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.

Determination of serum aluminum, platelet aggregation and lipid peroxidation in hemodialyzed patients

Aluminum (Al3+) overload is frequently associated with lipid peroxidation and neurological disorders. Aluminum accumulation is also reported to be related to renal impairment, anemia and other clinical complications in hemodialysis patients. The aim of the present study was to determine the degree of lipid peroxidation, platelet aggregation and serum aluminum in patients receiving regular hemodialytic treatment. The level of plasma lipid peroxidation was evaluated on the basis of thiobarbituric acid reactive substances (TBARS). Mean platelet peroxidation in patients undergoing hemodialysis was significantly higher than in normal controls (2.7 ± 0.03 vs 1.8 ± 0.06 nmol/l, P<0.05). Platelet aggregation and serum aluminum levels were determined by a turbidimetric method and atomic absorption spectrophotometry, respectively. Serum aluminum was significantly higher in patients than in normal controls (44.5 ± 29 vs 10.8 ± 2.5 µg/l, P<0.05). Human blood platelets were stimulated with collagen (2.2 µg/ml), adenosine diphosphate (6 µM) and epinephrine (6 µM) and showed reduced function with the three agonists utilized. No correlation between aluminum levels and platelet aggregation or between aluminum and peroxidation was observed in hemodialyzed patients.

Fungal infections in marrow transplant recipients under antifungal prophylaxis with fluconazole

Fungal infection is one of the most important causes of morbidity and mortality in bone marrow transplant (BMT) recipients. The growing incidence of these infections is related to several factors including prolonged granulocytopenia, use of broad-spectrum antibiotics, conditioning regimens, and use of immunosuppression to avoid graft-versus-host disease (GvHD). In the present series, we report five cases of invasive mold infections documented among 64 BMT recipients undergoing fluconazole antifungal prophylaxis: 1) A strain of Scedosporium prolificans was isolated from a skin lesion that developed on day +72 after BMT in a chronic myeloid leukemic patient. 2) Invasive pulmonary aspergillosis (Aspergillus fumigatus) was diagnosed on day +29 in a patient with a long period of hospitalization before being transplanted for severe aplastic anemia. 3) A tumoral lung lesion due to Rhizopus arrhizus (zygomycosis) was observed in a transplanted patient who presented severe chronic GvHD. 4) A tumoral lesion due to Aspergillus spp involving the 7th, 8th and 9th right ribs and local soft tissue was diagnosed in a BMT patient on day +110. 5) A patient with a history of Ph1-positive acute lymphocytic leukemia exhibited a cerebral lesion on day +477 after receiving a BMT during an episode of severe chronic GvHD. At that time, blood and spinal fluid cultures yielded Fusarium sp. Opportunistic infections due to fungi other than Candida spp are becoming a major problem among BMT patients receiving systemic antifungal prophylaxis with fluconazole.

ß-Spectrin São PauloII, a novel frameshift mutation of the ß-spectrin gene associated with hereditary spherocytosis and instability of the mutant mRNA

Hereditary spherocytosis (HS) is a common inherited anemia characterized by the presence of spherocytic red cells. Defects in several membrane protein genes have been involved in the pathogenesis of HS. ß-Spectrin-related HS seems to be common. We report here a new mutation in the ß-spectrin gene coding region in a patient with hereditary spherocytosis. The patient presented acanthocytosis and spectrin deficiency and, at the DNA level, a novel frameshift mutation leading to HS, i.e., a C deletion at codon 1392 (ß-spectrin São PauloII), exon 20. The mRNA encoding ß-spectrin São PauloII was very unstable and the mutant protein was not detected in the membrane or in other cellular compartments. It is interesting to note that frameshift mutations of the ß-spectrin gene at the 3' end allow the insertion of the mutant protein in the red cell membrane, leading to a defect in the auto-association of the spectrin dimers and consequent elliptocytosis. On the other hand, ß-spectrin São PauloII protein was absent in the red cell membrane, leading to spectrin deficiency, HS and the presence of acanthocytes.

