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.

Comparison of the quantitative competitive and semiquantitative RT-PCR methods for the determination of interferon-gamma mRNA levels in AIDS-free HIV-infected individuals

IFN-gamma mRNA expression was evaluated in nonstimulated peripheral blood mononuclear cells (PBMC) of HIV-infected and seronegative individuals using quantitative competitive and semiquantitative RT-PCR and the sensitivity of these methods was compared. A significant correlation was found between quantitative competitive and semiquantitative RT-PCR in samples of both HIV-seronegative (P = 0.004) and HIV-infected individuals (P = 0.0004). PBMC from HIV-infected individuals presented a remarkable increase of IFN-gamma mRNA expression, as determined by both types of RT-PCR methods. Semiquantitative RT-PCR even without an internal standard is also acceptable for measuring cytokine mRNA expression, but less reliable if small amounts are quantified. Moreover, we found that increased IFN-gammamRNA expression is independent of CD4+ cell count in AIDS-free HIV-infected patients.

Reporting on methods of subgroup analysis in clinical trials: a survey of four scientific journals

Results of subgroup analysis (SA) reported in randomized clinical trials (RCT) cannot be adequately interpreted without information about the methods used in the study design and the data analysis. Our aim was to show how often inaccurate or incomplete reports occur. First, we selected eight methodological aspects of SA on the basis of their importance to a reader in determining the confidence that should be placed in the author's conclusions regarding such analysis. Then, we reviewed the current practice of reporting these methodological aspects of SA in clinical trials in four leading journals, i.e., the New England Journal of Medicine, the Journal of the American Medical Association, the Lancet, and the American Journal of Public Health. Eight consecutive reports from each journal published after July 1, 1998 were included. Of the 32 trials surveyed, 17 (53%) had at least one SA. Overall, the proportion of RCT reporting a particular methodological aspect ranged from 23 to 94%. Information on whether the SA preceded/followed the analysis was reported in only 7 (41%) of the studies. Of the total possible number of items to be reported, NEJM, JAMA, Lancet and AJPH clearly mentioned 59, 67, 58 and 72%, respectively. We conclude that current reporting of SA in RCT is incomplete and inaccurate. The results of such SA may have harmful effects on treatment recommendations if accepted without judicious scrutiny. We recommend that editors improve the reporting of SA in RCT by giving authors a list of the important items to be reported.