Modeling the synergistic interplay between malaria dynamics and economic growth.

The mosquito-borne disease (malaria) imposes significant challenges on human health, healthcare systems, and economic growth/productivity in many countries. This study develops and analyzes a model to understand the interplay between malaria dynamics, economic growth, and transient events. It uncovers varied effects of malaria and economic parameters on model outcomes, highlighting the interdependence of the reproduction number (R0) on both malaria and economic factors, and a reciprocal relationship where malaria diminishes economic productivity, while higher economic output is associated with reduced malaria prevalence. This emphasizes the intricate interplay between malaria dynamics and socio-economic factors. The study offers insights into malaria control and underscores the significance of optimizing external aid allocation, especially favoring an even distribution strategy, with the most significant reduction observed in an equal monthly distribution strategy compared to longer distribution intervals. Furthermore, the study shows that controlling malaria in high mosquito biting areas with limited aid, low technology, inadequate treatment, or low economic investment is challenging. The model exhibits a backward bifurcation implying that sustainability of control and mitigation measures is essential even when R0 is slightly less than one. Additionally, there is a parameter regime for which long transients are feasible. Long transients are critical for predicting the behavior of dynamic systems and identifying factors influencing transitions; they reveal reservoirs of infection, vital for disease control. Policy recommendations for effective malaria control from the study include prioritizing sustained control measures, optimizing external aid allocation, and reducing mosquito biting.

Assessing the Effect of Global Travel and Contact Restrictions on Mitigating the COVID-19 Pandemic.

Travel restrictions and physical distancing have been implemented across the world to mitigate the coronavirus disease 2019 (COVID-19) pandemic, but studies are needed to understand their effectiveness across regions and time. Based on the population mobility metrics derived from mobile phone geolocation data across 135 countries or territories during the first wave of the pandemic in 2020, we built a metapopulation epidemiological model to measure the effect of travel and contact restrictions on containing COVID-19 outbreaks across regions. We found that if these interventions had not been deployed, the cumulative number of cases could have shown a 97-fold (interquartile range 79-116) increase, as of May 31, 2020. However, their effectiveness depended upon the timing, duration, and intensity of the interventions, with variations in case severity seen across populations, regions, and seasons. Additionally, before effective vaccines are widely available and herd immunity is achieved, our results emphasize that a certain degree of physical distancing at the relaxation of the intervention stage will likely be needed to avoid rapid resurgences and subsequent lockdowns.

The impact of within-vector parasite development on the extrinsic incubation period.

Mosquito-borne diseases, in particular malaria, have a significant burden worldwide leading to nearly half a million deaths each year. The malaria parasite requires a vertebrate host, such as a human, and a vector host, the Anopheles mosquito, to complete its full life cycle. Here, we focus on the parasite dynamics within the vector to examine the first appearance of sporozoites in the salivary glands, which indicates a first time of infectiousness of mosquitoes. The timing of this period of pathogen development in the mosquito until transmissibility, known as the extrinsic incubation period, remains poorly understood. We develop compartmental models of within-mosquito parasite dynamics fitted with experimental data on oocyst and sporozoite counts. We find that only a fraction of oocysts burst to release sporozoites and bursting must be delayed either via a time-dependent function or a gamma-distributed set of compartments. We use Bayesian inference to estimate distributions of parameters and determine that bursting rate is a key epidemiological parameter. A better understanding of the factors impacting the extrinsic incubation period will aid in the development of interventions to slow or stop the spread of malaria.

Effect of non-pharmaceutical interventions for containing the COVID-19 outbreak in China.

