Title: The pharmaco-, population and evolutionary dynamics of multidrug chemotherapy for tuberculosis: some theoretical and experimental considerations

Multidrug therapy is the standard-of-care treatment for tuberculosis, and is primarily used as a means of decreasing the incidence of treatment failure resulting from the evolution of resistance that would be anticipated were only single drugs used. Among the most important factors contributing to the efficacy of multidrug therapy is the quantitative interaction between the component drugs at different concentrations and its effect on the rate of growth/death of the target bacteria (pharmacodynamics). Despite this, most pharmacodynamic (PD) studies are restricted to single drugs, with multiple-drug PD receiving far less attention. In this study, I use mathematical models and in vitro experiments with Mycobacterium marinum (a model organism for M. tuberculosis) to examine the pharmacodynamics of two-drug therapy and the consequences of those dynamics on the course of treatment and the evolution of multi-drug resistance. I initially generate a Hill-function-based model that assumes a single, constant interaction parameter (?) for the two drugs and examine its suitability for describing in vitro pharmacodynamic activity. The results of treatment experiments with pairs of the antimycobacterial agents rifampin, amikacin, clarithromycin, streptomycin and moxifloxacin suggest that this single interaction parameter model fits well at high antibiotic concentrations, but not at low. At these lower concentrations, the rate of antibiotic-induced killing with two drugs is markedly less than anticipated from the model. However, if I assume a concentration-dependent biphasic interaction function that separately quantifies drug interactions at sub- and supra-MIC concentrations, the modified Hill function provides a reasonably good fit for the PD of all pairs. Using Monte Carlo simulations of antibiotic treatment based on the experimentally determined two-drug PD functions, I evaluate the microbiological (rate of clearance) and evolutionary (likelihood of multiple resistance) efficacy of these drug combinations.

Title: Optimal control strategy for controlling the spread of HIV/AIDS

We formulate the strategy for controlling the spread of the pandemic as an optimal control problem, using the dynamics of the disease with an appropriate cost functional. The state variables represent the different compartments into which a sexually active population is divided; the control variables represent the level of medical and other intervention efforts. The objective function is a combination of cost infectives as well as the cost of medical and other intervention efforts. The resulting OCP is analyzed within the framework of Pontryagin's maximum principle, to determine optimal policies for reducing spread of the pandemic.

Numerical solution of the optimal control problem show that providing ARV treatment at the pre-AIDS stage, reduces both the incidence and prevalence much faster than starting treatment after progression into AIDS.

Title: We are all Africans: Decoding recent human migration history from mutations

Mitochondria are organelles in eukaryotic cells responsible for energy production. They are of bacterial origin, their DNA (mtDNA) does not undergo recombination and is only transmitted maternally. The Y chromosome is paternally transmitted and only recombinant in a small region without genes with homology with the X chromosome. Mutations on mtDNA and the Y-Chromosome can be used to trace recent migration history of humans. These studies show that all humans (outside Africa) derived from two, almost coincident "Out of Africa" events, which occurred ~50,000-70,000 years ago. Tracing the evolutionary tree of mtDNA and Y-Chromosome to the most recent female and male common ancestors dates "Mitochondrial Eve" to ~150,000 - 200,000 years ago and "Y-Chromosome Adam" to ~70,000 years ago. I will describe the basic biology needed to understand these ideas and show how they reveal connections between diverse groups such as the European Gypsies and Banjaras from Rajasthan and between the Vikings and the Irish. The talk will be presented at a general level and will be accessible to non experts.

