An approximate threshold condition for a non-autonomous system: an application to a vector-borne infection

A non-autonomous system is proposed to model the seasonal pattern of dengue fever. We found that an approximate threshold condition for infection persistence describes all possible behavior of the system. As far as we know, the kind of analysis here proposed is entirely new. No precise mathematical theorems are demonstrated but we give enough numerical evidence to support the conclusions.Comment: 11 pages and 6 figure

The optimal age of vaccination against dengue with an age-dependent biting rate with application to Brazil

In this paper we introduce a single-serotype transmission model, including an age-dependent mosquito biting rate, to nd the optimal vaccination age against dengue in Brazil with Dengvaxia. The optimal vaccination age and minimal lifetime expected risk of hospitalisation are found by adapting a method due to Hethcote [1]. Any number and combination of the four dengue serotypes DENv1-4 is considered. Successful vaccination against a serotype corresponds to a silent infection. The effects of antibody dependent enhancement (ADE) and permanent cross-immunity after two heterologous infections are studied. ADE is assumed to imply risk-free primary infections, while permanent cross-immunity implies risk-free tertiary and quaternary infections. Data from trials of Dengvaxia indicate vaccine efficacy to be age- and serostatus-dependent, and vaccination of seronegative individuals to induce an increased risk of hospitalisation. Some of the scenarios are therefore reconsidered taking these findings into account. The optimal vaccination age is compared to that achievable under the current age-restriction of the vaccine. If vaccination is not considered to induce risk optimal vaccination ages are very low. The assumption of ADE generally leads to a higher optimal vaccination age in this case. For a single stereotype vaccination is not recommended in the case of ADE. Permanent cross-immunity results in a slightly lower optimal vaccination age. If vaccination induces a risk the optimal vaccination ages are much higher, particularly for permanent cross-immunity. ADE has no effect on the optimal vaccination age when permanent cross-immunity is considered, otherwise it leads to a slight increase in optimal vaccination age

A mathematical model for optimizing the indications of liver transplantation in patients with hepatocellular carcinoma

Abstract Background The criteria for organ sharing has developed a system that prioritizes liver transplantation (LT) for patients with hepatocellular carcinoma (HCC) who have the highest risk of wait-list mortality. In some countries this model allows patients only within the Milan Criteria (MC, defined by the presence of a single nodule up to 5 cm, up to three nodules none larger than 3 cm, with no evidence of extrahepatic spread or macrovascular invasion) to be evaluated for liver transplantation. This police implies that some patients with HCC slightly more advanced than those allowed by the current strict selection criteria will be excluded, even though LT for these patients might be associated with acceptable long-term outcomes. Methods We propose a mathematical approach to study the consequences of relaxing the MC for patients with HCC that do not comply with the current rules for inclusion in the transplantation candidate list. We consider overall 5-years survival rates compatible with the ones reported in the literature. We calculate the best strategy that would minimize the total mortality of the affected population, that is, the total number of people in both groups of HCC patients that die after 5 years of the implementation of the strategy, either by post-transplantation death or by death due to the basic HCC. We illustrate the above analysis with a simulation of a theoretical population of 1,500 HCC patients with tumor size exponentially. The parameter λ obtained from the literature was equal to 0.3. As the total number of patients in these real samples was 327 patients, this implied in an average size of 3.3 cm and a 95% confidence interval of [2.9; 3.7]. The total number of available livers to be grafted was assumed to be 500. Results With 1500 patients in the waiting list and 500 grafts available we simulated the total number of deaths in both transplanted and non-transplanted HCC patients after 5 years as a function of the tumor size of transplanted patients. The total number of deaths drops down monotonically with tumor size, reaching a minimum at size equals to 7 cm, increasing from thereafter. With tumor size equals to 10 cm the total mortality is equal to the 5 cm threshold of the Milan criteria. Conclusion We concluded that it is possible to include patients with tumor size up to 10 cm without increasing the total mortality of this population

Age and regional differences in clinical presentation and risk of hospitalization for dengue in Brazil, 2000-2014

OBJECTIVES: Dengue cases range from asymptomatic to severe, eventually leading to hospitalization and death. Timely and appropriate management is critical to reduce morbidity. Since 1980, dengue has spread throughout Brazil, affecting an increasing number of individuals. This paper describes age and regional differences in dengue’s clinical presentation and associated risk of hospitalization based on more than 5 million cases reported to the Brazilian Ministry of Health from 2000-2014. METHODS: We performed a retrospective analysis of ∼5,450,000 dengue cases, relating clinical manifestations and the risk of hospitalization to age, gender, previous infection by dengue, dengue virus serotype, years of formal education, delay to first attendance and the occurrence of dengue during outbreaks and in different Brazilian regions. RESULTS: Complicated forms of dengue occurred more frequently among those younger than 10 years (3.12% vs 1.92%) and those with dengue virus 2 infection (7.65% vs 2.42%), with a delay to first attendance >;2 days (3.18% vs 0.82%) and with ≤4 years of formal education (2.02% vs 1.46%). The risk of hospitalization was higher among those aged 6-10 years old (OR 4.57; 95% CI 1.43-29.96) and those who were infected by dengue virus 2 (OR 6.36; 95% CI 2.52-16.06), who lived in the Northeast region (OR 1.38; 95% CI 1.11-2.10) and who delayed first attendance by >;5 days (composite OR 3.15; 95% CI 1.33-8.9). CONCLUSIONS: In Brazil, the occurrence of severe dengue and related hospitalization is associated with being younger than 10 years old, being infected by dengue virus 2 or 3, living in the Northeast region (the poorest and the second most populated) and delaying first attendance for more than 2 days