BACKGROUND: The COVID-19 outbreak containment strategies in China based on non-pharmaceutical interventions (NPIs) appear to be effective. Quantitative research is still needed however to assess the efficacy of different candidate NPIs and their timings to guide ongoing and future responses to epidemics of this emerging disease across the World. METHODS: We built a travel network-based susceptible-exposed-infectious-removed (SEIR) model to simulate the outbreak across cities in mainland China. We used epidemiological parameters estimated for the early stage of outbreak in Wuhan to parameterise the transmission before NPIs were implemented. To quantify the relative effect of various NPIs, daily changes of delay from illness onset to the first reported case in each county were used as a proxy for the improvement of case identification and isolation across the outbreak. Historical and near-real time human movement data, obtained from Baidu location-based service, were used to derive the intensity of travel restrictions and contact reductions across China. The model and outputs were validated using daily reported case numbers, with a series of sensitivity analyses conducted. RESULTS: We estimated that there were a total of 114,325 COVID-19 cases (interquartile range [IQR] 76,776 - 164,576) in mainland China as of February 29, 2020, and these were highly correlated (p<0.001, R2=0.86) with reported incidence. Without NPIs, the number of COVID-19 cases would likely have shown a 67-fold increase (IQR: 44 - 94), with the effectiveness of different interventions varying. The early detection and isolation of cases was estimated to prevent more infections than travel restrictions and contact reductions, but integrated NPIs would achieve the strongest and most rapid effect. If NPIs could have been conducted one week, two weeks, or three weeks earlier in China, cases could have been reduced by 66%, 86%, and 95%, respectively, together with significantly reducing the number of affected areas. However, if NPIs were conducted one week, two weeks, or three weeks later, the number of cases could have shown a 3-fold, 7-fold, and 18-fold increase across China, respectively. Results also suggest that the social distancing intervention should be continued for the next few months in China to prevent case numbers increasing again after travel restrictions were lifted on February 17, 2020. CONCLUSION: The NPIs deployed in China appear to be effectively containing the COVID-19 outbreak, but the efficacy of the different interventions varied, with the early case detection and contact reduction being the most effective. Moreover, deploying the NPIs early is also important to prevent further spread. Early and integrated NPI strategies should be prepared, adopted and adjusted to minimize health, social and economic impacts in affected regions around the World.

Effect of non-pharmaceutical interventions to contain COVID-19 in China.

On 11 March 2020, the World Health Organization (WHO) declared coronavirus disease 2019 (COVID-19) a pandemic1. The strategies based on non-pharmaceutical interventions that were used to contain the outbreak in China appear to be effective2, but quantitative research is still needed to assess the efficacy of non-pharmaceutical interventions and their timings3. Here, using epidemiological data on COVID-19 and anonymized data on human movement4,5, we develop a modelling framework that uses daily travel networks to simulate different outbreak and intervention scenarios across China. We estimate that there were a total of 114,325 cases of COVID-19 (interquartile range 76,776-164,576) in mainland China as of 29 February 2020. Without non-pharmaceutical interventions, we predict that the number of cases would have been 67-fold higher (interquartile range 44-94-fold) by 29 February 2020, and we find that the effectiveness of different interventions varied. We estimate that early detection and isolation of cases prevented more infections than did travel restrictions and contact reductions, but that a combination of non-pharmaceutical interventions achieved the strongest and most rapid effect. According to our model, the lifting of travel restrictions from 17 February 2020 does not lead to an increase in cases across China if social distancing interventions can be maintained, even at a limited level of an on average 25% reduction in contact between individuals that continues until late April. These findings improve our understanding of the effects of non-pharmaceutical interventions on COVID-19, and will inform response efforts across the world.

Host density and habitat structure influence host contact rates and Batrachochytrium salamandrivorans transmission.

Batrachochytrium salamandrivorans (Bsal) is an emerging invasive pathogen that is highly pathogenic to salamander species. Modeling infection dynamics in this system can facilitate proactive efforts to mitigate this pathogen's impact on North American species. Given its widespread distribution and high abundance, the eastern newt (Notophthalmus viridescens) has the potential to significantly influence Bsal epidemiology. We designed experiments to 1) estimate contact rates given different host densities and habitat structure and 2) estimate the probability of transmission from infected to susceptible individuals. Using parameter estimates from data generated during these experiments, we modeled infection and disease outcomes for a population of newts using a system of differential equations. We found that host contact rates were density-dependent, and that adding habitat structure reduced contacts. The probability of Bsal transmission given contact between newts was very high (>90%) even at early stages of infection. Our simulations show rapid transmission of Bsal among individuals following pathogen introduction, with infection prevalence exceeding 90% within one month and >80% mortality of newts in three months. Estimates of basic reproductive rate (R0) of Bsal for eastern newts were 1.9 and 3.2 for complex and simple habitats, respectively. Although reducing host density and increasing habitat complexity might decrease transmission, these management strategies may be ineffective at stopping Bsal invasion in eastern newt populations due to this species' hyper-susceptibility.

Intermittent Preventive Treatment (IPT): Its Role in Averting Disease-Induced Mortality in Children and in Promoting the Spread of Antimalarial Drug Resistance.