Title: Evolution and mimicry in influenza and other RNA viruses

It is well known that the dinucleotide CpG is under-represented in the genomic DNA of many vertebrates. This is commonly thought to be due to the methylation of cytosine residues in this dinucleotide and the corresponding high rate of deamination of 5-methycytosine, which lowers the frequency of this dinucleotide in DNA. Surprisingly, many single stranded RNA viruses that replicate in these vertebrate hosts also have a very low presence of CpG dinucleotides in their genomes. Viruses are obligate intracellular parasites and the evolution of a virus is inexorably linked to the nature and fate of its host. One therefore expects that virus and host genomes should have common features. In this work, we compare evolutionary patterns in the genomes of ssRNA viruses and their hosts. In particular, we have analyzed dinucleotide patterns and found that the same patterns are pervasively over- or under-represented in many RNA viruses and their hosts suggesting that many RNA viruses evolve by mimicking some of the features of their host's genes (DNA) and likely also their corresponding mRNAs. When a virus crosses a species barrier into a different host, the pressure to replicate, survive and adapt, leaves a footprint in dinucleotide frequencies. For instance, since human genes seem to be under higher pressure to eliminate CpG dinucleotide motifs than avian genes, this pressure might be reflected in the genomes of human viruses (DNA and RNA viruses) when compared to those of the same viruses replicating in avian hosts. To test this idea we have analyzed the evolution of the influenza virus since 1918. We find that the influenza A virus, which originated from an avian reservoir and has been replicating in humans over many generations, evolves in a direction strongly selected to reduce the frequency of CpG dinucleotides in its genome. Consistent with this observation, we find that the influenza B virus, which has spent much more time in the human population, has adapted to its human host and exhibits an extremely low CpG dinucleotide content. We believe that these observations directly show that the evolution of RNA viral genomes can be shaped by pressures observed in the host genome. As a possible explanation, we suggest that the strong selection pressures acting on these RNA viruses are most likely related to the innate immune response and to nucleotide motifs in the host DNA and RNAs.

Title: Minimum Allele Frequency as a Predictive Tool for Analyzing Clonal Expansions Across Time

Clonal expansions that occur during viral pandemics represent a natural system that can be utilized to very effectively test phylogenetic methods. A pivotal inquiry regarding viral pandemics is the question of how and why they arise from reservoir populations in the environment, and more specifically, the defining of chronology between initial transition into humans and the full-scale escalation of a global health threat. Cancer is fundamentally a clonal expansion of mitotically deregulated tissue that theoretically holds origin within an individual cell. The chronology of the progression from an initial driving mutation to clinical presentation of disease is a trajectory that cannot be accurately predicted using current methods. Here we present a novel method utilizing the sum of allele frequencies as a diversity measure towards the ends of deriving hidden chronologic trajectories present in sequence datasets of sufficient nature.

Title: Network Analysis of Global Influenza Spread

Influenza is a negative-sense RNA orthomyxovirus that causes significant acute respiratory illness worldwide each year. Although vaccines pose the best means of preventing influenza infection, strain selection and optimal implementation remain difficult due to antigenic drift and reassortment. To prevent vaccine failure, a solid understanding of the global spread of influenza must inform the design process. If reservoirs for new viral strains can be identified, surveillance in these areas can improve prediction of seasonal variants in seeded regions. The recent influx of publicly available sequence data enables the detection of viral movement; however, skewed geographic and seasonal distributions in viral isolates complicate analysis.

We propose a probabilistic method that accounts for sampling bias through spatiotemporal clustering and modeling regional and seasonal transmission as a binomial process. Analysis of H3N2 hemagglutinin and neuraminidase not only confirmed the tropics and East-Southeast Asia as a source of new viral strains each year, but also increased the resolution of observed transmission to the level of countries. H1N1 data revealed a similar viral spread from the tropics. Graph theory applied to the global flu network captured the dynamic nature of influenza transmission. These techniques suggested China and Hong Kong as the origins of new seasonal strains of H3N2 and USA as a region where increased vaccination would maximally disrupt the spread of influenza around the world.

Conclusion:

Network analysis of worldwide influenza dynamics reveals a tropical East-Southeast Asian source and provides a rationale for vaccine strain selection and epidemiological intervention.

