Epidemic Spreading on Complex Networks as Front Propagation into an Unstable State.

We study epidemic arrival times in meta-population disease models through the lens of front propagation into unstable states. We demonstrate that several features of invasion fronts in the PDE context are also relevant to the network case. We show that the susceptible-infected-recovered model on a network is linearly determined in the sense that the arrival times in the nonlinear system are approximated by the arrival times of the instability in the system linearized near the disease-free state. Arrival time predictions are extended to general compartmental models with a susceptible-exposed-infected-recovered model as the primary example. We then study a recent model of social epidemics where higher-order interactions lead to faster invasion speeds. For these pushed fronts, we compute corrections to the estimated arrival time in this case. Finally, we show how inhomogeneities in local infection rates lead to faster average arrival times.

Constrained minimization problems for the reproduction number in meta-population models.

The basic reproduction number ([Formula: see text]) can be considerably higher in an SIR model with heterogeneous mixing compared to that from a corresponding model with homogeneous mixing. For example, in the case of measles, mumps and rubella in San Diego, CA, Glasser et al. (Lancet Infect Dis 16(5):599-605, 2016. https://doi.org/10.1016/S1473-3099(16)00004-9 ), reported an increase of 70% in [Formula: see text] when heterogeneity was accounted for. Meta-population models with simple heterogeneous mixing functions, e.g., proportionate mixing, have been employed to identify optimal vaccination strategies using an approach based on the gradient of the effective reproduction number ([Formula: see text]), which consists of partial derivatives of [Formula: see text] with respect to the proportions immune [Formula: see text] in sub-groups i (Feng et al. in J Theor Biol 386:177-187, 2015.  https://doi.org/10.1016/j.jtbi.2015.09.006 ; Math Biosci 287:93-104, 2017.  https://doi.org/10.1016/j.mbs.2016.09.013 ). These papers consider cases in which an optimal vaccination strategy exists. However, in general, the optimal solution identified using the gradient may not be feasible for some parameter values (i.e., vaccination coverages outside the unit interval). In this paper, we derive the analytic conditions under which the optimal solution is feasible. Explicit expressions for the optimal solutions in the case of [Formula: see text] sub-populations are obtained, and the bounds for optimal solutions are derived for [Formula: see text] sub-populations. This is done for general mixing functions and examples of proportionate and preferential mixing are presented. Of special significance is the result that for general mixing schemes, both [Formula: see text] and [Formula: see text] are bounded below and above by their corresponding expressions when mixing is proportionate and isolated, respectively.

Impact of Spring Bird Migration on the Range Expansion of Ixodes scapularis Tick Population.

Many observational studies suggest that seasonal migratory birds play an important role in spreading Ixodes scapularis, a vector of Lyme disease, along their migratory flyways, and they are believed to be responsible for geographic range expansion of I. scapularis in Canada. However, the interplay between the dynamics of I. scapularis on land and migratory birds in the air is not well understood. In this study, we develop a periodic delay meta-population model which takes into consideration the local landscape for tick reproduction within patches and the times needed for ticks to be transported by birds between patches. Assuming that the tick population is endemic in the source region, we find that bird migration may boost an already established tick population at the subsequent region and thus increase the risk to humans, or bird migration may help ticks to establish in a region where the local landscape is not appropriate for ticks to survive in the absence of bird migration, imposing risks to public health. This theoretical study reveals that bird migration plays an important role in the geographic range expansion of I. scapularis, and therefore our findings may suggest some strategies for Lyme disease prevention and control.

Modeling the effectiveness of targeting Rift Valley fever virus vaccination using imperfect network information.

