React or wait: which optimal culling strategy to control infectious diseases in wildlife

We applied optimal control theory to an SI epidemic model to identify optimal culling strategies for diseases management in wildlife. We focused on different forms of the objective function, including linear control, quadratic control, and control with limited amount of resources. Moreover, we identified optimal solutions under different assumptions on disease-free host dynamics, namely: self-regulating logistic growth, Malthusian growth, and the case of negligible demography. We showed that the correct characterization of the disease-free host growth is crucial for defining optimal disease control strategies. By analytical investigations of the model with negligible demography, we demonstrated that the optimal strategy for the linear control can be either to cull at the maximum rate at the very beginning of the epidemic (reactive culling) when the culling cost is low, or never to cull, when culling cost is high. On the other hand, in the cases of quadratic control or limited resources, we demonstrated that the optimal strategy is always reactive. Numerical analyses for hosts with logistic growth showed that, in the case of linear control, the optimal strategy is always reactive when culling cost is low. In contrast, if the culling cost is high, the optimal strategy is to delay control, i.e. not to cull at the onset of the epidemic. Finally, we showed that for diseases with the same basic reproduction number delayed control can be optimal for acute infections, i.e. characterized by high disease-induced mortality and fast dynamics, while reactive control can be optimal for chronic ones.     

Optimal Sampling Strategies for Detecting Zoonotic Disease Epidemics

The early detection of disease epidemics reduces the chance of successful introductions into new locales, minimizes the number of infections, and reduces the financial impact. We develop a framework to determine the optimal sampling strategy for disease detection in zoonotic host-vector epidemiological systems when a disease goes from below detectable levels to an epidemic. We find that if the time of disease introduction is known then the optimal sampling strategy can switch abruptly between sampling only from the vector population to sampling only from the host population. We also construct time-independent optimal sampling strategies when conducting periodic sampling that can involve sampling both the host and the vector populations simultaneously. Both time-dependent and -independent solutions can be useful for sampling design, depending on whether the time of introduction of the disease is known or not. We illustrate the approach with West Nile virus, a globally-spreading zoonotic arbovirus. Though our analytical results are based on a linearization of the dynamical systems, the sampling rules appear robust over a wide range of parameter space when compared to nonlinear simulation models. Our results suggest some simple rules that can be used by practitioners when developing surveillance programs. These rules require knowledge of transition rates between epidemiological compartments, which population was initially infected, and of the cost per sample for serological tests.     

Optimizing vaccine allocation at different points in time during an epidemic

Background

Pandemic influenza A(H1N1) 2009 began spreading around the globe in April of 2009 and vaccination started in October of 2009. In most countries, by the time vaccination started, the second wave of pandemic H1N1 2009 was already under way. With limited supplies of vaccine, we are left to question whether it may be a good strategy to vaccinate the high-transmission groups earlier in the epidemic, but it might be a better use of resources to protect instead the high-risk groups later in the epidemic. To answer this question, we develop a deterministic epidemic model with two age-groups (children and adults) and further subdivide each age group in low and high risk.

Methods and Findings

We compare optimal vaccination strategies started at various points in time in two different settings: a population in a developed country where children account for 24% of the population, and a population in a less developed country where children make up the majority of the population, 55%. For each of these populations, we minimize mortality or hospitalizations and we find an optimal vaccination strategy that gives the best vaccine allocation given a starting vaccination time and vaccine coverage level. We find that population structure is an important factor in determining the optimal vaccine distribution. Moreover, the optimal policy is dynamic as there is a switch in the optimal vaccination strategy at some time point just before the peak of the epidemic. For instance, with 25% vaccine coverage, it is better to protect the high-transmission groups before this point, but it is optimal to protect the most vulnerable groups afterward.

Conclusions

Choosing the optimal strategy before or early in the epidemic makes an important difference in minimizing the number of influenza infections, and consequently the number of influenza deaths or hospitalizations, but the optimal strategy makes little difference after the peak.     

Epidemiological determinants of the pattern and magnitude of the vCJD epidemic in Great Britain.