We develop an age-structured ODE model to investigate the role of intermittent preventive treatment (IPT) in averting malaria-induced mortality in children, and its related cost in promoting the spread of antimalarial drug resistance. IPT, a malaria control strategy in which a full curative dose of an antimalarial medication is administered to vulnerable asymptomatic individuals at specified intervals, has been shown to reduce malaria transmission and deaths in children and pregnant women. However, it can also promote drug resistance spread. Our mathematical model is used to explore IPT effects on drug resistance and deaths averted in holoendemic malaria regions. The model includes drug-sensitive and drug-resistant strains as well as human hosts and mosquitoes. The basic reproduction, and invasion reproduction numbers for both strains are derived. Numerical simulations show the individual and combined effects of IPT and treatment of symptomatic infections on the prevalence of both strains and the number of lives saved. Our results suggest that while IPT can indeed save lives, particularly in high transmission regions, certain combinations of drugs used for IPT and to treat symptomatic infection may result in more deaths when resistant parasite strains are circulating. Moreover, the half-lives of the treatment and IPT drugs used play an important role in the extent to which IPT may influence spread of the resistant strain. A sensitivity analysis indicates the model outcomes are most sensitive to the reduction factor of transmission for the resistant strain, rate of immunity loss, and the natural clearance rate of sensitive infections.

Challenges in modeling complexity of neglected tropical diseases: a review of dynamics of visceral leishmaniasis in resource limited settings.

OBJECTIVES: Neglected tropical diseases (NTD), account for a large proportion of the global disease burden, and their control faces several challenges including diminishing human and financial resources for those distressed from such diseases. Visceral leishmaniasis (VL), the second-largest parasitic killer (after malaria) and an NTD affects poor populations and causes considerable cost to the affected individuals. Mathematical models can serve as a critical and cost-effective tool for understanding VL dynamics, however, complex array of socio-economic factors affecting its dynamics need to be identified and appropriately incorporated within a dynamical modeling framework. This study reviews literature on vector-borne diseases and collects challenges and successes related to the modeling of transmission dynamics of VL. Possible ways of creating a comprehensive mathematical model is also discussed. METHODS: Published literature in three categories are reviewed: (i) identifying non-traditional but critical mechanisms for VL transmission in resource limited regions, (ii) mathematical models used for dynamics of Leishmaniasis and other related vector borne infectious diseases and (iii) examples of modeling that have the potential to capture identified mechanisms of VL to study its dynamics. RESULTS: This review suggests that VL elimination have not been achieved yet because existing transmission dynamics models for VL fails to capture relevant local socio-economic risk factors. This study identifies critical risk factors of VL and distribute them in six categories (atmosphere, access, availability, awareness, adherence, and accedence). The study also suggests novel quantitative models, parts of it are borrowed from other non-neglected diseases, for incorporating these factors and using them to understand VL dynamics and evaluating control programs for achieving VL elimination in a resource-limited environment. CONCLUSIONS: Controlling VL is expensive for local communities in endemic countries where individuals remain in the vicious cycle of disease and poverty. Smarter public investment in control programs would not only decrease the VL disease burden but will also help to alleviate poverty. However, dynamical models are necessary to evaluate intervention strategies to formulate a cost-effective optimal policy for eradication of VL.

Erratum to "A Model for Spheroid versus Monolayer Response of SK-N-SH Neuroblastoma Cells to Treatment with 15-Deoxy-PGJ2".

[This corrects the article DOI: 10.1155/2016/3628124.].

Simulating within-vector generation of the malaria parasite diversity.