Livestock movements contribute to the spread of several infectious diseases. Data on livestock movements can therefore be harnessed to guide policy on targeted interventions for controlling infectious livestock diseases, including Rift Valley fever (RVF)-a vaccine-preventable arboviral fever. Detailed livestock movement data are known to be useful for targeting control efforts including vaccination. These data are available in many countries, however, such data are generally lacking in others, including many in East Africa, where multiple RVF outbreaks have been reported in recent years. Available movement data are imperfect, and the impact of this uncertainty in the utility of movement data on informing targeting of vaccination is not fully understood. Here, we used a network simulation model to describe the spread of RVF within and between 398 wards in northern Tanzania connected by cattle movements, on which we evaluated the impact of targeting vaccination using imperfect movement data. We show that pre-emptive vaccination guided by only market movement permit data could prevent large outbreaks. Targeted control (either by the risk of RVF introduction or onward transmission) at any level of imperfect movement information is preferred over random vaccination, and any improvement in information reliability is advantageous to their effectiveness. Our modeling approach demonstrates how targeted interventions can be effectively used to inform animal and public health policies for disease control planning. This is particularly valuable in settings where detailed data on livestock movements are either unavailable or imperfect due to resource limitations in data collection, as well as challenges associated with poor compliance.

Epidemic local final size in a metapopulation network as indicator of geographical priority for control strategies in SIR type diseases.

The main limitation on designing epidemic control strategies lies in their economic and social costs. Thus, a practical and efficient approach takes into consideration these factors. Most epidemics evolve in a structured population, being the geographical structure the most evident. In this situation, having a criteria for identifying the most effective locations where control measures can optimize available resources is desirable. In this paper, a regional index based on the final epidemic size predicted by a metapopulation model is proposed. An efficient algorithm to calculate explicit index values was developed, and different control strategies that used the recommended index were compared with others that do not take the index information into account. We found that the proposed index represents an easy and fast criterion to guide simple control strategies. This type of index offers a new powerful approach where the information encoded in a deterministic mathematical model can be summarized to guide realistic and practical control strategies for disease spreading and epidemics.

Modeling Intervention Scenarios During Potential Foot-and-Mouth Disease Outbreaks Within U.S. Beef Feedlots.

Foot-and-mouth disease (FMD) is a highly contagious disease of livestock and has severely affected livestock industries during the past two decades in previously FMD-free countries. The disease was eliminated in North America in 1953 but remains a threat for re-introduction. Approximately 44% of the on-feed beef cattle in the U.S. are concentrated in feedlots <32,000 heads, but little information is available on dynamics of FMD in large feedlots. Therefore, there is a need to explore possible management and intervention strategies that might be implemented during potential FMD outbreaks on feedlots. We used a within home-pen stochastic susceptible-latent-infectious-recovered (SLIR) FMD dynamics model nested in a meta-population model of home-pens in a feedlot. The combinatory model was previously developed to simulate foot-and-mouth disease virus (FMDv) transmission within U.S. beef feedlots. We evaluated three intervention strategies initiated on the day of FMD detection: stopping movements of cattle between home-pens and hospital-pen(s) (NH), barrier depopulation combined with NH (NH-BD), and targeted depopulation of at-risk home-pens combined with NH (NH-TD). Depopulation rates investigated ranged from 500 to 4,000 cattle per day. We evaluated the projected effectiveness of interventions by comparing them with the no-intervention FMD dynamics in the feedlot. We modeled a small-size (4,000 cattle), medium-size (12,000 cattle), and large-size (24,000 cattle) feedlots. Implementation of NH delayed the outbreak progression, but it did not prevent infection of the entire feedlot. Implementation of NH-BD resulted in depopulation of 50% of cattle in small- and medium-size feedlots, and 25% in large-size feedlots, but the intervention prevented infection of the entire feedlot in 40% of simulated outbreaks in medium-size feedlots, and in 8% in large-size feedlots. Implementation of NH-TD resulted in depopulation of up to 50% of cattle in small-size feedlots, 75% in medium-size feedlots, and 25% in large-size feedlots, but rarely prevented infection of the entire feedlot. Number of hospital-pens in the feedlot was shown to weakly impact the success of NH-TD. Overall, the results suggest that stopping cattle movements between the home-pens and hospital-pens, without or with barrier or targeted cattle depopulation, would not be highly effective to interrupt FMDv transmission within a feedlot.

