Search Results (5)

This review comprehensively examines the advancements and challenges in anaerobic digestion (AD) for biogas production, emphasising technological, microbial, and policy perspectives. It highlights the AD significant potential for valorising diverse organic substrates, including manure, food waste, and microalgae, thereby contributing to renewable energy generation and greenhouse gas mitigation. Key operational factors influencing biogas yield include substrate composition, temperature (preferably mesophilic conditions), pH (6.5–7.5), and the substrate-to-inoculum ratio (SIR), all of which significantly affect microbial activity and process stability. Co-digestion strategies and pretreatments are examined for their roles in enhancing biodegradability and methane yield, respectively. Microbial community dynamics, particularly responses to feedstock heterogeneity and operational parameters, are integral to process optimisation. Advances in metagenomics have provided insights into microbial resilience and adaptation to conditions such as high ammonium levels. This review also discusses various modelling approaches, including kinetic models and machine learning techniques, for predicting and optimising biogas production. Additionally, policy frameworks within regions such as the European Union and Brazil, along with economic incentives and regulatory hurdles, are also considered crucial for scaling up deployment. Challenges such as digestate management and high capital costs persist, underscoring the need for integrated strategies to enhance the sustainability and viability of AD-based biogas projects. Full article

In this work, we first introduce a class of deterministic epidemic models with varying populations inspired by Arino et al. (2007), the parameterization of two matrices, demography, the waning of immunity, and vaccination parameters. Similar models have been focused on by Julien Arino, Fred Brauer, Odo Diekmann, and their coauthors, but mostly in the case of “closed populations” (models with varying populations have been studied in the past only in particular cases, due to the difficulty of this endeavor). Our Arino–Brauer models contain SIR–PH models of Riano (2020), which are characterized by the phase-type distribution $(\overrightarrow{\alpha },A)$, modeling transitions in “disease/infectious compartments”. The A matrix is simply the Metzler/sub-generator matrix intervening in the linear system obtained by making all new infectious terms 0. The simplest way to define the probability row vector $\overrightarrow{\alpha }$ is to restrict it to the case where there is only one susceptible class $\mathsf{s}$, and when matrix B (given by the part of the new infection matrix, with respect to $\mathsf{s}$) is of rank one, with $B=b\overrightarrow{\alpha }$. For this case, the first result we obtained was an explicit formula (12) for the replacement number (not surprisingly, accounting for varying demography, waning immunity and vaccinations led to several nontrivial modifications of the Arino et al. (2007) formula). The analysis of $(A,B)$ Arino–Brauer models is very challenging. As obtaining further general results seems very hard, we propose studying them at three levels: (A) the exact model, where only a few results are available—see Proposition 2; and (B) a “first approximation” (FA) of our model, which is related to the usually closed population model often studied in the literature. Notably, for this approximation, an associated renewal function is obtained in (7); this is related to the previous works of Breda, Diekmann, Graaf, Pugliese, Vermiglio, Champredon, Dushoff, and Earn. (C) Finally, we propose studying a second heuristic “intermediate approximation” (IA). Perhaps our main contribution is to draw attention to the importance of $(A,B)$ Arino–Brauer models and that the FA approximation is not the only way to tackle them. As for the practical importance of our results, this is evident, once we observe that the $(A,B)$ Arino–Brauer models include a large number of epidemic models (COVID, ILI, influenza, illnesses, etc.). Full article

Our paper presents three new classes of models: SIR-PH, SIR-PH-FA, and SIR-PH-IA, and states two problems we would like to solve about them. Recall that deterministic mathematical epidemiology has one basic general law, the “${\mathcal{R}}_0$ alternative” of Van den Driessche and Watmough, which states that the local stability condition of the disease-free equilibrium may be expressed as ${\mathcal{R}}_0<1$, where ${\mathcal{R}}_0$ is the famous basic reproduction number, which also plays a major role in the theory of branching processes. The literature suggests that it is impossible to find general laws concerning the endemic points. However, it is quite common that 1. When ${\mathcal{R}}_0>1$, there exists a unique fixed endemic point, and 2. the endemic point is locally stable when ${\mathcal{R}}_0>1$. One would like to establish these properties for a large class of realistic epidemic models (and we do not include here epidemics without casualties). We have introduced recently a “simple” but broad class of “SIR-PH models” with varying populations, with the express purpose of establishing for these processes the two properties above. Since that seemed still hard, we have introduced a further class of “SIR-PH-FA” models, which may be interpreted as approximations for the SIR-PH models, and which include simpler models typically studied in the literature (with constant population, without loss of immunity, etc.). For this class, the first “endemic law” above is “almost established”, as explicit formulas for a unique endemic point are available, independently of the number of infectious compartments, and it only remains to check its belonging to the invariant domain. This may yet turn out to be always verified, but we have not been able to establish that. However, the second property, the sufficiency of ${\mathcal{R}}_0>1$ for the local stability of an endemic point, remains open even for SIR-PH-FA models, despite the numerous particular cases in which it was checked to hold (via Routh–Hurwitz time-onerous computations, or Lyapunov functions). The goal of our paper is to draw attention to the two open problems above, for the SIR-PH and SIR-PH-FA, and also for a second, more refined “intermediate approximation” SIR-PH-IA. We illustrate the current status-quo by presenting new results on a generalization of the SAIRS epidemic model. Full article

