Optimizing antiviral treatment for seasonal influenza in the USA: a mathematical modeling analysis

BACKGROUND

Seasonal influenza remains a major cause of morbidity and mortality in the USA. Despite the US Centers for Disease Control and Prevention recommendation promoting the early antiviral treatment of high-risk patients, treatment coverage remains low.

METHODS

To evaluate the population-level impact of increasing antiviral treatment timeliness and coverage among high-risk patients in the USA, we developed an influenza transmission model that incorporates data on infectious viral load, social contact, and healthcare-seeking behavior. We modeled the reduction in transmissibility in treated individuals based on their reduced daily viral load. The reduction in hospitalizations following treatment was based on estimates from clinical trials. We calibrated the model to weekly influenza data from Texas, California, Connecticut, and Virginia between 2014 and 2019. We considered in the baseline scenario that 2.7-4.8% are treated within 48 h of symptom onset while an additional 7.3-12.8% are treated after 48 h of symptom onset. We evaluated the impact of improving the timeliness and uptake of antiviral treatment on influenza cases and hospitalizations.

RESULTS

Model projections suggest that treating high-risk individuals as early as 48 h after symptom onset while maintaining the current treatment coverage level would avert 2.9-4.5% of all symptomatic cases and 5.5-7.1% of all hospitalizations. Geographic variability in the effectiveness of earlier treatment arises primarily from variabilities in vaccination coverage and population demographics. Regardless of these variabilities, we found that when 20% of the high-risk individuals were treated within 48 h, the reduction in hospitalizations doubled. We found that treatment of the elderly population (> 65 years old) had the highest impact on reducing hospitalizations, whereas treating high-risk individuals aged 5-19 years old had the highest impact on reducing transmission. Furthermore, the population-level benefit per treated individual is enhanced under conditions of high vaccination coverage and a low attack rate during an influenza season.

CONCLUSIONS

Increased timeliness and coverage of antiviral treatment among high-risk patients have the potential to substantially reduce the burden of seasonal influenza in the USA, regardless of influenza vaccination coverage and the severity of the influenza season.

Emergence of antibiotic resistance in immunocompromised host populations: A case study of emerging antibiotic resistant tuberculosis in AIDS patients

Objective

The evolution of antibiotic resistance is far outpacing the development of new antibiotics, causing global public health concern about infections that will increasingly be unresponsive to antimicrobials. This risk of emerging antibiotic resistance may be meaningfully altered in highly AIDS-immunocompromised populations. Such populations fundamentally alter the bacterial evolutionary landscape in two ways, which we seek to model and analyze. First, widespread, population-level immunoincompetence creates a novel host environment with disrupted selective pressures. Second, within AIDS-prevalent populations, the recommendation that antibiotics be taken to treat and prevent opportunistic infection raises the risk of selection for drug-resistant pathogens.

Design

To determine the impact of HIV/AIDS on the emergence of antibiotic resistance–specifically in the developing world where high prevalence and economic challenges complicate disease management.

Methods

We present an SEIR epidemiological model of bacterial infection, and parametrize it to capture HIV/AIDS-attributable emergence of resistance under conditions of both high and low HIV/AIDS prevalence.

Results

We demonstrate that HIV/AIDS-immunocompromised hosts can be responsible for a disproportionately greater contribution to emergence of resistance than would be expected based on population-wide HIV/AIDS prevalence alone.

Conclusions

As such, the AIDS-immunocompromised have the potential become wellsprings of novel, resistant, opportunistic pathogen strains that can propagate into the broader global community. We discuss how public health policies for HIV/AIDS management can shape the evolutionary environment for opportunistic bacterial infections.

Spatial and Temporal Clustering of Chikungunya Virus Transmission in Dominica

Using geo-referenced case data, we present spatial and spatio-temporal cluster analyses of the early spread of the 2013–2015 chikungunya virus (CHIKV) in Dominica, an island in the Caribbean. Spatial coordinates of the locations of the first 417 reported cases observed between December 15^th, 2013 and March 11^th, 2014, were captured using the Global Positioning System (GPS). We observed a preponderance of female cases, which has been reported for CHIKV outbreaks in other regions. We also noted statistically significant spatial and spatio-temporal clusters in highly populated areas and observed major clusters prior to implementation of intensive vector control programs suggesting early vector control measures, and education had an impact on the spread of the CHIKV epidemic in Dominica. A dynamical identification of clusters can lead to local assessment of risk and provide opportunities for targeted control efforts for nations experiencing CHIKV outbreaks.