Plasmodium falciparum, the most virulent human malaria parasite, undergoes asexual reproduction within the human host, but reproduces sexually within its vector host, the Anopheles mosquito. Consequently, the mosquito stage of the parasite life cycle provides an opportunity to create genetically novel parasites in multiply-infected mosquitoes, potentially increasing parasite population diversity. Despite the important implications for disease transmission and malaria control, a quantitative mapping of how parasite diversity entering a mosquito relates to diversity of the parasite exiting, has not been undertaken. To examine the role that vector biology plays in modulating parasite diversity, we develop a two-part model framework that estimates the diversity as a consequence of different bottlenecks and expansion events occurring during the vector-stage of the parasite life cycle. For the underlying framework, we develop the first stochastic model of within-vector P. falciparum parasite dynamics and go on to simulate the dynamics of two parasite subpopulations, emulating multiply infected mosquitoes. We show that incorporating stochasticity is essential to capture the extensive variation in parasite dynamics, particularly in the presence of multiple parasites. In particular, unlike deterministic models, which always predict the most fit parasites to produce the most sporozoites, we find that occasionally only parasites with lower fitness survive to the sporozoite stage. This has important implications for onward transmission. The second part of our framework includes a model of sequence diversity generation resulting from recombination and reassortment between parasites within a mosquito. Our two-part model framework shows that bottlenecks entering the oocyst stage decrease parasite diversity from what is present in the initial gametocyte population in a mosquito's blood meal. However, diversity increases with the possibility for recombination and proliferation in the formation of sporozoites. Furthermore, when we begin with two parasite subpopulations in the initial gametocyte population, the probability of transmitting more than two unique parasites from mosquito to human is over 50% for a wide range of initial gametocyte densities.

Modeling the population dynamics and community impacts of Ambystoma tigrinum: A case study of phenotype plasticity.

Phenotypic plasticity is the ability of an organism to change its phenotype in response to changes in the environment. General mathematical descriptions of the phenomenon rely on an abstract measure of "viability" that, in this study, is instantiated in the case of the Tiger Salamander, Ambystoma tigrinum. This organism has a point in its development when, upon maturing, it may take two very different forms. One is a terrestrial salamander (metamorph)that visits ponds to reproduce and eat, while the other is an aquatic form (paedomorph) that remains in the pond to breed and which consumes a variety of prey including its own offspring. A seven dimensional nonlinear system of ordinary differential equations is developed, incorporating small (Z) and large (B) invertebrates, Ambystoma young of the year (Y), juveniles (J), terrestrial metamorphs (A) and aquatic paedomorphs (P). One parameter in the model controls the proportion of juveniles maturing into A versus P. Solutions are shown to remain non-negative. Every effort was made to justify parameters biologically through studies reported in the literature. A sensitivity analysis and equilibrium analysis of model parameters demonstrate that morphological choice is critical to the overall composition of the Ambystoma population. Various population viability measures were used to select optimal percentages of juveniles maturing into metamorphs, with optimal choices differing considerably depending on the viability measure. The model suggests that the criteria for viability for this organism vary, both from location to location and also in time. Thus, optimal responses change with spatiotemporal variation, which is consistent with other phenotypically plastic systems. Two competing hypotheses for the conditions under which metamorphosis occurs are examined in light of the model and data from an Ambystoma tigrinum population at Mexican Cut, Colorado. The model clearly supports one of these over the other for this data set. There appears to be a mathematical basis to the general tenet of spatiotemporal variation being important for the maintenance of polyphenisms, and our results suggest that such variation may have cascading effects on population, community, and perhaps ecosystem dynamics because it drives the production of a keystone, cannibalistic predator.

Modeling the Response of Anopheles gambiae (Diptera: Culicidae) Populations in the Kenya Highlands to a Rise in Mean Annual Temperature.

A dynamical model of Anopheles gambiae larval and adult populations is constructed that matches temperature-dependent maturation times and mortality measured experimentally as well as larval instar and adult mosquito emergence data from field studies in the Kenya Highlands. Spectral classification of high-resolution satellite imagery is used to estimate household density. Indoor resting densities collected over a period of one year combined with predictions of the dynamical model give estimates of both aquatic habitat and total adult mosquito densities. Temperature and precipitation patterns are derived from monthly records. Precipitation patterns are compared with average and extreme habitat estimates to estimate available aquatic habitat in an annual cycle. These estimates are coupled with the original model to produce estimates of adult and larval populations dependent on changing aquatic carrying capacity for larvae and changing maturation and mortality dependent on temperature. This paper offers a general method for estimating the total area of aquatic habitat in a given region, based on larval counts, emergence rates, indoor resting density data, and number of households.Altering the average daily temperature and the average daily rainfall simulates the effect of climate change on annual cycles of prevalence of An. gambiae adults. We show that small increases in average annual temperature have a large impact on adult mosquito density, whether measured at model equilibrium values for a single square meter of habitat or tracked over the course of a year of varying habitat availability and temperature.

Interplay between insecticide-treated bed-nets and mosquito demography: implications for malaria control.