The Mayaro virus and its potential epidemiological consequences in Colombia: an exploratory biomathematics analysis.

BACKGROUND: Mayaro virus (Togaviridae) is an endemic arbovirus of the Americas with epidemiological similarities with the agents of other more prominent diseases such as dengue (Flaviviridae), Zika (Flaviviridae), and chikungunya (Togaviridae). It is naturally transmitted in a sylvatic/rural cycle by Haemagogus spp., but, potentially, it could be incorporated and transmitted in an urban cycle by Aedes aegypti, a vector widely disseminated in the Americas. METHODS: The Mayaro arbovirus dynamics was simulated mathematically in the colombian population in the eight biogeographical provinces, bearing in mind the vector's population movement between provinces through passive transport via truck cargo. The parameters involved in the virus epidemiological dynamics, as well as the vital rates of Ae. aegypti in each of the biogeographical provinces were obtained from the literature. These data were included in a meta-population model in differential equations, represented by a model structured by age for the dynamic population of Ae. aegypti combined with an epidemiological SEI/SEIR-type model. In addition, the model was incorporated with a term of migration to represent the connectivity between the biogeographical provinces. RESULTS: The vital rates and the development cycle of Ae. aegypti varied between provinces, having greater biological potential between 23 °C and 28 °C in provinces of Imerí, biogeographical Chocó, and Magdalena, with respect to the North-Andean Moorland (9.33-21.38 °C). Magdalena and Maracaibo had the highest flow of land cargo. The results of the simulations indicate that Magdalena, Imerí, and biogeographical Chocó would be the most affected regarding the number of cases of people infected by Mayaro virus over time. CONCLUSIONS: The temperature in each of the provinces influences the local population dynamics of Ae. aegypti and passive migration via transport of land cargo plays an important role on how the Mayaro virus would be disseminated in the human population. Once this arbovirus begins an urban cycle, the most-affected departments would be Antioquia, Santander, Norte de Santander, Cesar (Provinces of Magdalena), and Valle del Cauca, and Chocó (biogeographical province of Chocó), which is why vector control programmes must aim their efforts at these departments and include some type of vector control to the transport of land cargo to avoid a future Mayaro epidemic.

Comparing spatial diversification and meta-population models in the Indo-Australian Archipelago.

Reconstructing the processes that have shaped the emergence of biodiversity gradients is critical to understand the dynamics of diversification of life on Earth. Islands have traditionally been used as model systems to unravel the processes shaping biological diversity. MacArthur and Wilson's island biogeographic model predicts diversity to be based on dynamic interactions between colonization and extinction rates, while treating islands themselves as geologically static entities. The current spatial configuration of islands should influence meta-population dynamics, but long-term geological changes within archipelagos are also expected to have shaped island biodiversity, in part by driving diversification. Here, we compare two mechanistic models providing inferences on species richness at a biogeographic scale: a mechanistic spatial-temporal model of species diversification and a spatial meta-population model. While the meta-population model operates over a static landscape, the diversification model is driven by changes in the size and spatial configuration of islands through time. We compare the inferences of both models to floristic diversity patterns among land patches of the Indo-Australian Archipelago. Simulation results from the diversification model better matched observed diversity than a meta-population model constrained only by the contemporary landscape. The diversification model suggests that the dynamic re-positioning of islands promoting land disconnection and reconnection induced an accumulation of particularly high species diversity on Borneo, which is central within the island network. By contrast, the meta-population model predicts a higher diversity on the mainlands, which is less compatible with empirical data. Our analyses highlight that, by comparing models with contrasting assumptions, we can pinpoint the processes that are most compatible with extant biodiversity patterns.