Chikungunya is a disease transmitted by mosquitoes. Currently, there is an epidemic of chikungunya in several islands and countries in the Americas. Despite efforts at understanding and predicting spread, there have been no studies assessing the spatio-temporal spread of chikungunya in any of the Caribbean islands, mainly due to a lack of data. Here, we present a spatio-temporal analysis of the spread of chikungunya virus in Dominica, an island in the Western Hemisphere, using geo-referenced case data. The findings in this study suggest that females are at higher risk for chikungunya virus transmission in Dominica. In addition, there is statistically significant clustering of cases in densely populated areas. Lack of data prevented additional analyses on the impact of mosquito population density, environmental factors and housing conditions on the location and timing of the clusters. This study is relevant for chikungunya control in Dominica, and other regions can use similar methods to assess chikungunya risk at the local level.

Comparing the impact of artemisinin-based combination therapies on malaria transmission in sub-Saharan Africa

Artemisinin-based combination therapies (ACTs) are currently considered the first-line treatments for uncomplicated Plasmodium falciparum malaria. Among these, artemether-lumefantrine (AL) has been the most widely prescribed ACT in sub-Saharan Africa. Recent clinical trials conducted in sub-Saharan Africa have shown that dihydroartemisinin-piperaquine (DP), a most recent ACT, may have a longer post-treatment prophylactic period and post-treatment infection period (duration of gametocyte carriage) than AL. Using epidemiological and clinical data on the efficacy of AL and DP, we developed and parameterized a mathematical transmission model that we used to compare the population-level impact of AL and DP for reducing P. falciparum malaria transmission in sub-Saharan Africa. Our results showed that DP is likely to more effectively reduce malaria incidence of clinical episodes than AL. However in low P. falciparum transmission areas, DP and AL are likely to be equally effective in reducing malaria prevalence. The predictions of our model were shown to be robust to the empirical uncertainty summarizing the epidemiological parameters. DP should be considered as a replacement for AL as first-line treatment of uncomplicated malaria in highly endemic P. falciparum communities. To optimize the effectiveness of ACTs, it is necessary to tailor treatment policies to the transmission intensity in different settings.

Dynamics and control of Ebola virus transmission in Montserrado, Liberia: a mathematical modelling analysis

BACKGROUND

A substantial scale-up in public health response is needed to control the unprecedented Ebola virus disease (EVD) epidemic in west Africa. Current international commitments seek to expand intervention capacity in three areas: new EVD treatment centres, case ascertainment through contact tracing, and household protective kit allocation. We aimed to assess how these interventions could be applied individually and in combination to avert future EVD cases and deaths.

METHODS

We developed a transmission model of Ebola virus that we fitted to reported EVD cases and deaths in Montserrado County, Liberia. We used this model to assess the effectiveness of expanding EVD treatment centres, increasing case ascertainment, and allocating protective kits for controlling the outbreak in Montserrado. We varied the efficacy of protective kits from 10% to 50%. We compared intervention initiation on Oct 15, 2014, Oct 31, 2014, and Nov 15, 2014. The status quo intervention was defined in terms of case ascertainment and capacity of EVD treatment centres on Sept 23, 2014, and all behaviour and contact patterns relevant to transmission as they were occurring at that time. The primary outcome measure was the expected number of cases averted by Dec 15, 2014.

FINDINGS

We estimated the basic reproductive number for EVD in Montserrado to be 2·49 (95% CI 2·38-2·60). We expect that allocating 4800 additional beds at EVD treatment centres and increasing case ascertainment five-fold in November, 2014, can avert 77 312 (95% CI 68 400-85 870) cases of EVD relative to the status quo by Dec 15, 2014. Complementing these measures with protective kit allocation raises the expectation as high as 97 940 (90 096-105 606) EVD cases. If deployed by Oct 15, 2014, equivalent interventions would have been expected to avert 137 432 (129 736-145 874) cases of EVD. If delayed to Nov 15, 2014, we expect the interventions will at best avert 53 957 (46 963-60 490) EVD cases.

