Mathematical modelling for Zoonotic Visceral Leishmaniasis dynamics: A new analysis considering updated parameters and notified human Brazilian data

Brazil is one of the highest endemic countries for Zoonotic Visceral Leishmaniasis: according to the Brazilian Ministry of Health, the annual number of new human cases and deaths due to this disease has been increasing for the last 20 years. In addition, regarding the Americas, the specific relationship between canine and human for Visceral Leishmaniasis dynamics is still not well understood. In this work we propose a new model for Zoonotic Visceral Leishmaniasis, based on the models previously published by Burattini et al. (1998) and Ribas et al. (2013). Herein, we modeled the disease dynamics using a modified set of differential equations from those two authors, considering the same assumptions (inclusion of human, dog and sandfly populations, all constants over time). From this set of equations we were able to calculate the basic reproduction number R 0 and to analyze the stability and sensitivity of the system to the parameters variability. As main result, when the stability of the system is reached, the normalized reporting human cases rate is estimated in 9.12E-08/day. This estimation is very close to the 2015 report from Araçatuba city, 5.69E-08/day. We also observed from stability and sensitivity analysis that the activity of sandfly population is critical to introduction and maintenance of Zoonotic Visceral Leishmaniasis in the population. In addition, the importance of dog as source of infection concentrates on latent dog, since it does not show clinical symptoms and signs and, therefore, has a great contribution to disease dissemination. As conclusion, considering the presently ethical issues regarding to elimination of positive dog in Brazil and the highly sensitivity of disease dynamics on sandfly population, we recommend that the sandfly population control should be prioritized.

A comparative analysis of three different methods for the estimation of the basic reproduction number of dengue

The basic reproduction number, R₀, is defined as the expected number of secondary cases of a disease produced by a single infection in a completely susceptible population, and can be estimated in several ways. For example, from the stability analysis of a compartmental model; through the use of the matrix of next generation, or from the final size of an epidemic, etc. In this paper we applied the method for estimating R₀ of dengue fever from the initial growth phase of an outbreak, without assuming exponential growth of cases, a common assumption in many studies. We used three different methods of calculating R₀ to compare the techniques' details and to evaluate how these techniques estimate the value of R₀ of dengue using data from the city of Ribeirão Preto (SE of Brazil) in two outbreaks. The results of the three methods are numerically different but, when we compare them using a system of differential equations developed for modeling only the first generation time, we can observe that the methods differ little in the initial growth phase. We conclude that the methods predict that dengue will spread in the city studied and the analysis of the data shows that the estimated values of R₀ have an equal pattern overtime.

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.

Estimated Zika virus importations to Europe by travellers from Brazil

BACKGROUND

Given the interconnectivity of Brazil with the rest of the world, Zika virus (ZIKV) infections have the potential to spread rapidly around the world via viremic travellers. The extent of spread depends on the travel volume and the endemicity in the exporting country. In the absence of reliable surveillance data, we did mathematical modelling to estimate the number of importations of ZIKV from Brazil into Europe.

DESIGN

We applied a previously developed mathematical model on importations of dengue to estimate the number of ZIKV importations into Europe, based on the travel volume, the probability of being infected at the time of travel, the population size of Brazil, and the estimated incidence of ZIKV infections.

RESULTS

Our model estimated between 508 and 1,778 imported infections into Europe in 2016, of which we would expect between 116 and 355 symptomatic Zika infections; with the highest number of importations being into France, Portugal and Italy.

CONCLUSIONS

Our model identified high-risk countries in Europe. Such data can assist policymakers and public health professionals in estimating the extent of importations in order to prepare for the scale up of laboratory diagnostic assays and estimate the occurrence of Guillain-Barré Syndrome, potential sexual transmission, and infants with congenital ZIKV syndrome.