Title: Birth Seasonality and Infectious Disease in sub-Saharan Africa

We analyze the interaction between population and disease dynamics in sub- Saharan Africa. In the first section, we analyze whether malaria incidence may be driving birth seasonality. The rationale is that pregnant women are more likely to get and have more severe malaria compared to other individuals; and the malarial induced fevers increase the likelihood of spontaneous abortions in the first few months of pregnancy. In the second section, we analyze the impact of birth seasonality on the dynamics of childhood infectious diseases such as measles. The role of seasonal birth rates has been well studied in wildlife models of infectious diseases. However unlike models of human diseases, these models are density dependent, have short life spans, and pulse births. Recently studies have looked at the role of seasonal forcing in childhood diseases, but these studies have looked at forcing in the contact rates driven by school terms. To our knowledge there is only one paper that looks at the effect of human birth seasonality on infectious disease dynamics (He and Earn, 2007), however we extend their analysis in several ways. First our model includes a much larger range of baseline birth rates and amplitudes that corresponds to empirical data from sub-Saharan Africa. Secondly we include both seasonal forcing in births (e) and contact rates (ß). Third, we incorporate stochasticity in the models and look to see if there are any qualitative effects.

Title: Emergent single-stranded viruses evolve as quickly as RNA viruses

Single-stranded DNA viruses are causing emergent and epidemic disease in agriculture worldwide, including in cassava in Ghana. The generation of novel genotypes in the plant pathogenic geminiviruses had long been attributed to frequent recombination. While ssDNA viruses recombine frequently, we used phylogenetic approaches to study long term ssDNA viral evolution and found that they have high nucleotide substitution rates even in the absence of recombination. These rates (~10-3 - 10-5 per site, per year) are identical to those of many RNA viruses. We discuss possible molecular mechanisms by which ssDNA viruses could achieve RNA virus-like rates of evolution, and present evidence for a biased mutational spectrum in ssDNA viruses.

Title: New pandemic influenza

Human pandemic influenza viruses are characterized by the presence of an antigenically novel viral hemagglutinin which allows viral replication even in the presence of pre-existing influenza virus immunity. Such hemagglutinins are derived from influenza virus strains that circulate in a non-human host animal. As viral strains adapted to non-human hosts are in general unable to transmit well in humans, pandemic influenza viruses require some levels of adaptation before being able to jump from one host to humans and initiate a pandemic. The novel pandemic H1N1 influenza virus, despite being genetically similar to other swine influenza virus, started the 2009 influenza human pandemic. We have been investigating the genetic and molecular characteristics responsible for the success of the novel H1N1 virus in humans. In contrast to typical swine H1N1 viruses, the swine-origin novel H1N1 virus transmits more efficiently in the guinea pig model. Interestingly, the new H1N1 virus is antigenically closely related to old seasonal human influenza H1N1 viruses, suggesting that the HA of the virus remained antigenically frozen in swine. This explains the high susceptibility of young adults to the pandemic virus as compared with the elderly, who have pre-existing immunity cross-reactive with the new pandemic virus. Finally, we have investigated the possibility that the virus might become more virulent and/or resistant to the neuraminidase inhibitor oseltamivir. While the insertion of mutations associated with increased pathogenicity in NS1 and PB1-F2 in another viral strains did not increase virulence, oseltamivir resistant new H1N1 viruses did replicate and transmit well in animal models, suggesting that this virus might easily become resistant to these inhibitors.

Title: Epidemiological approach to investigate a proper model to monitor the spread of the sickle cell heritage in the years in a controlled and eclouser population (Ankwanda Project)

A small village (called town) of about 1,000 people has been chosen in order to monitor the full population over a long period. In this way the research is aimed not only for assessing the true incidence of sicklier or carriers but and mainly to assess the family relationships among all the members of the town.

The project is divided into four phases: a) the demographic survey, including the drawing of the map of the town, b) the medical doctor intervention including a medical visit and the acquisition of blood sample as well as the most important clinical signs for each citizen, c) the establishment of a medical and pharmacological treatment for any new born sicklier, d) the organization of a continuous educational programs is to increase the people's awareness about how they can protect their future children from the spread of a sickle cell anemia.