INTERPRETATION

The number of beds at EVD treatment centres needed to effectively control EVD in Montserrado substantially exceeds the 1700 pledged by the USA to west Africa. Accelerated case ascertainment is needed to maximise effectiveness of expanding the capacity of EVD treatment centres. Distributing protective kits can further augment prevention of EVD, but it is not an adequate stand-alone measure for controlling the outbreak. Our findings highlight the rapidly closing window of opportunity for controlling the outbreak and averting a catastrophic toll of EVD cases and deaths.

FUNDING

US National Institutes of Health.

Impact of Schistosoma mansoni on malaria transmission in Sub-Saharan Africa

Background

Sub-Saharan Africa harbors the majority of the global burden of malaria and schistosomiasis infections. The co-endemicity of these two tropical diseases has prompted investigation into the mechanisms of coinfection, particularly the competing immunological responses associated with each disease. Epidemiological studies have shown that infection with Schistosoma mansoni is associated with a greater malaria incidence among school-age children.

Methodology

We developed a co-epidemic model of malaria and S. mansoni transmission dynamics which takes into account key epidemiological interaction between the two diseases in terms of elevated malaria incidence among individuals with S. mansoni high egg output. The model was parameterized for S. mansoni high-risk endemic communities, using epidemiological and clinical data of the interaction between S. mansoni and malaria among children in sub-Saharan Africa. We evaluated the potential impact of the S. mansoni–malaria interaction and mass treatment of schistosomiasis on malaria prevalence in co-endemic communities.

Principal Findings

Our results suggest that in the absence of mass drug administration of praziquantel, the interaction between S. mansoni and malaria may reduce the effectiveness of malaria treatment for curtailing malaria transmission, in S. mansoni high-risk endemic communities. However, when malaria treatment is used in combination with praziquantel, mass praziquantel administration may increase the effectiveness of malaria control intervention strategy for reducing malaria prevalence in malaria- S. mansoni co-endemic communities.

Conclusions/Significance

Schistosomiasis treatment and control programmes in regions where S. mansoni and malaria are highly prevalent may have indirect benefits on reducing malaria transmission as a result of disease interactions. In particular, mass praziquantel administration may not only have the direct benefit of reducing schistosomiasis infection, it may also reduce malaria transmission and disease burden.

Malaria and Schistosoma mansoni are co-endemic in many regions of sub-Saharan Africa. Evidence from clinical and epidemiological studies support the hypothesis that concurrent infection with S. mansoni is associated with greater malaria incidence among school-age children. We use mathematical modeling to evaluate the epidemiological impact of S. mansoni infection on malaria transmission in sub-Saharan Africa. Using epidemiological data on the increased risk of malaria incidence in S. mansoni endemic communities from Senegal, we developed a co-epidemic model of malaria and S. mansoni transmission dynamics to address key epidemiological interactions between the two diseases. Parameterizing our model for S. mansoni high-risk endemic communities, we show that the interaction between S. mansoni and malaria may reduce the effectiveness of malaria treatment for curtailing malaria transmission. Moreover, we show that in addition to reducing schistosomiasis health burden, mass praziquantel administration will generate indirect benefit in terms of reducing malaria transmission and disease burden in S. mansoni–malaria co-endemic communities. Our findings indicate the possible benefit of scaling up schistosomiasis control efforts in sub-Saharan Africa, and especially in areas were S. mansoni and malaria are highly prevalent.

