A mathematical model for malaria transmission relating global warming and local socioeconomic conditions

OBJECTIVE: Sensitivity analysis was applied to a mathematical model describing malaria transmission relating global warming and local socioeconomic conditions. METHODS: A previous compartment model was proposed to describe the overall transmission of malaria. This model was built up on several parameters and the prevalence of malaria in a community was characterized by the values assigned to them. To assess the control efforts, the model parameters can vary on broad intervals. RESULTS: By performing the sensitivity analysis on equilibrium points, which represent the level of malaria infection in a community, the different possible scenarios are obtained when the parameters are changed. CONCLUSIONS: Depending on malaria risk, the efforts to control its transmission can be guided by a subset of parameters used in the mathematical model.

Mathematical model to estimate of the deterioration of wooden poles in contact with soil used in rural areas

In São Paulo State, mainly in rural areas, the utilization of wooden poles is observed for different purposes. In this context, wood in contact with the ground presents faster deterioration, which is generally associated to environmental factors and, especially to the presence of fungi and insects. With the use of mathematical models, the useful life of wooden structures can be predicted by obtaining "climatic indexes" to indicate, comparatively among the areas studied, which have more or less tendency to fungi and insects attacks. In this work, by using climatological data of several cities at São Paulo State, a simplified mathematical model was obtained to measure the aggressiveness of the wood in contact with the soil.

Evaluation of a new mathematical model to describe Clostridium perfringens growth during the cooling of cooked ground beef

A mathematical model previously developed to study microbial growth in food products under an isothermal environment was adapted to a time-varying temperature regime. The resulting model was applied to study the growth of Clostridium perfringens in meat products. This micro-organism is of particular relevance to public health and economy due to the loss of productivity caused by it. Results showed a similar performance of the model used compared to the Baranyi model under an isothermal situation and a slightly better performance under a non-isothermal temperature profile.

A theoretical model of the evolution of virulence in sexually transmitted HIV/AIDS

INTRODUCTION: The evolution of virulence in host-parasite relationships has been the subject of several publications. In the case of HIV virulence, some authors suggest that the evolution of HIV virulence correlates with the rate of acquisition of new sexual partners. In contrast some other authors argue that the level of HIV virulence is independent of the sexual activity of the host population. METHODS: Provide a mathematical model for the study of the potential influence of human sexual behaviour on the evolution of virulence of HIV is provided. RESULTS: The results indicated that, when the probability of acquisition of infection is a function both of the sexual activity and of the virulence level of HIV strains, the evolution of HIV virulence correlates positively with the rate of acquisition of new sexual partners. CONCLUSION: It is concluded that in the case of a host population with a low (high) rate of exchange of sexual partners the evolution of HIV virulence is such that the less (more) virulent strain prevails.

Malaria transmission model for different levels of acquired immunity and temperature-dependent parameters (vector)

OBJECTIVE: Describe the overall transmission of malaria through a compartmental model, considering the human host and mosquito vector. METHODS: A mathematical model was developed based on the following parameters: human host immunity, assuming the existence of acquired immunity and immunological memory, which boosts the protective response upon reinfection; mosquito vector, taking into account that the average period of development from egg to adult mosquito and the extrinsic incubation period of parasites (transformation of infected but non-infectious mosquitoes into infectious mosquitoes) are dependent on the ambient temperature. RESULTS: The steady state equilibrium values obtained with the model allowed the calculation of the basic reproduction ratio in terms of the model's parameters. CONCLUSIONS: The model allowed the calculation of the basic reproduction ratio, one of the most important epidemiological variables.

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.

Auger-type granular fertylizer distributor: matemathical model and dynamic simulation

The objective of this study was to model mathematically and to simulate the dynamic behavior of an auger-type fertilizer applicator (AFA) in order to use the variable-rate application (VRA) and reduce the coefficient of variation (CV) of the application, proposing an angular speed controller θ' for the motor drive shaft. The input model was θ' and the response was the fertilizer mass flow, due to the construction, density of fertilizer, fill factor and the end position of the auger. The model was used to simulate a control system in open loop, with an electric drive for AFA using an armature voltage (V A) controller. By introducing a sinusoidal excitation signal in V A with amplitude and delay phase optimized and varying θ' during an operation cycle, it is obtained a reduction of 29.8% in the CV (constant V A) to 11.4%. The development of the mathematical model was a first step towards the introduction of electric drive systems and closed loop control for the implementation of AFA with low CV in VRA.

A temperature predicting model for manufacturing processes requiring coiling

A model for predicting temperature evolution for automatic controling systems in manufacturing processes requiring the coiling of bars in the transfer table is presented. Although the method is of a general nature, the presentation in this work refers to the manufacturing of steel plates in hot rolling mills. The predicting strategy is based on a mathematical model of the evolution of temperature in a coiling and uncoiling bar and is presented in the form of a parabolic partial differential equation for a shape changing domain. The mathematical model is solved numerically by a space discretization via geometrically adaptive finite elements which accomodate the change in shape of the domain, using a computationally novel treatment of the resulting thermal contact problem due to coiling. Time is discretized according to a Crank-Nicolson scheme. Since the actual physical process takes less time than the time required by the process controlling computer to solve the full mathematical model, a special predictive device was developed, in the form of a set of least squares polynomials, based on the off-line numerical solution of the mathematical model.