The paper focuses mainly on the possibility to recognize changes in transmitting the genetic mutation as a consequence of the continuous educational programs, enabling in recognizing different phenotypes proportions along the years.

In this way the paper provides a guideline about how to establish a theoretical phenotype stationary model at the beginning of the survey and how the collected data along the time should affect the model with changes.

Title: Emerging infectious disease: adaptation and evolutionary invasion across scales

Data on evolutionary genetics of cross-species adaptation and epidemiological surveillance of zoonotic events are becoming increasingly available, but an explicit framework is needed to link these data to interpret the selection pressures influencing pathogen emergence. Hierarchical selection pressures may have negative correlations at different scales, i.e. increased pathogen replication at the within-host scale may have fitness costs at the population-level scale of transmission between hosts, affecting pathogen fitness in ways not obvious when studying evolution at a single scale. I am currently utilizing evolutionary and population genetic theory to explore the effects of selection acting across scales. I am currently working on a baseline model addressing the cross-scale hierarchy of selection under a stochastic framework. The assumption of strong selection/weak mutation (SSWM), established by Gillespie in the 1980's, is used as a first approximation for within-host dynamics. In the limit of SSWM, fixed alleles can only be replaced by more beneficial alleles; the random processes of mutation and drift affect which beneficial allele fixes and when. At the between-host/transmission scale, multi-type branching processes are used as an approximation to the random processes of transmission and infection. This basic cross-scale model supplies a mathematically tractable approach in which to initially analyze how within-host selection interacts with between-host selection.

Title: The role of mathematical and computer simulation models in experimental studies of the population and evolutionary biology of bacteria.

In our Lab website ( ) we assert, ³Doing research in population biology without mathematical and/or computer simulation models is like playing tennis without a net or boundary lines² we also say ³Data may be a crutch for the insecure, but really self-confident scientists subject their hypotheses to tests that can reject them². In this talk, I will justify and expand on these statements. Using our own studies with bacteria and their plasmids and phage and antibiotic treatment, I will illustrate how mathematical and computer simulation models are used to design and interpret the results of experiments and generalize on those results. I will discuss some of the limitations of mathematical and computer simulation models for drawing inferences about the real world. I will also champion the use of simple mathematical models and why we should attempt maximize the reality and generality of models even at the expense of precision.

Title: The role of evolution in viral host jumps

Cross-species emergence of novel viruses is frequently associated with genetic changes, but the adaptive significance of those changes is often unknown. In this talk I will present a framework for classifying viral host jumps according to their underlying population dynamics. I will review evidence for ecological versus evolutionary drivers of well-studied host jumps, and outline current challenges where mathematical modellers can make valuable contributions. I will then summarize recent theoretical results pertaining to the case where viral adaptation to the new host species is required for emergence, addressing biological complexities arising from host heterogeneity and viral life history.

Title: Sero-prevalence of Crimean Congo Hemorrhagic Fever Virus in Out-patients attending Sangailu and Ijara Health Centres Kenya