Understanding the epidemiology and aetiology of new-variant Creutzfeldt-Jakob (vCJD) disease in humans has become increasingly important given the scientific evidence linking it to bovine spongiform encephalopathy (BSE) in cattle and hence the wide exposure of the population of Great Britain (GB) to potentially infectious tissue. The recent analysis undertaken to determine the risk to the population from dorsal route ganglia illustrated the danger in presenting point estimates rather than ranges of scenarios in the face of uncertainty. We present a mathematical template that relates the past pattern of the BSE epidemic in cattle to the future course of any vCJD epidemic in humans, and use extensive scenario analysis to explore the wide range of possible outcomes given the uncertainty in epidemiological determinants. We demonstrate that the average number of humans infected by one infectious bovine and the incubation period distribution are the two epidemiological factors that have the greatest impact on epidemic size and duration. Using the time-series of the BSE epidemic and the cases seen to date, we show that the minimum length of the incubation period is approximately nine years, and that at least 20% of the cases diagnosed to date were exposed prior to 1986. We also demonstrate that the current age distribution of vCJD cases can only arise if younger people were either exposed to a greater extent, more susceptible to infection, or have shorter incubation periods. Extensive scenario analyses show that given the information currently available, the very high degree of uncertainty in the future size of the epidemic will remain for the next 3-5 years. Furthermore, we demonstrate that this uncertainty is unlikely to be reduced by mass screening for late-stage infection.     

Human African Trypanosomiasis in South Sudan: How Can We Prevent a New Epidemic?

Human African trypanosomiasis (HAT) has been a major public health problem in South Sudan for the last century. Recurrent outbreaks with a repetitive pattern of responding-scaling down activities have been observed. Control measures for outbreak response were reduced when the prevalence decreased and/or socio-political crisis erupted, leading to a new increase in the number of cases. This paper aims to raise international awareness of the threat of another outbreak of sleeping sickness in South Sudan. It is a review of the available data, interventions over time, and current reports on the status of HAT in South Sudan. Since 2006, control interventions and treatments providing services for sleeping sickness have been reduced. Access to HAT diagnosis and treatment has been considerably diminished. The current status of control activities for HAT in South Sudan could lead to a new outbreak of the disease unless 1) the remaining competent personnel are used to train younger staff to resume surveillance and treatment in the centers where HAT activities have stopped, and 2) control of HAT continues to be given priority even when the number of cases has been substantially reduced. Failure to implement an effective and sustainable system for HAT control and surveillance will increase the risk of a new epidemic. That would cause considerable suffering for the affected population and would be an impediment to the socioeconomic development of South Sudan.     

Impact of Stakeholders Influence,Geographic Level and Risk Perception on Strategic Decisions in Simulated Foot and Mouth Disease Epizootics in France

Comparison of control strategies against animal infectious diseases allows determining optimal strategies according to their epidemiological and/or economic impacts. However, in real life, the choice of a control strategy does not always obey a pure economic or epidemiological rationality. The objective of this study was to analyze the choice of a foot and mouth disease (FMD) control strategy as a decision-making process in which the decision-maker is influenced by several stakeholders (government, agro-food industries, public opinion). For each of these, an indicator of epizootic impact was quantified to compare seven control strategies. We then determined how, in France, the optimal control strategy varied according to the relative weights of stakeholders and to the perception of risk by the decision-maker (risk-neutral/risk-averse). When the scope of decision was national, whatever their perception of risk and the stakeholders'' weights, decision-makers chose a strategy based on vaccination. This consensus concealed marked differences between regions, which were connected with the regional breeding characteristics. Vaccination-based strategies were predominant in regions with dense cattle and swine populations, and in regions with a dense population of small ruminants, combined with a medium density of cattle and swine. These differences between regions suggested that control strategies could be usefully adapted to local breeding conditions. We then analyzed the feasibility of adaptive decision-making processes depending on the date and place where the epizootic starts, or on the evolution of the epizootic over time. The initial conditions always explained at least half of the variance of impacts, the remaining variance being attributed to the variability of epizootics evolution. However, the first weeks of this evolution explained a large part of the impacts variability. Although the predictive value of the initial conditions for determining the optimal strategy was weak, adaptive strategies changing dynamically according to the evolution of the epizootic appeared feasible.     

<Emphasis Type="Italic">R</Emphasis><Subscript>0</Subscript>: Host Longevity Matters

