Mathematical modeling and optimal control of malaria

Malaria continues to infect millions and kill hundreds of thousands of people worldwide each year, despite over a century of research and attempts to control and eliminate this infectious disease. Challenges such as the development and spread of drug resistant malaria parasites, insecticide resistance to mosquitoes, climate change, the presence of individuals with subpatent malaria infections which normally are asymptomatic and behavioral plasticity in the mosquito hinder the prospects of malaria control and elimination. In this thesis, mathematical models of malaria transmission and control that address the role of drug resistance, immunity, iron supplementation and anemia, immigration and visitation, and the presence of asymptomatic carriers in malaria transmission are developed. A within-host mathematical model of severe Plasmodium falciparum malaria is also developed. First, a deterministic mathematical model for transmission of antimalarial drug resistance parasites with superinfection is developed and analyzed. The possibility of increase in the risk of superinfection due to iron supplementation and fortification in malaria endemic areas is discussed. The model results calls upon stakeholders to weigh the pros and cons of iron supplementation to individuals living in malaria endemic regions. Second, a deterministic model of transmission of drug resistant malaria parasites, including the inflow of infective immigrants, is presented and analyzed. The optimal control theory is applied to this model to study the impact of various malaria and vector control strategies, such as screening of immigrants, treatment of drug-sensitive infections, treatment of drug-resistant infections, and the use of insecticide-treated bed nets and indoor spraying of mosquitoes. The results of the model emphasize the importance of using a combination of all four controls tools for effective malaria intervention. Next, a two-age-class mathematical model for malaria transmission with asymptomatic carriers is developed and analyzed. In development of this model, four possible control measures are analyzed: the use of long-lasting treated mosquito nets, indoor residual spraying, screening and treatment of symptomatic, and screening and treatment of asymptomatic individuals. The numerical results show that a disease-free equilibrium can be attained if all four control measures are used. A common pitfall for most epidemiological models is the absence of real data; model-based conclusions have to be drawn based on uncertain parameter values. In this thesis, an approach to study the robustness of optimal control solutions under such parameter uncertainty is presented. Numerical analysis of the optimal control problem in the presence of parameter uncertainty demonstrate the robustness of the optimal control approach that: when a comprehensive control strategy is used the main conclusions of the optimal control remain unchanged, even if inevitable variability remains in the control profiles. The results provide a promising framework for the design of cost-effective strategies for disease control with multiple interventions, even under considerable uncertainty of model parameters. Finally, a separate work modeling the within-host Plasmodium falciparum infection in humans is presented. The developed model allows re-infection of already-infected red blood cells. The model hypothesizes that in severe malaria due to parasite quest for survival and rapid multiplication, the Plasmodium falciparum can be absorbed in the already-infected red blood cells which accelerates the rupture rate and consequently cause anemia. Analysis of the model and parameter identifiability using Markov chain Monte Carlo methods is presented.

In vivo and in vitro effect of imipramine and fluoxetine on Na+,K+-ATPase activity in synaptic plasma membranes from the cerebral cortex of rats

The effects of in vivo chronic treatment and in vitro addition of imipramine, a tricyclic antidepressant, or fluoxetine, a selective serotonin reuptake inhibitor, on the cortical membrane-bound Na+,K+-ATPase activity were studied. Adult Wistar rats received daily intraperitoneal injections of 10 mg/kg of imipramine or fluoxetine for 14 days. Twelve hours after the last injection rats were decapitated and synaptic plasma membranes (SPM) from cerebral cortex were prepared to determine Na+,K+-ATPase activity. There was a significant decrease (10%) in enzyme activity after imipramine but fluoxetine treatment caused a significant increase (27%) in Na+,K+-ATPase activity compared to control (P<0.05, ANOVA; N = 7 for each group). When assayed in vitro, the addition of both drugs to SPM of naive rats caused a dose-dependent decrease in enzyme activity, with the maximal inhibition (60-80%) occurring at 0.5 mM. We suggest that a) imipramine might decrease Na+,K+-ATPase activity by altering membrane fluidity, as previously proposed, and b) stimulation of this enzyme might contribute to the therapeutic efficacy of fluoxetine, since brain Na+,K+-ATPase activity is decreased in bipolar patients.