Modeling the risk of malaria for travelers to areas with stable malaria transmission

BACKGROUND: Malaria is an important threat to travelers visiting endemic regions. The risk of acquiring malaria is complex and a number of factors including transmission intensity, duration of exposure, season of the year and use of chemoprophylaxis have to be taken into account estimating risk. MATERIALS AND METHODS: A mathematical model was developed to estimate the risk of non-immune individual acquiring falciparum malaria when traveling to the Amazon region of Brazil. The risk of malaria infection to travelers was calculated as a function of duration of exposure and season of arrival. RESULTS: The results suggest significant variation of risk for non-immune travelers depending on arrival season, duration of the visit and transmission intensity. The calculated risk for visitors staying longer than 4 months during peak transmission was 0.5% per visit. CONCLUSIONS: Risk estimates based on mathematical modeling based on accurate data can be a valuable tool in assessing risk/benefits and cost/benefits when deciding on the value of interventions for travelers to malaria endemic regions

Laparoscopic peritoneal lavage: A definitive treatment for diverticular peritonitis or a "bridge" to elective laparoscopic sigmoidectomy?

To this day, the treatment of generalized peritonitis secondary to diverticular perforation is still controversial. Recently, in patients with acute sigmoid diverticulitis, laparoscopic lavage and drainage has gained a wide interest as an alternative to resection. Based on this backdrop, we decided to perform a systematic review of the literature to evaluate the safety, feasibility, and efficacy of peritoneal lavage in perforated diverticular disease. A bibliographic search was performed in PubMed for case series and comparative studies published between January 1992 and February 2014 describing laparoscopic peritoneal lavage in patients with perforated diverticulitis. A total of 19 articles consisting of 10 cohort studies, 8 case series, and 1 controlled clinical trial met the inclusion criteria and were reviewed. In total these studies analyzed data from 871 patients. The mean follow-up time ranged from 1.5 to 96 months when reported. In 11 studies, the success rate of laparoscopic peritoneal lavage, defined as patients alive without surgical treatment for a recurrent episode of diverticulitis, was 24.3%. In patients with Hinchey stage III diverticulitis, the incidence of laparotomy conversion was 1%, whereas in patients with stage IV it was 45%. The 30-day postoperative mortality rate was 2.9%. The 30-day postoperative reintervention rate was 4.9%, whereas 2% of patients required a percutaneous drainage. Readmission rate after the first hospitalization for recurrent diverticulitis was 6%. Most patients who were readmitted (69%) required redo surgery. A 2-stage laparoscopic intervention was performed in 18.3% of patients. Laparoscopic peritoneal lavage should be considered an effective and safe option for the treatment of patients with sigmoid diverticulitis with Hinchey stage III peritonitis; it can also be consider as a “bridge” surgical step combined with a delayed and elective laparoscopic sigmoidectomy in order to avoid a Hartmann procedure. This minimally invasive staged approach should be considered for patients without systemic toxicity and in centers experienced in minimally invasive surgery techniques. Further evidence is needed, and the ongoing RCTs will better define the role of the laparoscopic peritoneal lavage/drainage in the treatment of patients with complicated diverticulitis

Magnitude and frequency variations of vector-borne infection outbreaks using the Ross–Macdonald model : explaining and predicting outbreaks of dengue fever

The classical Ross–Macdonald model is often utilized to model vector-borne infections; however, this model fails on several fronts. First, using measured (or estimated) parameters, which values are accepted from the literature, the model predicts a much greater number of cases than what is usually observed. Second, the model predicts a single large outbreak that is followed by decades of much smaller outbreaks, which is not consistent with what is observed. Usually towns or cities report a number of recurrences for many years, even when environmental changes cannot explain the disappearance of the infection between the peaks. In this paper, we continue to examine the pitfalls in modelling this class of infections, and explain that, if properly used, the Ross–Macdonald model works and can be used to understand the patterns of epidemics and even, to some extent, be used to make predictions.We model several outbreaks of dengue fever and show that the variable pattern of yearly recurrence (or its absence) can be understood and explained by a simple Ross–Macdonald model modified to take into account human movement across a range of neighbourhoods within a city. In addition, we analyse the effect of seasonal variations in the parameters that determine the number, longevity and biting behaviour of mosquitoes. Based on the size of the first outbreak, we show that it is possible to estimate the proportion of the remaining susceptible individuals and to predict the likelihood and magnitude of the eventual subsequent outbreaks. This approach is described based on actual dengue outbreaks with different recurrence patterns from some Brazilian regions

Modelisation of transition and noble metal vicinal surfaces: energetics, vibrations and stability

The energetics of transition and noble metal (Rh, Pd, Cu) vicinal surfaces, i.e., surface energy, step energy, kink energy and electronic interactions between steps, is studied at 0K from electronic structure calculations in the tight-binding approximation using a {\it s, p} and {\it d} valence orbital basis set. Then, the surface phonon spectra of copper are investigated in the harmonic approximation with the help of a semi-empirical inter-atomic potential. This allows to derive the contribution of phonons at finite temperatures to the step free energy and to the interactions between steps. The last part is devoted to the stability of vicinal surfaces relative to faceting with special attention to the domain of orientations (100)-(111). Semi-empirical potentials are shown to be not realistic enough to give a reliable answer to this problem. The results derived from electronic structure calculations predict a variety of behaviors and, in particular, a possible faceting into two other vicinal orientations. Finally, temperature effects are discussed. Comparisons are made with other theoretical works and available experiments