The calcium-dependent protease of Loxosceles gaucho venom acts preferentially upon red cell band 3 transmembrane protein

Eighty micrograms red blood cell (RBC) ghosts from patients who had previously exhibited the cutaneous form of loxoscelism (presenting localized dermonecrosis) and the viscerocutaneous form of loxoscelism (presenting dermonecrosis, hemoglobinuria, hematuria, and jaundice) and from controls were incubated with 2.5 µg crude Loxosceles gaucho venom in 5 mM phosphate buffer, pH 7.4, at 37ºC. Among all membrane proteins, quantitative proteolysis of the important integral transmembrane protein 3 increased with venom dose and with incubation time from 30 to 120 min, as demonstrated by gel densitometry. Similar quantitative data were obtained for RBC ghosts from patients and from control subjects, a fact that argues against the possibility of genetic factors favoring the hemolytic viscerocutaneous form. These data suggest that the clinical forms may be different types of the same disease, with the viscerocutaneous form being the result of large amounts of intravascularly injected venom and the superficial form being the result of in situ venom action. Since protein 3 is a housekeeping integral membrane protein, whose genetic deficiency leads to hemolytic anemia, it is reasonable to relate it to the hemolysis which occurs in the viscerocutaneous form of loxoscelism. The venom protease responsible for the process was not inhibited after 120-min incubation by 0.2 mM paramethylsulfonyl fluoride or by 0.2 mM N-ethylmaleimide but was inhibited by 25 mM ethylenediaminetetraacetic acid (a calcium-chelating agent) in 5 mM phosphate buffer at pH 7.4, which suggests that the enzyme is a calcium-dependent metalloprotease.

The availability of full match sibling donors and feasibility of allogeneic bone marrow transplantation in Brazil

The feasibility of allogeneic bone marrow transplantation (alloBMT) in a developing country has not yet been demonstrated. Many adverse factors including social and economic limitations may reduce the overall results of this complex and expensive procedure. Our objective was to characterize the most important clinical, social and economic features of candidates for transplantation and their potential donors as well as the influence of these factors on overall survival in a retrospective and exploratory analysis at a university hospital. From July 1993 to July 2001, candidates for BMT were referred to the Bone Marrow Transplantation Unit by Hematology and Oncology Centers from several regions of Brazil. A total of 1138 patients were referred to us as candidates for alloBMT. Median age was 25 years (range: 2 months-60 years), 684 (60.1%) were males and 454 (39.9%) were females. The clinical indications were severe aplastic anemia and hematological malignancies. From the total of 1138 patients, 923 had HLA-typing; 497/923 (53.8%) candidates had full match donors; 352/1138 (30.8%) were eligible for alloBMT. Only 235 of 352 (66.7%) were transplanted. Schooling was 1st to 8th grade for 123/235 (52.3%); monthly family income ranged from US$60 (7%) to more than US$400 (36%). Overall survival for patients with chronic myeloid leukemia, severe aplastic anemia and acute myeloid leukemia was 58, 60 and 30%, respectively. Thus, overall survival rates for the most frequent hematological diseases were similar to those reported in the International Registry, except for acute myeloid leukemia. This descriptive and exploratory analysis suggests the feasibility of alloBMT in a developing country like Brazil.

Anti-leishmania antibodies in cerebrospinal fluid from dogs with visceral leishmaniasis

Visceral leishmaniasis in Brazil is caused by Leishmania (Leishmania) chagasi and the dog is its most important reservoir. The clinical features in dogs include loss of weight, lymphadenopathy, renal failure, skin lesions, fever, hypergammaglobulinemia, hepatosplenomegaly, anemia, and, rarely, neurological symptoms. Most infected animals develop active disease, characterized by high anti-leishmania antibody titers and depressed lymphoproliferative ability. Antibody production is not primarily important for protection but might be involved in the pathogenesis of tissue lesions. An ELISA test was used to determine if there is an association between neurological symptoms and the presence of anti-L. chagasi antibodies in cerebrospinal fluid (CSF). Thirty serum and CSF samples from symptomatic mixed breed dogs (three with neurological symptoms) from a region of high incidence of visceral leishmaniasis in Brazil were examined for antibody using total parasite antigen and anti-dog IgG peroxidase conjugate. A high level of L. chagasi antibodies was observed in sera (mean absorbance ± SD, 1.939 ± 0.405; negative control, N = 20, 0.154 ± 0.074) and CSF (1.571 ± 0.532; negative control, N = 10, 0.0195 ± 0.040) from all animals studied. This observation suggests that L. chagasi can cause breakdown of filtration barriers and the transfer of antibodies and antigens from the blood to the CSF compartment. No correlation was observed between antibody titer in CSF and neurological symptoms.