The role of reelin in the development and evolution of the cerebral cortex

Reelin is an extracellular matrix protein that is defective in reeler mutant mice and plays a key role in the organization of architectonic patterns, particularly in the cerebral cortex. In mammals, a "reelin signal" is activated when reelin, secreted by Cajal-Retzius neurons, binds to receptors of the lipoprotein receptor family on the surface of cortical plate cells, and triggers Dab1 phosphorylation. As reelin is a key component of cortical development in mammals, comparative embryological studies of reelin expression were carried out during cortical development in non-mammalian amniotes (turtles, squamates, birds and crocodiles) in order to assess the putative role of reelin during cortical evolution. The data show that reelin is present in the cortical marginal zone in all amniotes, and suggest that reelin has been implicated in the evolution of the radial organization of the cortical plate in the synapsid lineage leading from stem amniotes to mammals, as well as in the lineage leading to squamates, thus providing an example of homoplastic evolution (evolutionary convergence). The mechanisms by which reelin instructs radial cortical organization in these two lineages seem different: in the synapsid lineage, a drastic amplification of reelin production occurred in Cajal-Retzius cells, whereas in squamates, in addition to reelin-secreting cells in the marginal zone, a second layer of reelin-producing cells developed in the subcortex. Altogether, our results suggest that the reelin-signaling pathway has played a significant role in shaping the evolution of cortical development.

Visual maps in the adult primate cerebral cortex: some implications for brain development and evolution

In this paper, the topology of cortical visuotopic maps in adult primates is reviewed, with emphasis on recent studies. The observed visuotopic organisation can be summarised with reference to two basic rules. First, adjacent radial columns in the cortex represent partially overlapping regions of the visual field, irrespective of whether these columns are part of the same or different cortical areas. This primary rule is seldom, if ever, violated. Second, adjacent regions of the visual field tend to be represented in adjacent radial columns of a same area. This rule is not as rigid as the first, as many cortical areas form discontinuous, second-order representations of the visual field. A developmental model based on these physiological observations, and on comparative studies of cortical organisation, is then proposed, in order to explain how a combination of molecular specification steps and activity-driven processes can generate the variety of visuotopic organisations observed in adult cortex.

Interruption of the blood-stage cycle of the malaria parasite, Plasmodium chabaudi, by protein tyrosine kinase inhibitors

Malaria is a devastating disease caused by a unicellular protozoan, Plasmodium, which affects 3.7 million people every year. Resistance of the parasite to classical treatments such as chloroquine requires the development of new drugs. To gain insight into the mechanisms that control Plasmodium cell cycle, we have examined the effects of kinase inhibitors on the blood-stage cycle of the rodent malaria parasite, Plasmodium chabaudi. In vitro incubation of red blood cells for 17 h at 37ºC with the inhibitors led to a decrease in the percent of infected cells, compared to control treatment, as follows: genistein (200 µM - 75%), staurosporine (1 µM - 58%), R03 (1 µM - 75%), and tyrphostins B44 (100 µM - 66%) and B46 (100 µM - 68%). All these treatments were shown to retard or prevent maturation of the intraerythrocytic parasites. The diverse concentration ranges at which these inhibitors exert their effects give a clue as to the types of signals that initiate the transitions between the different developmental stages of the parasite. The present data support our hypothesis that the maturation of the intraerythrocytic cycle of malaria parasites requires phosphorylation. In this respect, we have recently reported a high Ca2+ microenvironment surrounding the parasite within red blood cells. Several kinase activities are modulated by Ca2+. The molecular identification of the targets of these kinases could provide new strategies against malaria.

Effects of autacoid inhibitors and of an antagonist on malaria infection in mice

The effects of p-chlorophenylalanine, an inhibitor of serotonin synthesis, indomethacin, an inhibitor of prostaglandin synthesis, cyproheptadine, a serotonin, bradykinin and histamine antagonist, were assessed separately and in combination with chloroquine (CQ) in Vom strains of Swiss albino mice (18-22 g) of either sex infected intraperitoneally with 1 x 10(7) Plasmodium yoelii nigeriensis-induced malaria. As prophylactic, these agents reduced from 31.9 ± 4.5 to 16.1 ± 8.1% the level of parasitemia relative to control but had no appreciable activity as curative agents when administered subcutaneously once daily for 4 days after 72 h of parasites innoculum in vivo. However, CQ alone and the combination of these agents with CQ in curative and prophylactic treatments significantly reduced (from 50.3 ± 5.8 to 4.9 ± 0.75%) the level of parasitemia (P < 0.05), which was taken only once 72 h after the parasites innoculum. The prophylactic result was shown to produce better results than the curative treatment. The data indicate that inhibitors and an antagonist can reduce the parasitemia load (the extent of damage and the severity of infection) as well as enhance the effects of CQ when combined with it for malaria therapy. The study reveals that the production of autacoids in established infection renders autacoid inhibitors and an antagonist ineffective for radical cure in malarial mice; however, selective inhibition of local hormones implicated in the pathological manifestations of malaria infection by autacoid inhibitors and an antagonist may be a possible pathway to reduce the severity of infection and the associated tissue damage and to enhance the efficacy of available anti-malarials.