Evaluating the potential impact of mass praziquantel administration for HIV prevention in Schistosoma haematobium high-risk communities

Genital infection with Schistosoma haematobium is prevalent in sub-Saharan Africa. Epidemiological studies have observed that genital schistosomiasis is associated with an increased odd of HIV infection among women. We used mathematical modeling to explore the potential impact of mass preventive chemotherapy against schistosomiasis on HIV transmission in three sub-Saharan Africa countries: Angola, Kenya, and Zambia. We developed a model of female genital schistosomiasis (FGS) and HIV transmission dynamics, fitting it to data of HIV and S. haematobium prevalences as well as co-infection. We simulated targeted mass drug administration (MDA) with praziquantel to school-age children and mass treatment of the entire community. We estimated that, in S. haematobium high-risk communities, targeted annual treatment of school-age children could reduce HIV prevalence by 20% (95% CI: 12-31%) in Angola, 16% (95% CI: 10-32%) in Kenya, and 6% (95% CI: 3-18%) in Zambia after the first 20 years of intervention; and would reduce HIV incidence by 15% (95% CI: 13-32%) in Angola, 22% (95% CI: 18-42%) in Kenya, and 9% (95% CI: 3-22%) in Zambia. Extending the intervention to adults could reduce HIV prevalence by an additional 2.2% (95% CI: 0.2-12.0%) in Angola, 1.8% (95% CI: 0.1-5.2%) in Kenya, and 0.3% (95% CI: 0.1-2.1%) in Zambia; and would reduce HIV incidence by an additional 1.8% (95% CI: 0.0-14.4%) in Angola, 6.1% (95% CI: 0.5-12.6%) in Kenya, and 0.8% (95% CI: 0.0-2.7%) in Zambia. We showed that the exacerbation of HIV transmission due to FGS and the probability of developing FGS as a result of childhood infection with S. haematobium, were the most important factors in determining the effectiveness of praziquantel MDA for reducing HIV transmission. Praziquantel MDA may be an innovative measure for reducing schistosomiasis and HIV transmission in sub-Saharan Africa, the effectiveness of which varies with HIV prevalence.

Optimal control of disease infestations on a lattice

The design of durable and sustainable strategies for the control of plant diseases is not possible without due consideration of landscape structure and economic factors. However, many studies on control strategies of plant infestation have overlooked these considerations. In this paper, we address the problem of how best to deploy resources for the control of disease outbreaks during a single agricultural season. We consider a spatial model for the spread of a plant pathogen over an agricultural region, and model the effect of control on disease dynamics. We associate with a control strategy a 'costs function' that balances amount invested for treatment to the cost incurred by disease infestation. Our objective is to minimize the level of disease infestation and the effort of control. We prove the existence of a solution to the optimal control problem, and devise a numerical algorithm to compute it. We present results of our numerical studies, and show that the solution depends on the interplay between economic and epidemiological factors, as well as the nature of the control agent.

Country- and age-specific optimal allocation of dengue vaccines

Several dengue vaccines are under development, and some are expected to become available imminently. Concomitant with the anticipated release of these vaccines, vaccine allocation strategies for dengue-endemic countries in Southeast Asia and Latin America are currently under development. We developed a model of dengue transmission that incorporates the age-specific distributions of dengue burden corresponding to those in Thailand and Brazil, respectively, to determine vaccine allocations that minimize the incidence of dengue hemorrhagic fever, taking into account limited availability of vaccine doses in the initial phase of production. We showed that optimal vaccine allocation strategies vary significantly with the demographic burden of dengue hemorrhagic fever. Consequently, the strategy that is optimal for one country may be sub-optimal for another country. More specifically, we showed that, during the first years following introduction of a dengue vaccine, it is optimal to target children for dengue mass vaccination in Thailand, whereas young adults should be targeted in Brazil.

HIV and Schistosoma haematobium prevalences correlate in sub-Saharan Africa

OBJECTIVE

Epidemiological studies have observed that genital schistosomiasis increases the risk of HIV infection in Africa. We analysed the correlation between Schistosoma haematobium prevalence and HIV prevalence across sub-Saharan African countries.

DESIGN

Regression analysis of prevalence of HIV and S. haematobium across sub-Saharan African countries.

METHODS

Using compiled country-level S. haematobium prevalence, HIV prevalence and other demographic and economic data from published sources, we applied univariate and multivariate regression models to assess the correlations between S. haematobium prevalence and HIV prevalence while controlling for risk factors associated with each infection.