Crimean Congo Hemorrhagic Fever (CCHF) is a tick-borne viral disease reported in Africa, Asia, South East Europe and Middle East. Majority of human cases are pastoralists who come in contact with animals infested with Hyalomma species of ticks which are the vectors of CCHF virus. A total of 517 human serum samples were collected from patients presenting with febrile illness or including fevers of unknown origin at Sangailu Dispensary and Ijara Health Centres. Out of the 517 serum samples, 269 samples were from Sangailu and 248 samples were from Ijara Health Centres. 61.5% of the samples were females and 38% were males. These samples were screened for the presence of anti-CCHF IgG using CCHF IgG VECTOR BEST Kit. A multiple logistic regression model was used to analyze these data. The results indicate 18.6% of the total sera were positive for anti-CCHF IgG of which 64.6% were those seen at Sangailu and 35.4% seen at Ijara Health Centres. Overall, 52.1% those testing positive were females and 47.9% were males. In Sangailu health centre, 51.6% of those testing positive were females and 48.4% males. In Ijara, 52.9% of those testing positive were females and 47% males. Median age those testing positive was 29 years. Out of those testing positive, 29.3 were farmers, 17.9 housewives and 7.7 businessmen. 100% of those testing positive and 98.6% of the negatives had contact with goats. 84.4% of the positives and 76.6% of the negatives had contact with donkeys. Results indicated that having controlled for other the factors age, location, and contact with donkeys were significant (p-values equal 0.0038, 0.0296, and 0.044, respectively). Therefore age, location and contact with donkeys are risk factors to CCHF virus exposure. This study confirms the circulation of CCHF virus amongst human population in Ijara District and therefore surveillance programs should sustained to enhance early detection of this viral that has potential to cause outbreaks.

Title: Mathematical modeling of latent TB infection using latency and dormancy time course gene expression.

The majority of individuals infected with Mycobacterium tuberculosis (Mtb) bacilli develop latent infection. Mtb becomes dormant and phenotypically drug resistant when it encounters multiple stresses within the host, and expresses a set of genes known as the dormancy regulon in vivo. These genes are expressed in vitro in response to nitric oxide (NO), hypoxia (oxygen deprivation), and nutrient starvation. The occurrence and reactivation of latent tuberculosis (TB) is not clearly understood. The ability of the pathogen to enter and exit from different states is associated with its ability to cause persistent infection. During infection it is not known whether the organism is in a persistent slow replicating state or a dormant non-replicating state, with the latter ultimately causing a latent infection with the potential to reactivate to active disease. We collected gene expression data for Mtb bacilli under different stress conditions that simulate latency or dormancy. Time course experiments were selected and differentially expressed gene profiles were determined at each time point. A mathematical model was then developed to show the dynamics of Mtb latency based on the profile of differentially expressed genes. Analysis of the time course data shows the dynamics of latency occurrence in vitro and the mathematical model reveals all possible scenarios of Mtb latency development with respect to the different conditions that may be experienced by the immune response in vivo. The mathematical model provides a biological explanation of how Mtb latency occurs based on observed gene expression changes in in-vitro latency models.

Title: A contact-waiting time metric for RNA folding

Over the last three decades, various bioinformatics tools have been developed for RNA structure prediction. Through structure prediction efforts, scientists hope to better understand RNA folding and the genetic role RNA plays in the cell. Several metrics have been developed to compute RNA folding rates. The Contact-Waiting Time (CWT) metric is an expression that correlates with the logarithmic value of the folding rate of RNA sequences. It uses parameters such as the energetic contributions and entropic costs of base pairs. This work focuses on converting a CWT algorithm from MATLAB to Perl and applying it to a dataset of HIV-1 RNA sequences. The dataset is a collection of four stem loops (domains SL1, SL2, SL3, and SL4) from the sigma-region of the HIV-1 RNA genome. This region is important for genomic packaging of the HIV-1 RNA molecule. The purpose of creating the Perl implementation was to make the CWT metric more widely available as a bioinformatics tool. As a result of applying the CWT algorithm to the sigma-region it was suggested that stem loops fold quickly in comparison to other RNA sequences. Thus, it is believed that the computation of the folding rates may give new insights into the genomic packaging of the HIV-1 RNA molecule, as well as potentially help with the design of vaccines and treatment of HIV.