Thalassemia intermedia as a result of heterozygosis for ß0-thalassemia and aaaanti-3.7/aa genotype in a Brazilian patient

We report a case in which the interaction of heterozygosis for both the ß0-IVS-II-1 (G->A) mutation and the aaaanti-3.7 allele was the probable cause for the clinical occurrence of thalassemia intermedia. The propositus, a 6-year-old Caucasian Brazilian boy of Portuguese descent, showed a moderately severe chronic anemia in spite of having the ß-thalassemia trait. Investigation of the alpha-globin gene status revealed heterozygosis for alpha-gene triplication (aaa/aa). The patient's father, also presenting mild microcytic and hypochromic anemia, had the same alpha and ß genotypes as his son, while the mother, not related to the father and hematologically normal, was also a carrier of the aaaanti-3.7 allele. The present case emphasizes the need for considering the possibility of alpha-gene triplication in ß-thalassemia heterozygotes who display an unexpected severe phenotype. The ß-thalassemia mutation found here is being described for the first time in Brazil.

Karyotype of cryopreserved bone marrow cells

The analysis of chromosomal abnormalities is important for the study of hematological neoplastic disorders since it facilitates classification of the disease. The ability to perform chromosome analysis of cryopreserved malignant marrow or peripheral blast cells is important for retrospective studies. In the present study, we compared the karyotype of fresh bone marrow cells (20 metaphases) to that of cells stored with a simplified cryopreservation method, evaluated the effect of the use of granulocyte-macrophage colony-stimulating factor (GM-CSF) as an in vitro mitotic index stimulator, and compared the cell viability and chromosome morphology of fresh and cryopreserved cells whenever possible (sufficient metaphases for analysis). Twenty-five bone marrow samples from 24 patients with hematological disorders such as acute myeloid leukemia, acute lymphoblastic leukemia, myelodysplastic syndrome, chronic myeloid leukemia, megaloblastic anemia and lymphoma (8, 3, 3, 8, 1, and 1 patients, respectively) were selected at diagnosis, at relapse or during routine follow-up and one sample was obtained from a bone marrow donor after informed consent. Average cell viability before and after freezing was 98.8 and 78.5%, respectively (P < 0.05). Cytogenetic analysis was successful in 76% of fresh cell cultures, as opposed to 52% of cryopreserved samples (P < 0.05). GM-CSF had no proliferative effect before or after freezing. The morphological aspects of the chromosomes in fresh and cryopreserved cells were subjectively the same. The present study shows that cytogenetic analysis of cryopreserved bone marrow cells can be a reliable alternative when fresh cell analysis cannot be done, notwithstanding the reduced viability and lower percent of successful analysis that are associated with freezing.

An experimental model of hemolysis-induced acute pancreatitis

The literature indicates that acute pancreatitis is a complication of massive hemolysis with a prevalence of about 20%. We describe an experimental model of hemolysis-induced acute pancreatitis. Hemolytic anemia was induced in rats by a single ip injection of 60 mg/kg of 20 mg/ml acetylphenylhydrazine (APH) in 20% (v/v) ethanol on the first experimental day (day 0). One hundred and fifty Wistar albino rats weighing 180-200 g were divided into three groups of 50 animals each: groups 1, 2 and 3 were injected ip with APH, 20% ethanol, and physiological saline, respectively. Ten rats from each group were sacrificed on study days 1, 2, 3, 4 and 5. Serum amylase, lipase levels and pancreatic tissue tumor necrosis factor-alpha (TNF-alpha) and platelet-activating factor (PAF) contents were determined and a histological examination of the pancreas was performed. No hemolysis or pancreatitis was observed in any of the rats in groups 2 and 3. In group 1, massive hemolysis was observed in 35 (70%) of 50 rats, moderate hemolysis in seven (14%), and no hemolysis in eight (16%). Thirty-three of 35 (94.2%) rats with massive hemolysis had hyperamylasemia, and 29 of these rats (82.8%) had histologically proven pancreatitis. The most severe pancreatitis occurred on day 3, as demonstrated by histology. Tissue TNF-alpha and PAF levels were statistically higher in group 1 than in groups 2 and 3. Acute massive hemolysis induced acute pancreatitis, as indicated by histology, in almost 80% of cases. Hemolysis may induce acute pancreatitis by triggering the release of proinflammatory and immunoregulatory cytokines.