RESULTS

In 43 sub-Saharan African countries, the mean prevalence of S. haematobium was 22.4% [standard deviation (SD): 9.8%] and for HIV was 6.21% (SD: 5.71%). In multivariate analysis, adjusted for prevalence of male circumcision, years since a country's first HIV/AIDS diagnosis, geographical region and immunization coverage, each S. haematobium infection per 100 individuals was associated with a 2.9% (95% CI: 0.2-5.8%) relative increase in HIV prevalence. S. haematobium was not associated with Schistosoma mansoni, HSV-2, hepatitis C, malaria or syphilis.

CONCLUSIONS

Schistosoma haematobium prevalence was associated with HIV prevalence in sub-Saharan Africa. Controlling S. haematobium may be an effective means of reducing HIV transmission in sub-Saharan Africa.

Potential cost-effectiveness of schistosomiasis treatment for reducing HIV transmission in Africa--the case of Zimbabwean women

Background

Epidemiological data from Zimbabwe suggests that genital infection with Schistosoma haematobium may increase the risk of HIV infection in young women. Therefore, the treatment of Schistosoma haematobium with praziquantel could be a potential strategy for reducing HIV infection. Here we assess the potential cost-effectiveness of praziquantel as a novel intervention strategy against HIV infection.

Methods

We developed a mathematical model of female genital schistosomiasis (FGS) and HIV infections in Zimbabwe that we fitted to cross-sectional data of FGS and HIV prevalence of 1999. We validated our epidemic projections using antenatal clinic data on HIV prevalence. We simulated annual praziquantel administration to school-age children. We then used these model predictions to perform a cost-effectiveness analysis of annual administration of praziquantel as a potential measure to reduce the burden of HIV in sub-Saharan Africa.

Findings

We showed that for a variation of efficacy between 30–70% of mass praziquantel administration for reducing the enhanced risk of HIV transmission per sexual act due to FGS, annual administration of praziquantel to school-age children in Zimbabwe could result in net savings of US$16–101 million compared with no mass treatment of schistosomiasis over a ten-year period. For a variation in efficacy between 30–70% of mass praziquantel administration for reducing the acquisition of FGS, annual administration of praziquantel to school-age children could result in net savings of US$36−92 million over a ten-year period.

Conclusions

In addition to reducing schistosomiasis burden, mass praziquantel administration may be a highly cost-effective way of reducing HIV infections in sub-Saharan Africa. Program costs per case of HIV averted are similar to, and under some conditions much better than, other interventions that are currently implemented in Africa to reduce HIV transmission. As a cost-saving strategy, mass praziquantel administration should be prioritized over other less cost-effective public health interventions.

Evidence from epidemiological and clinical studies supports the hypothesis that genital infection with Schistosoma haematobium increases the risk of becoming infected with HIV among women in sub-Saharan Africa. Praziquantel is an oral, nontoxic, inexpensive medication recommended for treatment of schistosomiasis, which might be able to prevent the development of genital schistosomiasis. We constructed a mathematical model of female genital schistosomiasis and HIV infections, which we calibrated using epidemiological data from Zimbabwe. We used this model to investigate the potential cost-effectiveness of mass drug administration with praziquantel as an intervention strategy for reducing HIV transmission in sub-Saharan Africa. We showed that mass drug administration with praziquantel may be a timely, innovative, and cost-saving intervention strategy for HIV prevention in sub-Saharan Africa. As a cost-saving strategy, mass drug administration with praziquantel should be prioritized over other less cost-effective public health interventions. Our findings indicate the possible benefit of scaling up schistosomiasis control efforts in sub-Saharan Africa, and especially in areas were Schistosoma haematobium and HIV are highly prevalent.