The risk of dengue for non-immune foreign visitors to the 2016 summer olympic games in Rio de Janeiro, Brazil

BACKGROUND

Rio de Janeiro in Brazil will host the Summer Olympic Games in 2016. About 400,000 non-immune foreign tourists are expected to attend the games. As Brazil is the country with the highest number of dengue cases worldwide, concern about the risk of dengue for travelers is justified.

METHODS

A mathematical model to calculate the risk of developing dengue for foreign tourists attending the Olympic Games in Rio de Janeiro in 2016 is proposed. A system of differential equation models the spread of dengue amongst the resident population and a stochastic approximation is used to assess the risk to tourists. Historical reported dengue time series in Rio de Janeiro for the years 2000-2015 is used to find out the time dependent force of infection, which is then used to estimate the potential risks to a large tourist cohort. The worst outbreak of dengue occurred in 2012 and this and the other years in the history of Dengue in Rio are used to discuss potential risks to tourists amongst visitors to the forthcoming Rio Olympics.

RESULTS

The individual risk to be infected by dengue is very much dependent on the ratio asymptomatic/symptomatic considered but independently of this the worst month of August in the period studied in terms of dengue transmission, occurred in 2007.

CONCLUSIONS

If dengue returns in 2016 with the pattern observed in the worst month of August in history (2007), the expected number of symptomatic and asymptomatic dengue cases among tourists will be 23 and 206 cases, respectively. This worst case scenario would have an incidence of 5.75 (symptomatic) and 51.5 (asymptomatic) per 100,000 individuals.

Climate Change and Aedes Vectors: 21st Century Projections for Dengue Transmission in Europe

Warming temperatures may increase the geographic spread of vector-borne diseases into temperate areas. Although a tropical mosquito-borne viral disease, a dengue outbreak occurred in Madeira, Portugal, in 2012; the first in Europe since 1920s. This outbreak emphasizes the potential for dengue re-emergence in Europe given changing climates. We present estimates of dengue epidemic potential using vectorial capacity (VC) based on historic and projected temperature (1901–2099). VC indicates the vectors' ability to spread disease among humans. We calculated temperature-dependent VC for Europe, highlighting 10 European cities and three non-European reference cities. Compared with the tropics, Europe shows pronounced seasonality and geographical heterogeneity. Although low, VC during summer is currently sufficient for dengue outbreaks in Southern Europe to commence–if sufficient vector populations (either Ae. aegypti and Ae. albopictus) were active and virus were introduced. Under various climate change scenarios, the seasonal peak and time window for dengue epidemic potential increases during the 21st century. Our study maps dengue epidemic potential in Europe and identifies seasonal time windows when major cities are most conducive for dengue transmission from 1901 to 2099. Our findings illustrate, that besides vector control, mitigating greenhouse gas emissions crucially reduces the future epidemic potential of dengue in Europe.

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Past and present assessments of VC indicate strong seasonal patterns in temperate climates' dengue epidemic potential.

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Current VC intensity could permit summer dengue epidemics in Southern Europe driven by either Aedes vector, where present.

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Extent of spatial and temporal VC changes depend on vector characteristics and projected greenhouse gas emissions scenarios.

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With climate change, future VC intensifies: shifting northward and prolonging the season suitable for dengue epidemics.

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By the 21st century's end, seasonal dengue outbreaks could emerge in much more of Europe if Aedes vectors were established.

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Achieving the Paris Agreement's emission reduction commitments could decelerate the increasing threat of dengue to Europe.

Globalization and climate change can increase the geographic spread of vector-borne diseases. Among those, dengue, a mosquito-transmitted viral disease, causes up to 390 million human infections annually. This study evaluates potential for dengue outbreaks in Europe based on climate conditions. Estimated suitability (1901–2099) for dengue outbreaks is expanding presently from Southern Europe northward and lengthening seasonally up to eight months around the summer; however, the projected extent, intensity and duration depend partially on greenhouse gas emissions. We conclude that limiting emissions thereby mitigating climate change could substantially reduce the likelihood of dengue transmission events in Europe during the 21st century.