Although malaria prevalence has witnessed a significant reduction within the past decade, malaria still constitutes a major health and economic problem, especially to low-income countries. Insecticide-treated nets (ITNs) remain one of the primary measures for preventing the malignant disease. Unfortunately, the success of ITN campaigns is hampered by improper use and natural decay in ITN-efficacy over time. Many models aimed at studying malaria transmission and control fail to account for this decay, as well as mosquito demography and feeding preferences exhibited by mosquitoes towards humans. Omitting these factors can misrepresent disease risk, while understanding their effects on malaria dynamics can inform control policy. We present a model for malaria dynamics that incorporates these factors, and a systematic analysis, including stability and sensitivity analyses of the model under different conditions. The model with constant ITN-efficacy exhibits a backward bifurcation emphasizing the need for sustained control measures until the basic reproduction number, R0, drops below a critical value at which control is feasible. The infectious and partially immune human populations and R0 are highly sensitive to the probability that a mosquito feeds successfully on a human, ITN coverage and the maximum biting rate of mosquitoes, irrespective of whether ITN-efficacy is constant or declines over time. This implies that ITNs play an important role in disease control. When ITN-efficacy wanes over time, we identify disease risks and corresponding ITN coverage, as well as feeding preference levels for which the disease can be controlled or eradicated. Our study leads to important insights that could assist in the design and implementation of better malaria control strategies. We conclude that ITNs that can retain their effectiveness for longer periods will be more appropriate in the fight against malaria and that making more ITNs available to highly endemic regions is necessary for malaria containment.

A Model for Spheroid versus Monolayer Response of SK-N-SH Neuroblastoma Cells to Treatment with 15-Deoxy-PGJ2.

Researchers have observed that response of tumor cells to treatment varies depending on whether the cells are grown in monolayer, as in vitro spheroids or in vivo. This study uses data from the literature on monolayer treatment of SK-N-SH neuroblastoma cells with 15-deoxy-PGJ2 and couples it with data on growth rates for untreated SK-N-SH neuroblastoma cells grown as multicellular spheroids. A linear model is constructed for untreated and treated monolayer data sets, which is tuned to growth, death, and cell cycle data for the monolayer case for both control and treatment with 15-deoxy-PGJ2. The monolayer model is extended to a five-dimensional nonlinear model of in vitro tumor spheroid growth and treatment that includes compartments of the cell cycle (G1, S, G2/M) as well as quiescent (Q) and necrotic (N) cells. Monolayer treatment data for 15-deoxy-PGJ2 is used to derive a prediction of spheroid response under similar treatments. For short periods of treatment, spheroid response is less pronounced than monolayer response. The simulations suggest that the difference in response to treatment of monolayer versus spheroid cultures observed in laboratory studies is a natural consequence of tumor spheroid physiology rather than any special resistance to treatment.

Spatial heterogeneity, host movement and mosquito-borne disease transmission.

Mosquito-borne diseases are a global health priority disproportionately affecting low-income populations in tropical and sub-tropical countries. These pathogens live in mosquitoes and hosts that interact in spatially heterogeneous environments where hosts move between regions of varying transmission intensity. Although there is increasing interest in the implications of spatial processes for mosquito-borne disease dynamics, most of our understanding derives from models that assume spatially homogeneous transmission. Spatial variation in contact rates can influence transmission and the risk of epidemics, yet the interaction between spatial heterogeneity and movement of hosts remains relatively unexplored. Here we explore, analytically and through numerical simulations, how human mobility connects spatially heterogeneous mosquito populations, thereby influencing disease persistence (determined by the basic reproduction number R0), prevalence and their relationship. We show that, when local transmission rates are highly heterogeneous, R0 declines asymptotically as human mobility increases, but infection prevalence peaks at low to intermediate rates of movement and decreases asymptotically after this peak. Movement can reduce heterogeneity in exposure to mosquito biting. As a result, if biting intensity is high but uneven, infection prevalence increases with mobility despite reductions in R0. This increase in prevalence decreases with further increase in mobility because individuals do not spend enough time in high transmission patches, hence decreasing the number of new infections and overall prevalence. These results provide a better basis for understanding the interplay between spatial transmission heterogeneity and human mobility, and their combined influence on prevalence and R0.

Optimal vaccination and bednet maintenance for the control of malaria in a region with naturally acquired immunity.