Title: Modeling and analysis the dynamics of the transmission of tuberculosis in sub-Saharan Africa

A deterministic model of tuberculosis under the direct observation therapy strategy (DOTS) program in sub-Saharan Africa is designed and analyzed into its transmission dynamics. The model is shown to exhibit the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with one or more stable endemic equilibria when the associated basic reproduction number is less than unity. Using real data from Cameroon where the average TB notification rate is close to 93 per 100,000 habitants per year, we estimate some parameters of the model and establish conditions for the eradication of tuberculosis in Cameroon based on the fraction of diagnosed infectious placed under DOTS for treatment. The results show that DOTS expansion in Cameroon must include a significant increase in the diagnostic rate of infection; otherwise, the effect in reducing the incidence in Cameroon will not be achieved disregarding the tremendous efforts in any other direction, and the huge number of undiagnosed cases will make DOTS insignificant with respect to tuberculosis control.

Title: Genetic drive of engineered refractoriness in disease-vectoring mosquitoes

A novel and relatively new proposal for controlling vector-borne diseases like malaria and Dengue fever is to engineer genetically modified mosquitoes (GMMs) that are incapable of transmitting the disease (i.e., are refractory to it) and release them into wild populations. However, GMMs are likely to have lower fitness than their wild counterparts and are therefore unlikely to propagate refractoriness. To promote their spread in wild mosquito populations, refractoriness genes must be linked to selfish genetic elements that bias inheritance in favor of refractory offspring, a process called genetic drive. In this talk, I will discuss a number of issues that mathematical models can address in planning such control efforts, including (1) release requirements for successful invasion of GMMs into wild populations, (2) probable equilibrium frequencies of GMMs, (3) impacts on disease prevalence, (4) requirements for spatial spread, and (5) containment strategies should GMMs ever need to be recalled. Biological details on which these results depend include types and magnitudes of fitness costs, the dominance of those costs, the efficacy of refractoriness, and the efficacy of genetic drive. These issues will be compared among a number of proposed genetic drive mechanisms, including Medea, Wolbachia, homing endonuclease genes, transposable elements, and Y-linked meiotic drive.

Title: Multi-Disciplinary Approach to Rabies Control

Over the centuries, man has made strenuous efforts through incantations, surgery, potions and prayers to maintain animal health. Veterinary medicine has made many significant successes in the field of animal health from the days when animal disease control was wrestled from the hands of priest, leech-doctors, furriers and quacks.

Rabies (hydrophobia in man), a serious zoonotic disease, has been recognised to be enzootic in Mesopotamia and was first mentioned in the Eshuna Code of 2300 BC which called for action as soon as rabies was noticed in a dog.

Rabies has been one of the most feared disease throughout human history and has the highest human case fatality proportion of any infectious disease, killing globally over 55,000 people annually. It is estimated that more than 99% of all human deaths from rabies occur in the developing world, with 7,000 to 46,000 annual human deaths from rabies in Africa.

There are many sources of the disease to man. This makes control of rabies very difficult especially in mainland countries. During the last 2 decades, conventional veterinary rabies control measures have been largely in- effective in reducing the incidence of the disease. Most scientists therefore advocate multi-sectorial control of rabies.

This presentation looks at the role of various professionals and Institutions in the currently proposed multi-sector control of this deadly zoonotic disease in man's closest friend, dog, the largest single source of rabies.

Title: Models to Assess the Efficacy and Impact of Genetically Controlled Mosqutoes

New approaches to control malaria and other diseases are being developed. These include genetically modified mosquitoes (GMMs) designed to either reduce population sizes or to replace existing populations with vectors unable to transmit the disease. Trial releases of such mosquitoes have been made. Mathematical models play an important role in developing these methods and in estimating their efficacy.

It is anticipated that such GMMs will eventually be tried in Africa. It is important that African scientists participate in the planning and evaluation of these trials. In my talk I will review 3 promising approaches now being tried -- sterile males, Medea elements and homing endonucleases -- and describe mathematical models for estimating their effects.

In a second talk I could possibly talk about population structure of Anopheles Gambiae ss, the leading vector(s) of malaria in Africa. Historically this has not been an area much influenced by computer modeling, but the problem and the tools for describing such structure should be relevant to those concerned with malaria in Africa.