Age specific differences in efficacy and safety for the CYD-tetravalent dengue vaccine

CYD-TDV is the first dengue vaccine to have completed Phase 3 efficacy trials. Efficacy was consistently higher in those aged 9 and above for all variables studied: efficacy against virologically confirmed dengue of any severity and serotype, serotype specific efficacy, efficacy dependent on baseline seropositivity, efficacy against hospitalizations and efficacy against severe disease. Because of the higher efficacy and the absence of a safety signal, the age group with the best benefit of the use of CYD-TDV is individuals aged 9 and above - the age group for which licensure is now being sought.

Modeling Importations and Exportations of Infectious Diseases via Travelers

This paper is an attempt to estimate the risk of infection importation and exportation by travelers. Two countries are considered: one disease-free country and one visited or source country with a running endemic or epidemic infectious disease. Two models are considered. In the first model (disease importation), susceptible individuals travel from their disease-free home country to the endemic country and come back after some weeks. The risk of infection spreading in their home country is then estimated supposing the visitors are submitted to the same force of infection as the local population but do not contribute to it. In the second model (disease exportation), it is calculated the probability that an individual from the endemic (or epidemic) country travels to a disease-free country in the condition of latent infected and eventually introduces the infection there. The input of both models is the force of infection at the visited/source country, assumed known. The models are deterministic, but a preliminary stochastic formulation is presented as an appendix. The models are exemplified with two distinct real situations: the risk of dengue importation from Thailand to Europe and the risk of Ebola exportation from Liberia to the USA.

Potential for international spread of wild poliovirus via travelers

BACKGROUND

The endgame of polio eradication is hampered by the international spread of poliovirus via travelers. In response to ongoing importations of poliovirus into polio-free countries, on 5 May 2014, WHO's Director-General declared the international spread of wild poliovirus a public health emergency of international concern. Our objective was to develop a mathematical model to estimate the international spread of polio infections.

METHODS

Our model took into account polio endemicity in polio-infected countries, population size, polio immunization coverage rates, infectious period, the asymptomatic-to-symptomatic ratio, and also the probability of a traveler being infectious at the time of travel. We applied our model to three scenarios: (1) number of exportations of both symptomatic and asymptomatic polio infections out of currently polio-infected countries, (2) the risk of spread of poliovirus to Saudi Arabia via Hajj pilgrims, and (3) the importation risk of poliovirus into India.

RESULTS

Our model estimated 665 polio exportations (>99 % of which were asymptomatic) from nine polio-infected countries in 2014, of which 78.3 % originated from Pakistan. Our model also estimated 21 importations of poliovirus into Saudi Arabia via Hajj pilgrims and 20 poliovirus infections imported to India in the same year.

CONCLUSION

The extent of importations of asymptomatic and symptomatic polio infections is substantial. For countries that are vulnerable to polio outbreaks due to poor national polio immunization coverage rates, our newly developed model may help guide policy-makers to decide whether imposing an entry requirement in terms of proof of vaccination against polio would be justified.

A public health risk assessment for yellow fever vaccination: a model exemplified by an outbreak in the state of São Paulo, Brazil

We propose a method to analyse the 2009 outbreak in the region of Botucatu in the state of São Paulo (SP), Brazil, when 28 yellow fever (YF) cases were confirmed, including 11 deaths. At the time of the outbreak, the Secretary of Health of the State of São Paulo vaccinated one million people, causing the death of five individuals, an unprecedented number of YF vaccine-induced fatalities. We apply a mathematical model described previously to optimise the proportion of people who should be vaccinated to minimise the total number of deaths. The model was used to calculate the optimum proportion that should be vaccinated in the remaining, vaccine-free regions of SP, considering the risk of vaccine-induced fatalities and the risk of YF outbreaks in these regions.

Plasmodium falciparum in the southeastern Atlantic forest: a challenge to the bromeliad-malaria paradigm?