The basic reproduction ratio, R₀, is a fundamental concept in epidemiology. It is defined as the total number of secondary infections brought on by a single primary infection, in a totally susceptible population. The value of R₀ indicates whether a starting epidemic reaches a considerable part of the population and causes a lot of damage, or whether it remains restricted to a relatively small number of individuals. To calculate R₀ one has to evaluate an integral that ranges over the duration of the infection of the host. This duration is, of course, limited by remaining host longevity. So, R₀ depends on remaining host longevity and in this paper we show that for long-lived hosts this aspect may not be ignored for long-lasting infections. We investigate in particular how this epidemiological measure of pathogen fitness depends on host longevity. For our analyses we adopt and combine a generic within- and between-host model from the literature. To find the optimal strategy for a pathogen from an evolutionary point of view, we focus on the indicator \(R_0^{{opt}}\), i.e., the optimum of R₀ as a function of its replication and mutation rates. These are the within-host parameters that the pathogen has at its disposal to optimize its strategy. We show that \(R_0^{{opt}}\) is highly influenced by remaining host longevity in combination with the contact rate between hosts in a susceptible population. In addition, these two parameters determine whether a killer-like or a milker-like strategy is optimal for a given pathogen. In the killer-like strategy the pathogen has a high rate of reproduction within the host in a short time span causing a relatively short disease, whereas in the milker-like strategy the pathogen multiplies relatively slowly, producing a continuous small amount of offspring over time with a small effect on host health. The present research allows for the determination of a bifurcation line in the plane of host longevity versus contact rate that forms the boundary between the milker-like and killer-like regions. This plot shows that for short remaining host longevities the killer-like strategy is optimal, whereas for very long remaining host longevities the milker-like strategy is advantageous. For in-between values of host longevity, the contact rate determines which of both strategies is optimal.     

Discrete-time host–parasitoid models with pest control

We propose a simple discrete-time host–parasitoid model to investigate the impact of external input of parasitoids upon the host–parasitoid interactions. It is proved that the input of the external parasitoids can eventually eliminate the host population if it is above a threshold and it also decreases the host population level in the unique interior equilibrium. It can simplify the host–parasitoid dynamics when the host population practices contest competition. We then consider a corresponding optimal control problem over a finite time period. We also derive an optimal control model using a chemical as a control for the hosts. Applying the forward–backward sweep method, we solve the optimal control problems numerically and compare the optimal host populations with the host populations when no control is applied. Our study concludes that applying a chemical to eliminate the hosts directly may be a more effective control strategy than using the parasitoids to indirectly suppress the hosts.     

Discrete-time host-parasitoid models with pest control

We propose a simple discrete-time host-parasitoid model to investigate the impact of external input of parasitoids upon the host-parasitoid interactions. It is proved that the input of the external parasitoids can eventually eliminate the host population if it is above a threshold and it also decreases the host population level in the unique interior equilibrium. It can simplify the host-parasitoid dynamics when the host population practices contest competition. We then consider a corresponding optimal control problem over a finite time period. We also derive an optimal control model using a chemical as a control for the hosts. Applying the forward-backward sweep method, we solve the optimal control problems numerically and compare the optimal host populations with the host populations when no control is applied. Our study concludes that applying a chemical to eliminate the hosts directly may be a more effective control strategy than using the parasitoids to indirectly suppress the hosts.     

Primary Culture of Human Embryonic Kidney Cells as the Medium for Isolation of ECHO 6 Virus

A large epidemic of aseptic meningitis due to ECHO 6 virus swept over Japan in the summer months of 1965. In our studies on 89 cases of aseptic meningitis in the epidemic, primary culture of human embryonic kidney cells was shown to provide a highly sensitive host system for isolation of ECHO 6 virus from clinical materials. Virus was recovered from cerebrospinal fluid in 72% of 89 cases, from throat swabs in 64% of 36 cases, and from rectal swabs in 59% of 37 cases. Most significant is the finding that the rate of virus isolation from cerebrospinal fluid in this host system was considerably higher as compared with that obtained by other investigators in other host systems such as primary monkey kidney cells or human amniotic cells (primary or EL). This finding should be emphasized particularly because isolation of a virus from cerebrospinal fluid, in contrast to throat secretions or feces, is of much greater importance in establishing the etiologic relationship to the disease in the diagnosis of aseptic meningitis. The neutralization test was shown to be efficient in detecting ECHO 6 virus infection; acute serums should be taken preferably by the 4th day of illness and convalescent serums in the second week. Epidemiologic findings, such as the predominance of male patients and occurrence of the epidemic in summer months, generally coincide with the previous reports. However, our cases were in much younger age groups in contrast with the previous reports; 90% of our 89 patients were 6 years of age or younger, and 15 children or 17% were less than 1 year of age, including 3 less than 6 months of age. The clinical observations on our cases confirmed the previous reports.     

Maximum sustainable yield of populations with continuous age-structure.

We address the problem of finding the harvesting policy that will maximize the yield and maintain a population in a steady state. The population is characterized by continuous age classes and therefore follows differential equations. Here, we assume that the equations are linear (no density dependence). Two possible constraints are considered: either recruitment or total population are fixed to a constant. Under these conditions, the optimal policy is to harvest the fraction theta of a younger age class ? and to harvest totally an older age class b. The optimal solution (theta, ?, b) can be calculated explicitly if the fecundity and mortality schedules are given. The solution is compared to the simpler strategy of harvesting all individuals beyond a single age class a. It is shown that the latter strategy can be much less profitable than harvesting two age classes because it cannot take account of the different values of individuals according to their age.     