Changes in red blood cell osmotic fragility induced by total plasma and plasma fractions obtained from rats bearing progressive and regressive variants of the Walker 256 tumor

Two variants (A and B) of the widely employed Walker 256 rat tumor cells are known. When inoculated sc, the A variant produces solid, invasive, highly metastasizing tumors that cause severe systemic effects and death. We have obtained a regressive variant (AR) whose sc growth is slower, resulting in 70-80% regression followed by development of immunity against A and AR variants. Simultaneously with the beginning of tumor regression, a temporary anemia developed (~8 days duration), accompanied by marked splenomegaly (~300%) and changes in red blood cell osmotic fragility, with mean corpuscular fragility increasing from 4.1 to 6.5 g/l NaCl. The possibility was raised that plasma factors associated with the immune response induced these changes. In the present study, we identify and compare the osmotic fragility increasing activity of plasma fractions obtained from A and AR tumor bearers at different stages of tumor development. The results showed that by day 4 compounds precipitating in 60% (NH4)2SO4 and able to increase red blood cell osmotic fragility appeared in the plasma of A and AR tumor bearers. Later, these compounds disappeared from the plasma of A tumor bearers but slightly increased in the plasma of AR tumor bearers. Furthermore, by day 10, compounds precipitating between 60 and 80% (NH4)2SO4 and with similar effects appeared only in plasma of AR tumor bearers. The salt solubility, production kinetics and hemolytic activity of these compounds resemble those of the immunoglobulins. This, together with their preferential increase in rats bearing the AR variant, suggest their association with an immune response against this tumor.

Hemochromatosis (HFE) gene mutations in Brazilian chronic hemodialysis patients

Patients with chronic renal insufficiency (CRI) have reduced hemoglobin levels, mostly as a result of decreased kidney production of erythropoietin, but the relation between renal insufficiency and the magnitude of hemoglobin reduction has not been well defined. Hereditary hemochromatosis is an inherited disorder of iron metabolism. The importance of the association of hemochromatosis with treatment for anemia among patients with CRI has not been well described. We analyzed the frequency of the C282Y and H63D mutations in the HFE gene in 201 Brazilian individuals with CRI undergoing hemodialysis. The analysis of the effects of HFE mutations on iron metabolism and anemia with biochemical parameters was possible in 118 patients of this study (hemoglobin, hematocrit, ferritin levels, transferrin saturation, and serum iron). A C282Y heterozygous mutation was found in 7/201 (3.4%) and H63D homozygous and heterozygous mutation were found in 2/201 (1.0%) and 46/201 (22.9%), respectively. The allelic frequencies of the HFE mutations (0.017 for C282Y mutation and 0.124 for H63D mutation) did not differ between patients with CRI and healthy controls. Regarding the biochemical parameters, no differences were observed between HFE heterozygous and mutation-negative patients, although ferritin levels were not higher among patients with the H63D mutation (P = 0.08). From what we observed in our study, C282Y/H63D HFE gene mutations are not related to degrees of anemia or iron stores in CRI patients receiving intravenous iron supplementation (P > 0.10). Nevertheless, the present data suggest that the H63D mutation may have an important function as a modulating factor of iron overload in these patients.

Prevalence of hepatitis C virus (HCV) infection and HCV genotypes of hemodialysis patients in Salvador, Northeastern Brazil