Following over two decades of research, the malaria vaccine candidate RTS,S has reached the final stages of vaccine trials, demonstrating an efficacy of roughly 50% in young children. Regions with high malaria prevalence tend to have high levels of naturally acquired immunity (NAI) to severe malaria; NAI is caused by repeated exposure to infectious bites and results in large asymptomatic populations. To address concerns about how these vaccines will perform in regions with existing NAI, we developed a simple malaria model incorporating vaccination and NAI. Typically, if the basic reproduction number (R0) for malaria is greater than unity, the disease will persist; otherwise, the disease will become extinct. However, analysis of this model revealed that NAI, compounded by a subpopulation with only partial protection to malaria, may render vaccination efforts ineffective and potentially detrimental to malaria control, by increasing R0 and increasing the likelihood of malaria persistence even when R0<1. The likelihood of this scenario increases when non-immune infected individuals are treated disproportionately compared with partially immune individuals - a plausible scenario since partially immune individuals are more likely to be asymptomatically infected. Consequently, we argue that active case-detection of asymptomatic infections is a critical component of an effective malaria control program. We then investigated optimal vaccination and bednet control programs under two endemic settings with varying levels of naturally acquired immunity: a typical setting under which prevalence decays when R0<1, and a setting in which subthreshold endemic equilibria exist. A qualitative comparison of the optimal control results under the first setting revealed that the optimal policy differs depending on whether the goal is to reduce total morbidity, or to reduce clinical infections. Furthermore, this comparison dictates that control programs should place less effort in vaccination as the level of NAI in a population, and as disease prevalence, increases. In the second setting, we demonstrated that the optimal policy is able to confer long-term benefits with a 10-year control program by pushing the system into a new state where the disease-free equilibrium becomes the attracting equilibrium. While this result suggests that one can theoretically achieve long-term benefits with a short-term strategy, we illustrate that in this second setting, a small environmental change, or the introduction of new cases via immigration, places the population at high risk for a malaria epidemic.

Place-based attributes predict community membership in a mobile phone communication network.

Social networks can be organized into communities of closely connected nodes, a property known as modularity. Because diseases, information, and behaviors spread faster within communities than between communities, understanding modularity has broad implications for public policy, epidemiology and the social sciences. Explanations for community formation in social networks often incorporate the attributes of individual people, such as gender, ethnicity or shared activities. High modularity is also a property of large-scale social networks, where each node represents a population of individuals at a location, such as call flow between mobile phone towers. However, whether or not place-based attributes, including land cover and economic activity, can predict community membership for network nodes in large-scale networks remains unknown. We describe the pattern of modularity in a mobile phone communication network in the Dominican Republic, and use a linear discriminant analysis (LDA) to determine whether geographic context can explain community membership. Our results demonstrate that place-based attributes, including sugar cane production, urbanization, distance to the nearest airport, and wealth, correctly predicted community membership for over 70% of mobile phone towers. We observed a strongly positive correlation (r = 0.97) between the modularity score and the predictive ability of the LDA, suggesting that place-based attributes can accurately represent the processes driving modularity. In the absence of social network data, the methods we present can be used to predict community membership over large scales using solely place-based attributes.

Impact of enhanced malaria control on the competition between Plasmodium falciparum and Plasmodium vivax in India.

The primary focus of malaria research and control has been on Plasmodium falciparum, the most severe of the four Plasmodium species causing human disease. However, the presence of both P. falciparum and Plasmodium vivax occurs in several countries, including India. We developed a mathematical model describing the dynamics of P. vivax and P. falciparum in the human and mosquito populations and fit this model to Indian clinical case data to understand how enhanced control measures affect the competition between the two Plasmodium species. Around 1997, funding for malaria control in India increased dramatically. Our model predicts that if India had not improved its control strategy, the two species of Plasmodium would continue to coexist. To determine which control measures contributed the most to the decline in the number of cases after 1997, we compared the fit of seven models to the 1997-2010 clinical case data. From this, we determined that increased use of bednets contributed the most to case reduction. During the enhanced control period, the best model predicts that P. vivax is out-competing P. falciparum. However, the reproduction numbers are extremely close to the invasion boundaries. Consequently, we cannot be confident that this outcome is the true future of malaria in India. We address this uncertainty by performing a parametric bootstrapping procedure for each of the seven models. This procedure, applied to the enhanced control period, revealed that the best model predicts that P. vivax outcompeting P. falciparum is the most likely outcome, whereas the remaining candidate models predict the opposite. Moreover, the predictions of the top model are counter to what one expects based on the case data alone. Although the proportion of cases due to falciparum has been increasing, the best fitting model reveals that this observation is insufficient to draw conclusions about the longterm competitive outcome of the two species.