Age-structured homogeneous epidemic systems with application to the MSEIR epidemic model

In this paper, we develop a new approach to deal with asymptotic behavior of the age-structured homogeneous epidemic systems and discuss its application to the MSEIR epidemic model. For the homogeneous system, there is no attracting nontrivial equilibrium, instead we have to examine existence and stability of persistent solutions. Assuming that the host population dynamics can be described by the stable population model, we rewrite the basic system into the system of ratio age distribution, which is the age profile divided by the stable age profile. If the host population has the stable age profile, the ratio age distribution system is reduced to the normalized system. Then we prove the stability principle that the local stability or instability of steady states of the normalized system implies that of the corresponding persistent solutions of the original homogeneous system. In the latter half of this paper, we prove the threshold and stability results for the normalized system of the age-structured MSEIR epidemic model.      

Epidemiology and disease-control under gene-for-gene plant-pathogen interaction

An introduction of disease-resistant variety of a crop plant often leads to the development of a virulent race in pathogen species that restores the pathogenicity to the resistant crop. This often makes disease control of crop plants extremely difficult. In this paper, we theoretically explore the optimal 'multiline' control, which makes use of several different resistant varieties, that minimizes the expected degree of crop damages caused by epidemic outbreaks of the pathogen. We examine both single-locus and two-locus gene-for-gene (GFG) systems for the compatibility relationship between host genotypes and pathogen genotypes, in which host haplotype has either susceptible or resistant allele in each resistance locus, and the pathogen haplotype has either avirulent or virulent allele in the corresponding virulence locus. We then study the optimal planting strategy of host resistant genotypes based on standard epidemiological dynamics with pathogen spore stages. The most striking result of our single-locus GFG model is that there exists an intermediate optimum mixing ratio for the susceptible and resistant crops that maximizes the final yield, in spite of the fact that the susceptible crop has no use to fight against either avirulent or virulent race of the pathogen. The intermediate mixture is optimum except when the initial pathogen spore population in the season consists exclusively of the virulent race. The optimal proportion of resistant crops is approximately 1/R(0), where R(0) is the basic reproductive ratio of pathogen--the rest (the vast majority if R(0) is large) of crops should be the susceptible genotype. By mixing susceptible and resistant crops, we can force the pathogen races to compete with each other for their available hosts. This competition between avirulent and virulent races prevents the fatal outbreak of the virulent race (the super-race) that can infect all the host genotypes. In the two-locus GFG control, there again exists the optimal mixing ratio for the fraction of universally susceptible genotype and the total fraction of various resistant genotypes, with the ratio close to 1/R(0).     

Age-Based Hiring Discrimination as a Function of Equity Norms and Self-Perceived Objectivity

Participants completed a questionnaire priming them to perceive themselves as either objective or biased, either before or after evaluating a young or old job applicant for a position linked to youthful stereotypes. Participants agreed that they were objective and tended to disagree that they were biased. Extending past research, both the objective and bias priming conditions led to an increase in age discrimination compared to the control condition. We also investigated whether equity norms reduced age discrimination, by manipulating the presence or absence of an equity statement reminding decision-makers of the legal prohibitions against discrimination “on the basis of age, disability, national or ethnic origin, race, religion, or sex.” The presence of equity norms increased enthusiasm for both young and old applicants when participants were not already primed to think of themselves as objective, but did not reduce age-based hiring discrimination. Equity norms had no effect when individuals thought of themselves as objective – they preferred the younger more than the older job applicant. However, the presence of equity norms did affect individuals’ perceptions of which factors were important to their hiring decisions, increasing the perceived importance of applicants’ expertise and decreasing the perceived importance of the applicants’ age. The results suggest that interventions that rely exclusively on decision-makers'' intentions to behave equitably may be ineffective.     