Distribution of microglial cells in the cerebral hemispheres of embryonic and neonatal chicks

The distribution, morphology and morphometry of microglial cells in the chick cerebral hemispheres from embryonic day 4 (E4) to the first neonatal day (P1) were studied by histochemical labeling with a tomato (Lycopersicon esculentum) lectin. The histochemical analysis revealed lectin-reactive cells in the nervous parenchyma on day E4. Between E4 (5.7 ± 1.35 mm length) and E17 (8.25 ± 1.2 mm length), the lectin-reactive cells were identified as ameboid microglia and observed starting from the subventricular layer, distributed throughout the mantle layer and in the proximity of the blood vessels. After day E13, the lectin-reactive cells exhibited elongated forms with small branched processes, and were considered primitive ramified microglia. Later, between E18 (5.85 ± 1.5 mm cell body length) and P1 (3.25 ± 0.6 mm cell body length), cells with more elongated branched processes were observed, constituting the ramified microglia. Our findings provide additional information on the migration and differentiation of microglial cells, whose ramified form is observed at the end of embryonic development. The present paper focused on the arrangement of microglial cells in developing cerebral hemispheres of embryonic and neonatal chicks, which are little studied in the literature. Details of morphology, morphometry and spatial distribution of microglial cells contributed to the understanding of bird and mammal central nervous system ontogeny. Furthermore, the identification and localization of microglial cells during the normal development could be used as a morphological guide for embryonic brain injury researches.

Patterns of cerebral activation during lexical and phonological reading in Portuguese

According to the concepts of cognitive neuropsychology, there are two principal routes of reading processing: a lexical route, in which global reading of words occurs and a phonological route, responsible for the conversion of the graphemes into their respective phonemes. In the present study, functional magnetic resonance imaging (fMRI) was used to investigate the patterns of cerebral activation in lexical and phonological reading by 13 healthy women with a formal educational level greater than 11 years. Participants were submitted to a silent reading task containing three types of stimuli: real words (irregular and foreign words), nonwords and illegitimate graphic stimuli. An increased number of activated voxels were identified by fMRI in the word reading (lexical processing) than in the nonword reading (phonological processing) task. In word reading, activation was greater than for nonwords in the following areas: superior, middle and inferior frontal gyri, and bilateral superior temporal gyrus, right cerebellum and the left precentral gyrus, as indicated by fMRI. In the reading of nonwords, the activation was predominant in the right cerebellum and in the left superior temporal gyrus. The results of the present study suggest the existence of differences in the patterns of cerebral activation during lexical and phonological reading, with greater involvement of the right hemisphere in reading words than nonwords.

Comparison of the diagnosis of malaria by microscopy, immunochromatography and PCR in endemic areas of Venezuela

Whole blood samples (N = 295) were obtained from different locations in Amazonas and Sucre States, in Venezuela. Malaria was diagnosed by microscopy, OptiMAL™ and polymerase chain reaction (PCR), with Plasmodium vivax, P. falciparum, and P. malariae being detected when possible. We identified 93 infections, 66 of which were caused by P. vivax, 26 by P. falciparum, and 1 was a mixed infection. No infection caused by P. malariae was detected. The sensitivity and specificity of each diagnostic method were high: 95.7 and 97.9% for microscopy, 87.0 and 97.9% for OptiMAL, and 98.0 and 100% for PCR, respectively. Most samples (72.2%) showed more than 5000 parasites/µL blood. The sensitivity of the diagnosis by microscopy and OptiMAL decreased with lower parasitemia. All samples showing disagreement among the methods were reevaluated, but the first result was used for the calculations. Parasites were detected in the 6 false-negative samples by microscopy after the second examination. The mixed infection was only detected by PCR, while the other methods diagnosed it as P. falciparum (microscopy) or P. vivax (OptiMAL) infection. Most of the false results obtained with the OptiMAL strip were related to the P. falciparum-specific band, including 3 species misdiagnoses, which could be related to the test itself or to genetic variation of the Venezuelan strains. The use of the microscopic method for malaria detection is recommended for its low cost but is very difficult to implement in large scale, population-based studies; thus, we report here more efficient methods suitable for this purpose.

Vitamin B1 and B6 in the malaria parasite: requisite or dispensable?

Vitamins are essential compounds mainly involved in acting as enzyme co-factors or in response to oxidative stress. In the last two years it became apparent that apicomplexan parasites are able to generate B vitamers such as vitamin B1 and B6 de novo. The biosynthesis pathways responsible for vitamin generation are considered as drug targets, since both provide a high degree of selectivity due to their absence in the human host. This report updates the current knowledge about vitamin B1 and B6 biosynthesis in malaria and other apicomplexan parasites. Owing to the urgent need for novel antimalarials, the significance of the biosynthesis and salvage of these vitamins is critically discussed in terms of parasite survival and their exploitation for drug development.