Dengue dynamics and vaccine cost-effectiveness in Brazil

Recent Phase 2b dengue vaccine trials have demonstrated the safety of the vaccine and estimated the vaccine efficacy with further trials underway. In anticipation of vaccine roll-out, cost-effectiveness analysis of potential vaccination policies that quantify the dynamics of disease transmission are fundamental to the optimal allocation of available doses. We developed a dengue transmission and vaccination model and calculated, for a range of vaccination costs and willingness-to-pay thresholds, the level of vaccination coverage necessary to sustain herd-immunity, the price at which vaccination is cost-effective and is cost-saving, and the sensitivity of our results to parameter uncertainty. We compared two vaccine efficacy scenarios, one a more optimistic scenario and another based on the recent lower-than-expected efficacy from the latest clinical trials. We found that herd-immunity may be achieved by vaccinating 82% (95% CI 58-100%) of the population at a vaccine efficacy of 70%. At this efficacy, vaccination may be cost-effective for vaccination costs up to US$ 534 (95% CI $369-1008) per vaccinated individual and cost-saving up to $204 (95% CI $39-678). At the latest clinical trial estimates of an average of 30% vaccine efficacy, vaccination may be cost-effective and cost-saving at costs of up to $237 (95% CI $159-512) and $93 (95% CI $15-368), respectively. Our model provides an assessment of the cost-effectiveness of dengue vaccination in Brazil and incorporates the effect of herd immunity into dengue vaccination cost-effectiveness. Our results demonstrate that at the relatively low vaccine efficacy from the recent Phase 2b dengue vaccine trials, age-targeted vaccination may still be cost-effective provided the total vaccination cost is sufficiently low.

Optimal targeting of seasonal influenza vaccination toward younger ages is robust to parameter uncertainty

Identification of the optimal vaccine allocation for the control of influenza requires consideration of uncertainty arising from numerous unpredictable factors, including viral evolution and diversity within the human population's immunity as well as variation in vaccine efficacy. The best policy must account for diverse potential outcomes based on these uncertainties. Here we used a mathematical model parametrized with survey-based contact data, demographic, and epidemiological data from seasonal influenza in the United States to determine the optimal vaccine allocation for five outcome measures: infections, hospitalizations, deaths, years of life loss, and contingent valuation. We incorporated uncertainty of epidemiological parameters and derive probability distributions of optimal age- and risk-specific allocation of vaccine. Our analysis demonstrated that previous recommendations of targeting schoolchildren (ages 5-17 years) and young adults (18-44 years) are generally robust in the face of uncertainty. However, when the outcome measure is to minimize deaths, years of life loss, or contingent valuation, uncertainty analysis identified scenarios under which it is optimal to target people at high risk for complications, even when vaccine are in abundance.

The impact of imitation on vaccination behavior in social contact networks

Previous game-theoretic studies of vaccination behavior typically have often assumed that populations are homogeneously mixed and that individuals are fully rational. In reality, there is heterogeneity in the number of contacts per individual, and individuals tend to imitate others who appear to have adopted successful strategies. Here, we use network-based mathematical models to study the effects of both imitation behavior and contact heterogeneity on vaccination coverage and disease dynamics. We integrate contact network epidemiological models with a framework for decision-making, within which individuals make their decisions either based purely on payoff maximization or by imitating the vaccination behavior of a social contact. Simulations suggest that when the cost of vaccination is high imitation behavior may decrease vaccination coverage. However, when the cost of vaccination is small relative to that of infection, imitation behavior increases vaccination coverage, but, surprisingly, also increases the magnitude of epidemics through the clustering of non-vaccinators within the network. Thus, imitation behavior may impede the eradication of infectious diseases. Calculations that ignore behavioral clustering caused by imitation may significantly underestimate the levels of vaccination coverage required to attain herd immunity.

Both infectious diseases and behavioral traits can spread via social contacts. Using network-based mathematical models, our study addresses the interplay between these two processes, as disease spreads through a population and individuals copy their social contacts when making vaccination decisions. Imitation can produce clusters of non-vaccinating, susceptible individuals that facilitate relatively large outbreaks of infectious diseases despite high overall vaccination coverage. This may explain, for example, recent measles outbreaks observed in many countries with universal measles vaccination policies. Given that vaccine decisions are likely to be influenced by social contacts and that such imitation can have detrimental epidemiological effects, it is important that policy makers understand its causes, magnitude and implications for disease eradication.