BACKGROUND

Recently an unexpectedly high prevalence of Plasmodium falciparum was found in asymptomatic blood donors living in the southeastern Brazilian Atlantic forest. The bromeliad-malaria paradigm assumes that transmission of Plasmodium vivax and Plasmodium malariae involves species of the subgenus Kerteszia of Anopheles and only a few cases of P. vivax malaria are reported annually in this region. The expectations of this paradigm are a low prevalence of P. vivax and a null prevalence of P. falciparum. Therefore, the aim of this study was to verify if P. falciparum is actively circulating in the southeastern Brazilian Atlantic forest remains.

METHODS

In this study, anophelines were collected with Shannon and CDC-light traps in seven distinct Atlantic forest landscapes over a 4-month period. Field-collected Anopheles mosquitoes were tested by real-time PCR assay in pools of ten, and then each mosquito from every positive pool, separately for P. falciparum and P. vivax. Genomic DNA of P. falciparum or P. vivax from positive anophelines was then amplified by traditional PCR for sequencing of the 18S ribosomal DNA to confirm Plasmodium species. Binomial probabilities were calculated to identify non-random results of the P. falciparum-infected anopheline findings.

RESULTS

The overall proportion of anophelines naturally infected with P. falciparum was 4.4% (21/480) and only 0.8% (4/480) with P. vivax. All of the infected mosquitoes were found in intermixed natural and human-modified environments and most were Anopheles cruzii (22/25 = 88%, 18 P. falciparum plus 4 P. vivax). Plasmodium falciparum was confirmed by sequencing in 76% (16/21) of positive mosquitoes, whereas P. vivax was confirmed in only 25% (1/4). Binomial probabilities suggest that P. falciparum actively circulates throughout the region and that there may be a threshold of the forested over human-modified environment ratio upon which the proportion of P. falciparum-infected anophelines increases significantly.

CONCLUSIONS

These results show that P. falciparum actively circulates, in higher proportion than P. vivax, among Anopheles mosquitoes of fragments of the southeastern Brazilian Atlantic forest. This finding challenges the classical bromeliad-malaria paradigm, which considers P. vivax circulation as the driver for the dynamics of residual malaria transmission in this region.

Attention performance among Brazilian truck drivers and its association with amphetamine use: pilot study

The aim of this article was to describe the attention functioning of twenty-two truck drivers and its relationship with amphetamine use. Those drivers who reported using amphetamines in the twelve months previous to the interview had the best performance in a test evaluating sustained attention functioning. Although amphetamine use may initially seem advantageous to the drivers, it may actually impair safe driving. The findings suggest the importance of monitoring the laws regarding amphetamine use in this country.

Hematologic profile of hematophagous Desmodus rotundus bats before and after experimental infection with rabies virus

INTRODUCTION

Hematophagous Desmodus rotundus bats play an important role in the rabies lifecycle. This study describes the hematological profile of these bats before and after experimental infection with rabies virus.

METHODS

Cells counts were performed in a Neubauer chamber.

RESULTS

The average values of erythrocytes and leucocytes counts in blood before experimental infections were 9.97 × 10(6)mm3 and 4.80 × 10(3)mm3, respectively. Neutrophils represented 69.9% of white blood cells and the lymphocytes represented 26.9%. Following the experimental infections, the average numbers of erythrocytes and leucocytes was 9.43 × 106mm3 and 3.98 × 10(3)mm3, respectively. Neutrophils represented 40% of white blood cells and the lymphocytes represented 59%.

CONCLUSIONS

The hematological profile given in this study can serve as reference values for D. rotundus bats.