Photodynamic antimicrobial chemotherapy (PACT) for the treatment of malaria, leishmaniasis and trypanosomiasis

A photodynamic effect occurs when photosensitiser molecules absorb light and dissipate the absorbed energy by transferring it to biological acceptors (usually oxygen), generating an excess of reactive species that are able to force cells into death pathways. Several tropical diseases present physiopathological aspects that are accessible to the application of a photosensitiser and local illumination. In addition, disease may be transmitted through infected blood donations, and many of the aetiological agents associated with tropical diseases have been shown to be susceptible to the photodynamic approach. However, there has been no systematic investigation of the application of photoantimicrobial agents in the various presentations, whether to human disease or to the disinfection of blood products or even as photo-insecticides. We aim in this review to report the advances in the photoantimicrobial approach that are beneficial to the field of anti-parasite therapy and also have the potential to facilitate the development of low-cost/high-efficiency protocols for underserved populations.

Experimental models in vaccine research: malaria and leishmaniasis

Animal models have a long history of being useful tools, not only to test and select vaccines, but also to help understand the elaborate details of the immune response that follows infection. Different models have been extensively used to investigate putative immunological correlates of protection against parasitic diseases that are important to reach a successful vaccine. The greatest challenge has been the improvement and adaptation of these models to reflect the reality of human disease and the screening of vaccine candidates capable of overcoming the challenge of natural transmission. This review will discuss the advantages and challenges of using experimental animal models for vaccine development and how the knowledge achieved can be extrapolated to human disease by looking into two important parasitic diseases: malaria and leishmaniasis.

Ischemia preconditioning is neuroprotective in a rat cerebral ischemic injury model through autophagy activation and apoptosis inhibition

Sublethal ischemic preconditioning (IPC) is a powerful inducer of ischemic brain tolerance. However, its underlying mechanisms are still not well understood. In this study, we chose four different IPC paradigms, namely 5 min (5 min duration), 5×5 min (5 min duration, 2 episodes, 15-min interval), 5×5×5 min (5 min duration, 3 episodes, 15-min intervals), and 15 min (15 min duration), and demonstrated that three episodes of 5 min IPC activated autophagy to the greatest extent 24 h after IPC, as evidenced by Beclin expression and LC3-I/II conversion. Autophagic activation was mediated by the tuberous sclerosis type 1 (TSC1)-mTor signal pathway as IPC increased TSC1 but decreased mTor phosphorylation. Terminal deoxynucleotidyl transferase dUTP nick end labeling (TUNEL) and hematoxylin and eosin staining confirmed that IPC protected against cerebral ischemic/reperfusion (I/R) injury. Critically, 3-methyladenine, an inhibitor of autophagy, abolished the neuroprotection of IPC and, by contrast, rapamycin, an autophagy inducer, potentiated it. Cleaved caspase-3 expression, neurological scores, and infarct volume in different groups further confirmed the protection of IPC against I/R injury. Taken together, our data indicate that autophagy activation might underlie the protection of IPC against ischemic injury by inhibiting apoptosis.

Detection of acute cerebral hemorrhage in rabbits by magnetic induction

Acute cerebral hemorrhage (ACH) is an important clinical problem that is often monitored and studied with expensive devices such as computed tomography, magnetic resonance imaging, and positron emission tomography. These devices are not readily available in economically underdeveloped regions of the world, emergency departments, and emergency zones. We have developed a less expensive tool for non-contact monitoring of ACH. The system measures the magnetic induction phase shift (MIPS) between the electromagnetic signals on two coils. ACH was induced in 6 experimental rabbits and edema was induced in 4 control rabbits by stereotactic methods, and their intracranial pressure and heart rate were monitored for 1 h. Signals were continuously monitored for up to 1 h at an exciting frequency of 10.7 MHz. Autologous blood was administered to the experimental group, and saline to the control group (1 to 3 mL) by injection of 1-mL every 5 min. The results showed a significant increase in MIPS as a function of the injection volume, but the heart rate was stable. In the experimental (ACH) group, there was a statistically significant positive correlation of the intracranial pressure and MIPS. The change of MIPS was greater in the ACH group than in the control group. This high-sensitivity system could detect a 1-mL change in blood volume. The MIPS was significantly related to the intracranial pressure. This observation suggests that the method could be valuable for detecting early warning signs in emergency medicine and critical care units.