Gas-solid two-phase flow in the riser of circulating fluidized beds: mathematical modelling and numerical simulation

A mathematical model is developed for gas-solids flows in circulating fluidized beds. An Eulerian formulation is followed based on the two-fluids model approach where both the fluid and the particulate phases are treated as a continuum. The physical modelling is discussed, including the formulation of boundary conditions and the description of the numerical methodology. Results of numerical simulation are presented and discussed. The model is validated through comparison to experiment, and simulation is performed to investigate the effects on the flow hydrodynamics of the solids viscosity.

Comparison of anaerobic threshold determined by visual and mathematical methods in healthy women

Several methods are used to estimate anaerobic threshold (AT) during exercise. The aim of the present study was to compare AT obtained by a graphic visual method for the estimate of ventilatory and metabolic variables (gold standard), to a bi-segmental linear regression mathematical model of Hinkley's algorithm applied to heart rate (HR) and carbon dioxide output (VCO2) data. Thirteen young (24 ± 2.63 years old) and 16 postmenopausal (57 ± 4.79 years old) healthy and sedentary women were submitted to a continuous ergospirometric incremental test on an electromagnetic braking cycloergometer with 10 to 20 W/min increases until physical exhaustion. The ventilatory variables were recorded breath-to-breath and HR was obtained beat-to-beat over real time. Data were analyzed by the nonparametric Friedman test and Spearman correlation test with the level of significance set at 5%. Power output (W), HR (bpm), oxygen uptake (VO2; mL kg-1 min-1), VO2 (mL/min), VCO2 (mL/min), and minute ventilation (VE; L/min) data observed at the AT level were similar for both methods and groups studied (P > 0.05). The VO2 (mL kg-1 min-1) data showed significant correlation (P < 0.05) between the gold standard method and the mathematical model when applied to HR (r s = 0.75) and VCO2 (r s = 0.78) data for the subjects as a whole (N = 29). The proposed mathematical method for the detection of changes in response patterns of VCO2 and HR was adequate and promising for AT detection in young and middle-aged women, representing a semi-automatic, non-invasive and objective AT measurement.

Mathematical modeling of microbial growth in milk

A mathematical model to predict microbial growth in milk was developed and analyzed. The model consists of a system of two differential equations of first order. The equations are based on physical hypotheses of population growth. The model was applied to five different sets of data of microbial growth in dairy products selected from Combase, which is the most important database in the area with thousands of datasets from around the world, and the results showed a good fit. In addition, the model provides equations for the evaluation of the maximum specific growth rate and the duration of the lag phase which may provide useful information about microbial growth.

Periodic dynamic systems for infected hosts and mosquitoes

A mathematical model for the purpose of analysing the dynamic of the populations of infected hosts anf infected mosquitoes when the populations of mosquitoes are periodic in time is here presented. By the computation of a parameter lambda (the spectral radius of a certain monodromy matrix) one can state that either the infection peters out naturally) (lambda <= 1) or if lambda > 1 the infection becomes endemic. The model generalizes previous models for malaria by considering the case of periodic coefficients; it is also a variation of that for gonorrhea. The main motivation for the consideration of this present model was the recent studies on mosquitoes at an experimental rice irrigation system, in the South-Eastern region of Brazil.

Assessing the effects of global warming and local social and economic conditions on the malaria transmission

OBJECTIVE: To show how a mathematical model can be used to describe and to understand the malaria transmission. METHODS: The effects on malaria transmission due to the impact of the global temperature changes and prevailing social and economic conditions in a community were assessed based on a previously presented compartmental model, which describes the overall transmission of malaria. RESULTS/CONCLUSIONS: The assessments were made from the scenarios produced by the model both in steady state and dynamic analyses. Depending on the risk level of malaria, the effects on malaria transmission can be predicted by the temperature ambient or local social and-economic conditions.

The effect of temperature on mobility of Angiostrongylus costaricensis third stage larvae

Third stage larvae (L3) from Angiostrongylus costaricensis were incubated in water at room temperature and at 5 ° C and their mobility was assessed daily for 17 days. Viability was associated with the mobility and position of the L3, and it was confirmed by inoculation per os in albino mice. The number of actively moving L3 sharply decreased within 3 to 4 days, but there were some infective L3 at end of observation. A mathematical model estimated 80 days as the time required to reduce the probability of infective larvae to zero. This data does not support the proposition of refrigerating vegetables and raw food as an isolated procedure for prophylaxis of human abdominal angiostrongylosis infection.