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1. A generalized ODE susceptible-infectious-susceptible compartmental model with potentially periodic behavior

   https://doi.org/10.1016/j.idm.2023.11.007  

   Greenhalgh, Scott; Dumas, Anna (December 2023, Infectious Disease Modelling)

   Differential equation compartmental models are crucial tools for forecasting and analyzing disease trajectories. Among these models, those dealing with only susceptible and infectious individuals are particularly useful as they offer closed-form expressions for solutions, namely the logistic equation. However, the logistic equation has limited ability to describe disease trajectories since its solutions must converge monotonically to either the disease-free or endemic equilibrium, depending on the parameters. Unfortunately, many diseases exhibit periodic cycles, and thus, do not converge to equilibria. To address this limitation, we developed a generalized susceptible-infectious-susceptible compartmental model capable of accurately incorporating the duration of infection distribution and describing both periodic and non-periodic disease trajectories. We characterized how our model’s parameters influence its behavior and applied the model to predict gonorrhea incidence in the US, using Akaike Information Criteria to inform on its merit relative to the traditional SIS model. The significance of our work lies in providing a novel susceptible-infected-susceptible model whose solutions can have closed-form expressions that may be periodic or non-periodic depending on the parameterization. Our work thus provides disease modelers with a straightforward way to investigate the potential periodic behavior of many diseases and thereby may aid ongoing efforts to prevent recurrent outbreaks. 

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2. A Parrondo paradox in susceptible-infectious-susceptible dynamics over periodic temporal networks

   https://doi.org/10.1016/j.mbs.2024.109336  

   Sejunti, Maisha Islam; Taylor, Dane; Masuda, Naoki (November 2024, Mathematical Biosciences)
3. Susceptible–infected epidemics on evolving graphs

   https://doi.org/10.1214/22-EJP828  

   Durrett, Rick; Yao, Dong (January 2022, Electronic Journal of Probability)
4. Engineered Water Repellency in Frost Susceptible Soils

   https://doi.org/10.1061/9780784484012.047  

   Uduebor, Micheal; Daniels, John; Naqvi, Mohammad Wasif; Cetin, Bora (March 2022, Geo-Congress 2022: Soil Improvement, Geosynthetics, and Innovative Geomaterials)

   Anne Lemnitzer, Ph.D.; Armin W. Stuedlein (Ed.)

   Selected papers from sessions of Geo-Congress 2022, held in Charlotte, North Carolina, March 20–23, 2022. Sponsored by the Society of Exploration Geophysicists and the Geo-Institute of ASCE. This Geotechnical Special Publication contains 66 peer-reviewed papers on geosynthetics, innovative geomaterials, and soil improvement techniques. Topics include: rigid inclusions and stone columns; soil stabilization; bio-grouting and bio-inspired solutions; geosynthetics; and innovative geomaterials and methods. GSP 331 will be valuable to practitioners and researchers working in the area of soil improvement. 

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5. Systems Biology Modeling of the Complement System Under Immune Susceptible Pathogens

   https://doi.org/10.3389/fphy.2021.603704  

   Zewde, Nehemiah T.; Hsu, Rohaine V.; Morikis, Dimitrios; Palermo, Giulia (April 2021, Frontiers in Physics)

   null (Ed.)

   The complement system is assembled from a network of proteins that function to bring about the first line of defense of the body against invading pathogens. However, complement deficiencies or invasive pathogens can hijack complement to subsequently increase susceptibility of the body to infections. Moreover, invasive pathogens are increasingly becoming resistant to the currently available therapies. Hence, it is important to gain insights into the highly dynamic interaction between complement and invading microbes in the frontlines of immunity. Here, we developed a mathematical model of the complement system composed of 670 ordinary differential equations with 328 kinetic parameters, which describes all three complement pathways (alternative, classical, and lectin) and includes description of mannose-binding lectin, collectins, ficolins, factor H-related proteins, immunoglobulin M, and pentraxins. Additionally, we incorporate two pathogens: (type 1) complement susceptible pathogen and (type 2) Neisseria meningitidis located in either nasopharynx or bloodstream. In both cases, we generate time profiles of the pathogen surface occupied by complement components and the membrane attack complex (MAC). Our model shows both pathogen types in bloodstream are saturated by complement proteins, whereas MACs occupy <<1.0% of the pathogen surface. Conversely, the MAC production in nasopharynx occupies about 1.5–10% of the total N. meningitidis surface, thus making nasal MAC levels at least about eight orders of magnitude higher. Altogether, we predict complement-imbalance, favoring overactivation, is associated with nasopharynx homeostasis. Conversely, orientating toward complement-balance may cause disruption to the nasopharynx homeostasis. Thus, for sporadic meningococcal disease, our model predicts rising nasal levels of complement regulators as early infection biomarkers. 

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