Title: Cost-Effectiveness Analyses of Drug Resistance Management Strategies for River Blindness

Ivermectin resistance is widespread in livestock parasitic nematodes and there are growing concerns that it will develop in Onchocerca volvulus, the nematode that causes onchocerciasis ("river blindness"). These concerns are supported by a recent study in Ghana which has confirmed that in some communities adult female worms had a lower embryostatic response to ivermectin (the temporary inhibition of release of the transmission stage of the parasite from adult female worms).

The aim of this project is to evaluate the cost-effectiveness of different resistant management strategies for reducing the spread of ivermectin resistance in O. volvulus. This will be done by extending an existing age and sex-structured deterministic infection intensity model of human onchocerciasis, which has already been parameterised for a number of settings in Africa and which incorporates the effects of drug treatment on the parasite population dynamics. The model will be modified to investigate the spread of anthelmintic resistance under more realistic assumptions of the population genetics of ivermectin resistance.

A disease model based on a model developed by the most recent iteration of the Global Burden of Disease Study will be incorporated into this modelling framework to track the number of disease cases associated with onchocerciasis. The model will be linked to the infection intensity model and therefore will be able to quantify the reduction in disease associated with onchocerciasis due to an intervention. The model(s) will be used to compare a range of different resistance management strategies with cost-effectiveness analyses. These may include changing from annual to biannual ivermectin treatment; introducing anti-Wolbachia therapy, or introducing focal vector control.

Title: Biofilm contributions to antimicrobial pharmacodynamics in vitro

The development of antimicrobial treatment regimen to prevent resistance arising and improve infectious disease control often involves the use of mathematical models. Such models take into account the relationship between the pharmacodynamics (PD, bug : drug concentration relationship) and pharmacokinetics (PK, drug concentration changes in vivo). It is hotly debated whether clinically relevant information is obtained from the in vitro pharmacodynamics of antimicrobials. This is not unexpected as the in vitro measure of efficacy, the minimum inhibitory concentration (MIC), is the sole PD parameter used. This MIC is however, defined within very narrow boundaries of bacterial density (105 cfu / ml) and physiology (exponential phase, planktonic bacteria), taking into account little to do with the natural environments and densities of infections observed. The latter is particularly relevant due to the generality of the density effect, a reduced efficacy of antibiotics against high densities of bacteria. The often-observed lack of congruence between clinically proven efficacy and in vitro measures of efficacy may be exacerbated by these unrealistic test conditions. Continuous flow conditions in antimicrobial study are used to mimic in vitro, the changing concentration of antibiotics in treated patients. In our studies of the pharmacodynamics of Staphylococcus aureus under continuous flow conditions, we observed that daily-dosed antibiotic populations of this bacterium, rather than decline to extinction, cycled between doses. Each of the six clinically relevant antibiotics tested showed similar results over the six days of treatment. We designed a mathematical model to define this relationship between the fluctuating drug concentrations and bacterial density. Our model predicted the existence of a refuge-dwelling population (biofilm) driving the dynamics of the bacterial population. Testing our predictions experimentally, we observe that there is such a sizeable population of wall-dwelling bacteria seeding into the planktonic population. We conclude that the use of complex broth, continuous flow cultures are more representative of the pharmacodynamics of antibiotic treatment in vivo. In combination with mathematical models such as ours which takes into account resource concentration and the density effect, this continuous flow setup may aid in the design and improvement of antibiotic treatment regimen.

Title: Optimal Treated Mosquito Bed Nets and Insecticides For Eradication of Malaria in Missira

In this talk, we will extend the deterministic mathematical malaria model framework of Dembele et al. and use it to study the impact of protecting humans from mosquito bites and mass killing of mosquito vectors on malaria incidence in Missira, a village in Mali. As a case study, we will fit our model to Missira malaria incidence data. Using the fitted model, we will compute the optimal proportion of protected human population from infected mosquito bites and optimal proportion of killed moquitoes that would lead to the eradication of malaria in Missira.