Hepatitis C virus (HCV) infection has been identified as the major cause of chronic liver disease among patients on chronic hemodialysis (HD), despite the important reduction in risks obtained by testing candidate blood donors for anti-HCV antibodies and the use of recombinant erythropoietin to treat anemia. A cross-sectional study was performed to estimate the prevalence of HCV infection and genotypes among HD patients in Salvador, Northeastern Brazil. Anti-HCV seroprevalence was determined by ELISA in 1243 HD patients from all ten different dialysis centers of the city. HCV infection was confirmed by RT-PCR and genotyping was performed by restriction fragment length polymorphism. Anti-HCV seroprevalence among HD patients was 10.5% (95% CI: 8.8-12.3) (Murex anti-HCV, Abbott Murex, Chicago, IL, USA). Blood samples for qualitative HCV detection and genotyping were collected from 125/130 seropositive HD patients (96.2%). HCV-RNA was detected in 92/125 (73.6%) of the anti-HCV-positive patients. HCV genotype 1 (77.9%) was the most prevalent, followed by genotype 3 (10.5%) and genotype 2 (4.6%). Mixed infections of genotypes 1 and 3 were found in 7.0% of the total number of patients. The present results indicate a significant decrease in anti-HCV prevalence from 23.8% detected in a study carried out in 1994 to 10.5% in the present study. The HCV genotype distribution was closely similar to that observed in other hemodialysis populations in Brazil, in local candidate blood donors and in other groups at risk of transfusion-transmitted infection.

The clinical impact of MTHFR polymorphism on the vascular complications of sickle cell disease

Sickle cell disease (SCD) is one of the most common inherited diseases in the world and the patients present notorious clinical heterogeneity. It is known that patients with SCD present activation of the blood coagulation and fibrinolytic systems, especially during vaso-occlusive crises, but also during the steady state of the disease. We determined if the presence of the factor V gene G1691A mutation (factor V Leiden), the prothrombin gene G20210A variant, and methylenetetrahydrofolate reductase (MTHFR) C677T polymorphism may be risk factors for vascular complications in individuals with SCD. We studied 53 patients with SCD (60% being women), 29 with SS (sickle cell anemia; 28 years, range: 13-52 years) and 24 with SC (sickle-hemoglobin C disease; 38.5 years, range: 17-72 years) hemoglobinopathy. Factor V Leiden, MTHFR C677T polymorphism, and prothrombin G20210A variant were identified by PCR followed by further digestion of the PCR product with specific endonucleases. The following vascular complications were recorded: stroke, retinopathy, acute thoracic syndrome, and X-ray-documented avascular necrosis. Only one patient was heterozygous for factor V Leiden (1.8%) and there was no prothrombin G20210A variant. MTHFR 677TT polymorphism was detected in 1 patient (1.8%) and the heterozygous form 677TC was observed in 18 patients (34%, 9 with SS and 9 with SC disease), a prevalence similar to that reported by others. No association was detected between the presence of the MTHFR 677T allele and other genetic modulation factors, such as alpha-thalassemia, ß-globin gene haplotype and fetal hemoglobin. The presence of the MTHFR 677T allele was associated with the occurrence of vascular complications in SCD, although this association was not significant when each complication was considered separately. In conclusion, MTHFR C677T polymorphism might be a risk factor for vascular complications in SCD.

Cytoadhesion of Plasmodium falciparum-infected erythrocytes and the infected placenta: a two-way pathway

Malaria is undoubtedly the world's most devastating parasitic disease, affecting 300 to 500 million people every year. Some cases of Plasmodium falciparum infection progress to the deadly forms of the disease responsible for 1 to 3 million deaths annually. P. falciparum-infected erythrocytes adhere to host receptors in the deep microvasculature of several organs. The cytoadhesion of infected erythrocytes to placental syncytiotrophoblast receptors leads to pregnancy-associated malaria (PAM). This specific maternal-fetal syndrome causes maternal anemia, low birth weight and the death of 62,000 to 363,000 infants per year in sub-Saharan Africa, and thus has a poor outcome for both mother and fetus. However, PAM and non-PAM parasites have been shown to differ antigenically and genetically. After multiple pregnancies, women from different geographical areas develop adhesion-blocking antibodies that protect against placental parasitemia and clinical symptoms of PAM. The recent description of a new parasite ligand encoded by the var2CSA gene as the only gene up-regulated in PAM parasites renders the development of an anti-PAM vaccine more feasible. The search for a vaccine to prevent P. falciparum sequestration in the placenta by eliciting adhesion-blocking antibodies and a cellular immune response, and the development of new methods for evaluating such antibodies should be key priorities in mother-child health programs in areas of endemic malaria. This review summarizes the main molecular, immunological and physiopathological aspects of PAM, including findings related to new targets in the P. falciparum var gene family. Finally, we focus on a new methodology for mimicking cytoadhesion under blood flow conditions in human placental tissue.