Background and Objectives: In the intensive care unit (ICU), renal failure and respiratory failure are two of the most common organ failures in patients with systemic inflammatory response syndrome (SIRS). These clinical symptoms usually result from sepsis, trauma, hypermetabolism or shock. If this syndrome is caused by septic shock, the Surviving Sepsis Campaign Bundle suggests that vasopressin be given to maintain mean arterial pressure (MAP) > 65 mmHg if the patient is hypotensive after fluid resuscitation. Nevertheless, it is important to note that some studies found an effect of various mean arterial pressures on organ function; for example, a MAP of less than 75 mmHg was associated with the risk of acute kidney injury (AKI). However, no published study has evaluated the risk factors of mortality in the subgroup of acute kidney injury with respiratory failure, and little is known of the impact of general risk factors that may increase the mortality rate. Materials and Methods: The objective of this study was to determine the risk factors that might directly affect survival in critically ill patients with multiple organ failure in this subgroup. We retrospectively constructed a cohort study of patients who were admitted to the ICUs, including medical, surgical, and neurological, over 24 months (2015.1 to 2016.12) at Chiayi Chang Gung Memorial Hospital. We only considered patients who met the criteria of acute renal injury according to the Acute Kidney Injury Network (AKIN) and were undergoing mechanical ventilator support due to acute respiratory failure at admission. Results: Data showed that the overall ICU and hospital mortality rate was 63.5%. The most common cause of ICU admission in this cohort study was cardiovascular disease (31.7%) followed by respiratory disease (28.6%). Most patients (73%) suffered sepsis during their ICU admission and the mean length of hospital stay was 24.32 ± 25.73 days. In general, the factors independently associated with in-hospital mortality were lactate > 51.8 mg/dL, MAP ≤ 77.16 mmHg, and pH ≤ 7.22. The risk of in-patient mortality was analyzed using a multivariable Cox regression survival model. Adjusting for other covariates, MAP ≤ 77.16 mmHg was associated with higher probability of in-hospital death [OR = 3.06 (1.374–6.853), p = 0.006]. The other independent outcome predictor of mortality was pH ≤ 7.22 [OR = 2.40 (1.122–5.147), p = 0.024]. Kaplan-Meier survival curves were calculated and the log rank statistic was highly significant. Conclusions: Acute kidney injury combined with respiratory failure is associated with high mortality. High mean arterial pressure and normal blood pH might improve these outcomes. Therefore, the acid–base status and MAP should be considered when attempting to predict outcome. Moreover, the blood pressure targets for acute kidney injury in critical care should not be similar to those recommended for the general population and might prevent mortality. Full article

Many of the models used nowadays in mathematical epidemiology, in particular in COVID-19 research, belong to a certain subclass of compartmental models whose classes may be divided into three “$(x,y,z)$” groups, which we will call respectively “susceptible/entrance, diseased, and output” (in the classic SIR case, there is only one class of each type). Roughly, the ODE dynamics of these models contains only linear terms, with the exception of products between x and y terms. It has long been noticed that the reproduction number $\mathcal{R}$ has a very simple Formula in terms of the matrices which define the model, and an explicit first integral Formula is also available. These results can be traced back at least to Arino, Brauer, van den Driessche, Watmough, and Wu (2007) and to Feng (2007), respectively, and may be viewed as the “basic laws of SIR-type epidemics”. However, many papers continue to reprove them in particular instances. This motivated us to redraw attention to these basic laws and provide a self-contained reference of related formulas for $(x,y,z)$ models. For the case of one susceptible class, we propose to use the name SIR-PH, due to a simple probabilistic interpretation as SIR models where the exponential infection time has been replaced by a PH-type distribution. Note that to each SIR-PH model, one may associate a scalar quantity $Y(t)$ which satisfies “classic SIR relations”,which may be useful to obtain approximate control policies. Full article