Risk of symptomatic dengue for foreign visitors to the 2014 FIFA World Cup in Brazil

Brazil will host the FIFA World Cup™, the biggest single-event competition in the world, from June 12-July 13 2014 in 12 cities. This event will draw an estimated 600,000 international visitors. Brazil is endemic for dengue. Hence, attendees of the 2014 event are theoretically at risk for dengue. We calculated the risk of dengue acquisition to non-immune international travellers to Brazil, depending on the football match schedules, considering locations and dates of such matches for June and July 2014. We estimated the average per-capita risk and expected number of dengue cases for each host-city and each game schedule chosen based on reported dengue cases to the Brazilian Ministry of Health for the period between 2010-2013. On the average, the expected number of cases among the 600,000 foreigner tourists during the World Cup is 33, varying from 3-59. Such risk estimates will not only benefit individual travellers for adequate pre-travel preparations, but also provide valuable information for public health professionals and policy makers worldwide. Furthermore, estimates of dengue cases in international travellers during the World Cup can help to anticipate the theoretical risk for exportation of dengue into currently non-infected areas.

A comparative analysis of the relative efficacy of vector-control strategies against dengue fever

Dengue is considered one of the most important vector-borne infection, affecting almost half of the world population with 50 to 100 million cases every year. In this paper, we present one of the simplest models that can encapsulate all the important variables related to vector control of dengue fever. The model considers the human population, the adult mosquito population and the population of immature stages, which includes eggs, larvae and pupae. The model also considers the vertical transmission of dengue in the mosquitoes and the seasonal variation in the mosquito population. From this basic model describing the dynamics of dengue infection, we deduce thresholds for avoiding the introduction of the disease and for the elimination of the disease. In particular, we deduce a Basic Reproduction Number for dengue that includes parameters related to the immature stages of the mosquito. By neglecting seasonal variation, we calculate the equilibrium values of the model's variables. We also present a sensitivity analysis of the impact of four vector-control strategies on the Basic Reproduction Number, on the Force of Infection and on the human prevalence of dengue. Each of the strategies was studied separately from the others. The analysis presented allows us to conclude that of the available vector control strategies, adulticide application is the most effective, followed by the reduction of the exposure to mosquito bites, locating and destroying breeding places and, finally, larvicides. Current vector-control methods are concentrated on mechanical destruction of mosquitoes' breeding places. Our results suggest that reducing the contact between vector and hosts (biting rates) is as efficient as the logistically difficult but very efficient adult mosquito's control.

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

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.

Brain activity and medical diagnosis: an EEG study

Background

Despite new brain imaging techniques that have improved the study of the underlying processes of human decision-making, to the best of our knowledge, there have been very few studies that have attempted to investigate brain activity during medical diagnostic processing. We investigated brain electroencephalography (EEG) activity associated with diagnostic decision-making in the realm of veterinary medicine using X-rays as a fundamental auxiliary test. EEG signals were analysed using Principal Components (PCA) and Logistic Regression Analysis

Results

The principal component analysis revealed three patterns that accounted for 85% of the total variance in the EEG activity recorded while veterinary doctors read a clinical history, examined an X-ray image pertinent to a medical case, and selected among alternative diagnostic hypotheses. Two of these patterns are proposed to be associated with visual processing and the executive control of the task. The other two patterns are proposed to be related to the reasoning process that occurs during diagnostic decision-making.

Conclusions

PCA analysis was successful in disclosing the different patterns of brain activity associated with hypothesis triggering and handling (pattern P₁); identification uncertainty and prevalence assessment (pattern P₃), and hypothesis plausibility calculation (pattern P₂); Logistic regression analysis was successful in disclosing the brain activity associated with clinical reasoning success, and together with regression analysis showed that clinical practice reorganizes the neural circuits supporting clinical reasoning.

Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations

A dimensional analysis of the classical equations related to the dynamics of vector-borne infections is presented. It is provided a formal notation to complete the expressions for the Ross' Threshold Theorem, the Macdonald's basic reproduction "rate" and sporozoite "rate", Garret-Jones' vectorial capacity and Dietz-Molineaux-Thomas' force of infection. The analysis was intended to provide a formal notation that complete the classical equations proposed by these authors.