasciitis of the perianal, perineal, and genital. Diagnosis can be established through clinical examination. Main principle of therapy is adequate resuscitation, parenteral antibiotic, and debridement. Urine and fecal diversion, hyperbaric treatment, and reconstructive surgery can improve the outcome. Some scoring system for diagnostic accuracy and mortality predictions are Laboratory Risk Indicator for Necrotizing Fasciitis Score(LRINEC) and Fournier Gangrene Severity Index(FGSI). Mortality rate is still high despite appropriate treatment. Management of Fournier’s gangrene in type C hospital was discussed. |