Assessing the role of spatial heterogeneity and human movement in malaria dynamics and control.

Mathematical models developed for studying malaria dynamics often focus on a single, homogeneous population. However, human movement connects environments with potentially different malaria transmission characteristics. To address the role of human movement and spatial heterogeneity in malaria transmission and malaria control, we consider a simple malaria metapopulation model incorporating two regions, or patches, connected by human movement, with different degrees of malaria transmission in each patch. Using our two-patch model, we calculate and analyze the basic reproduction number, R(0), an epidemiologically important threshold quantity that indicates whether malaria will persist or go extinct in a population. Although R(0) depends on the rates of human movement, we show that R(0) is always bounded between the two quantities R(01) and R(02)-the reproduction numbers for the two patches if isolated. If without migration, the disease is endemic in one patch but not in the other, then the addition of human migration can cause the disease to persist in both patches. This result indicates that regions with low malaria transmission should have an interest in helping to control or eliminate malaria in regions with higher malaria endemicity if human movement connects them. Performing a sensitivity analysis of R(0) and the endemic equilibrium to various parameters in the two-patch model allowed us to determine, under different parameterizations of the model, which patch will be the better target for control measures, and within that patch, what type of control measure should be implemented. In the analysis of R(0), we found that if the extrinsic incubation period is shorter than the average mosquito lifespan, the control measures should be targeted towards reducing the mosquito biting rate. On the other hand, if the extrinsic incubation period is longer than the average mosquito lifespan, control measures targeting the mosquito death rate will be more effective. Intuitively, one might think that resources for malaria control should be allocated to the region with higher malaria transmission. However, our sensitivity analyses indicated that this is not always the case. In fact, if migration into the lower transmission patch is much faster than migration into the higher transmission patch, the lower transmission patch is potentially the better target for malaria control efforts. While human movement between regions poses challenges to malaria control and elimination, if estimates of relevant parameters in the model are known, including migration rates, our results can help inform which region to target and what type of control measure to implement for the greatest success.

Modeling control strategies for concurrent epidemics of seasonal and pandemic H1N1 influenza.

The lessons learned from the 2009-2010 H1N1 influenza pandemic, as it moves out of the limelight, should not be under-estimated, particularly since the probability of novel influenza epidemics in the near future is not negligible and the potential consequences might be huge. Hence, as the world, particularly the industrialized world, responded to the potentially devastating effects of this novel A-H1N1 strain with substantial resources, reminders of the recurrent loss of life from a well established foe, seasonal influenza, could not be ignored. The uncertainties associated with the reported and expected levels of morbidity and mortality with this novel A-H1N1 live in a backdrop of deaths, over 200,000 hospitalizations, and millions of infections (20% of the population) attributed to seasonal influenza in the USA alone, each year. So, as the Northern Hemisphere braced for the possibility of a potentially "lethal" second wave of the novel A-H1N1 without a vaccine ready to mitigate its impact, questions of who should be vaccinated first if a vaccine became available, came to the forefront of the discussion. Uncertainty grew as we learned that the vaccine, once available, would be unevenly distributed around the world. Nations capable of acquiring large vaccine supplies soon became aware that those who could pay would have to compete for a limited vaccine stockpile. The challenges faced by nations dealing jointly with seasonal and novel A-H1N1 co-circulating strains under limited resources, that is, those with no access to novel A-H1N1 vaccine supplies, limited access to the seasonal influenza vaccine, and limited access to antivirals (like Tamiflu) are explored in this study. One- and two-strain models are introduced to mimic the influenza dynamics of a single and co-circulating strains, in the context of a single epidemic outbreak. Optimal control theory is used to identify and evaluate the "best" control policies. The controls account for the cost associated with social distancing and antiviral treatment policies. The optimal policies identified might have, if implemented, a substantial impact on the novel H1N1 and seasonal influenza co-circulating dynamics. Specifically, the implementation of antiviral treatment might reduce the number of influenza cases by up to 60% under a reasonable seasonal vaccination strategy, but only by up to 37% when the seasonal vaccine is not available. Optimal social distancing policies alone can be as effective as the combination of multiple policies, reducing the total number of influenza cases by more than 99% within a single outbreak, an unrealistic but theoretically possible outcome for isolated populations with limited resources.