Optimal immune specificity at the intersection of host life history and parasite epidemiology

Hosts diverge widely in how, and how well, they defend themselves against infection and immunopathology. Why are hosts so heterogeneous? Both epidemiology and life history are commonly hypothesized to influence host immune strategy, but the relationship between immune strategy and each factor has commonly been investigated in isolation. Here, we show that interactions between life history and epidemiology are crucial for determining optimal immune specificity and sensitivity. We propose a demographically-structured population dynamics model, in which we explore sensitivity and specificity of immune responses when epidemiological risks vary with age. We find that variation in life history traits associated with both reproduction and longevity alters optimal immune strategies–but the magnitude and sometimes even direction of these effects depends on how epidemiological risks vary across life. An especially compelling example that explains previously-puzzling empirical observations is that depending on whether infection risk declines or rises at reproductive maturity, later reproductive maturity can select for either greater or lower immune specificity, potentially illustrating why studies of lifespan and immune variation across taxa have been inconclusive. Thus, the sign of selection on the life history-immune specificity relationship can be reversed in different epidemiological contexts. Drawing on published life history data from a variety of chordate taxa, we generate testable predictions for this facet of the optimal immune strategy. Our results shed light on the causes of the heterogeneity found in immune defenses both within and among species and the ultimate variability of the relationship between life history and immune specificity.     

Optimal mating strategies to manage a heterozygous advantage major gene in sheep

Some mutations (or ‘major genes’) have a desirable effect in heterozygous carriers but an undesirable effect in homozygous carriers. When these mutations affect a trait of significant economic importance, their eradication, depending on their effect and frequency, may be counterproductive. This is especially the case of major genes affecting the ovulation rate and thus the prolificacy in meat sheep populations. To manage such situations, a mating design based on the major genotypes of reproducers has to be optimized. Both the effect of the major gene and the cost of genotyping candidates at this locus influence the expected genetic progress and profitability of the breeding plan. The aim of this study was to determine the optimal combination of matings that maximizes profitability at the level of the whole population (nucleus + commercial flocks). A deterministic model was developed and, using sequential quadratic programming methodology, the optimal strategy (optimal combination of matings) that maximized the economic gain achieved by the population across a range of genotype effects and genotyping costs was determined. The optimal strategy was compared with simpler and more practical strategies based on a limited number of parental genotype mating types. Depending on the genotype effect and genotyping costs, the optimal strategy varied, such that either the heterozygous frequency and/or polygenic gain was maximized with a large number of animals genotyped, or when genotyping costs were higher, the optimization led to lower heterozygous frequency and/or polygenic gain with fewer animals genotyped. Comparisons showed that some simpler strategies were close to the optimal strategy. An overlapping model was then derived as an application of the real case of the French Lacaune meat sheep OVI-TEST breeding program. Results showed that a practical strategy based on mating non-carriers to heterozygous carriers was only slightly less effective than the optimal strategy, with a reduction in efficiency from 3% to 8%, depending on the genotyping costs. Based on only two different parental genotype mating types, this strategy would be easy to implement.     

Maturation of the humoral immune response as an optimization problem.

Efficient immune response often depends on the production of high affinity antibodies. We show analytically that the optimal strategy for a fast production of high affinity antibodies is to utilize a step-function mutation rate, i.e. a minimal mutation rate in early stages of the immune response, followed by a discontinuous switch to the maximal possible rate when the proliferating population of B-cells exceeds a threshold value. Our results are in accordance with the biological observations concerning the time of onset of the hypermutation process, and with the mutation rate during the later stages of the primary immune response. Indeed the hypermutation process plays a crucial role in responding to a prevailing pathogen at each round of immune response, and not only for coping with future infections. Moreover, as the effect of hypermutations is shown to be crucially dependent on the number of proliferating B-cells, its onset is not expected to depend on an external signal, but rather to be related to the clone's age. This suggests that the onset is host species specific, rather than pathogen specific. Another implication of the present results is that activation of hypermutations before the B-cell population has reached the critical size may impede the efficiency of the response.     

Partitioning the influence of ecology across scales on parasite evolution

Vector‐borne parasites must succeed at three scales to persist: they must proliferate within a host, establish in vectors, and transmit back to hosts. Ecology outside the host undergoes dramatic seasonal and human‐induced changes, but predicting parasite evolutionary responses requires integrating their success across scales. We develop a novel, data‐driven model to titrate the evolutionary impact of ecology at multiple scales on human malaria parasites. We investigate how parasites invest in transmission versus proliferation, a life‐history trait that influences disease severity and spread. We find that transmission investment controls the pattern of host infectiousness over the course of infection: a trade‐off emerges between early and late infectiousness, and the optimal resolution of that trade‐off depends on ecology outside the host. An expanding epidemic favors rapid proliferation, and can overwhelm the evolutionary influence of host recovery rates and mosquito population dynamics. If transmission investment and recovery rate are positively correlated, then ecology outside the host imposes potent selection for aggressive parasite proliferation at the expense of transmission. Any association between transmission investment and recovery represents a key unknown, one that is likely to influence whether the evolutionary consequences of interventions are beneficial or costly for human health.