Resource allocation for epidemic control in metapopulations

Deployment of limited resources is an issue of major importance for decision-making in crisis events. This is especially true for large-scale outbreaks of infectious diseases. Little is known when it comes to identifying the most efficient way of deploying scarce resources for control when disease outbreaks occur in different but interconnected regions. The policy maker is frequently faced with the challenge of optimizing efficiency (e.g. minimizing the burden of infection) while accounting for social equity (e.g. equal opportunity for infected individuals to access treatment). For a large range of diseases described by a simple SIRS model, we consider strategies that should be used to minimize the discounted number of infected individuals during the course of an epidemic. We show that when faced with the dilemma of choosing between socially equitable and purely efficient strategies, the choice of the control strategy should be informed by key measurable epidemiological factors such as the basic reproductive number and the efficiency of the treatment measure. Our model provides new insights for policy makers in the optimal deployment of limited resources for control in the event of epidemic outbreaks at the landscape scale.

Economically optimal timing for crop disease control under uncertainty: an options approach

Severe large-scale disease and pest infestations in agricultural regions can cause significant economic damage. Understanding if and when disease control measures should be taken in the presence of risk and uncertainty is a key issue. We develop a framework to examine the economically optimal timing of treatment. The decision to treat should only be undertaken when the benefits exceed the costs by a certain amount and not if they are merely equal to or greater than the costs as standard net-present-value (NPV) analysis suggests. This criterion leads to a reduction in fungicide use. We investigate the effect of the model for disease progress on the value required for immediate treatment by comparing two standard models for disease increase (exponential and logistic growth). Analyses show that the threshold value of benefits required for immediate release of treatment varies significantly with the relative duration of the agricultural season, the intrinsic rate of increase of the disease and the level of uncertainty in disease progression. In comparing the performance of the delay strategy introduced here with the conventional NPV approach, we show how the degree of uncertainty affects the benefits of delaying control.

Balancing detection and eradication for control of epidemics: sudden oak death in mixed-species stands

Culling of infected individuals is a widely used measure for the control of several plant and animal pathogens but culling first requires detection of often cryptically-infected hosts. In this paper, we address the problem of how to allocate resources between detection and culling when the budget for disease management is limited. The results are generic but we motivate the problem for the control of a botanical epidemic in a natural ecosystem: sudden oak death in mixed evergreen forests in coastal California, in which species composition is generally dominated by a spreader species (bay laurel) and a second host species (coast live oak) that is an epidemiological dead-end in that it does not transmit infection but which is frequently a target for preservation. Using a combination of an epidemiological model for two host species with a common pathogen together with optimal control theory we address the problem of how to balance the allocation of resources for detection and epidemic control in order to preserve both host species in the ecosystem. Contrary to simple expectations our results show that an intermediate level of detection is optimal. Low levels of detection, characteristic of low effort expended on searching and detection of diseased trees, and high detection levels, exemplified by the deployment of large amounts of resources to identify diseased trees, fail to bring the epidemic under control. Importantly, we show that a slight change in the balance between the resources allocated to detection and those allocated to control may lead to drastic inefficiencies in control strategies. The results hold when quarantine is introduced to reduce the ingress of infected material into the region of interest.

Optimization of control strategies for epidemics in heterogeneous populations with symmetric and asymmetric transmission

There is growing interest in incorporating economic factors into epidemiological models in order to identify optimal strategies for disease control when resources are limited. In this paper we consider how to optimize the control of a pathogen that is capable of infecting multiple hosts with different rates of transmission within and between species. Our objective is to find control strategies that maximize the discounted number of healthy individuals. We consider two classes of host-pathogen system, comprising two host species and a common pathogen, one with asymmetrical and the other with symmetrical transmission rates, applicable to a wide range of SI (susceptible-infected) epidemics of plant and animal pathogens. We motivate the analyses with an example of sudden oak death in California coastal forests, caused by Phytophthora ramorum, in communities dominated by bay laurel (Umbellularia californica) and tanoak (Lithocarpus densiflorus). We show for the asymmetric case that it is optimal to give priority in treating disease to the more infectious species, and to treat the other species only when there are resources left over. For the symmetric case, we show that although a switching strategy is an optimum, in which preference is first given to the species with the lower level of susceptibles and then to the species with the higher level of susceptibles, a simpler strategy that favors treatment of infected hosts for the more susceptible species is a robust alternative for practical application when the optimal switching time is unknown. Finally, since transmission rates are notoriously difficult to estimate, we analyze the robustness of the strategies when the true state with respect to symmetry or otherwise is unknown but one or other is assumed.