Mathematical Modeling of Mating Probability and Fertile Egg Production in Helminth Parasites.

In this work, we obtained a general formulation for the mating probability and fertile egg production in helminth parasites, focusing on the reproductive behavior of polygamous parasites and its implications for transmission dynamics. By exploring various reproductive variables in parasites with density-dependent fecundity, such as helminth parasites, we departed from the traditional assumptions of Poisson and negative binomial distributions to adopt an arbitrary distribution model. Our analysis considered critical factors such as mating probability, fertile egg production, and the distribution of female and male parasites among hosts, whether they are distributed together or separately. We show that the distribution of parasites within hosts significantly influences transmission dynamics, with implications for parasite persistence and, therefore, with implications in parasite control. Using statistical models and empirical data from Monte Carlo simulations, we provide insights into the complex interplay of reproductive variables in helminth parasites, enhancing our understanding of parasite dynamics and the transmission of parasitic diseases.

Disease dynamics and mean field models for clustered networks.

Social networks are clustered networks with short mean path length. In this work we analyze the disease dynamics in a class of this type of small-world networks composed of set of households and a set of workplaces. Individuals from each household are randomly assigned to workplaces. In both environments we assumed complete mixing and therefore we obtain highly clustered networks with short mean path lengths. Basic reproduction numbers were computed numerically and we show that at endemic equilibrium the average susceptible proportion is different from the inverse of the basic reproduction number (R0-1). Therefore exist an exponent p≠1 for which p=R0-1. Using this exponent we developed a mean field model which closely capture the disease dynamics in the network. Finally we outline how this model could be use to model vector-borne diseases in social networks.

Vector-Borne Disease Models with Active and Inactive Vectors: A Simple Way to Consider Biting Behavior.

Vector-borne diseases are a serious public health problem, mosquitoes being one of the most important vectors. To analyze the dynamics of this type of disease, Ross-Macdonald models are commonly used. In its simplest formulation and the most common in scientific literature, it is assumed that all mosquitoes are biting at a given rate. To improve this general assumption, we developed a vector-borne disease model with active and inactive vectors as a simple way to incorporate the more general characteristics of mosquito feeding behavior into disease dynamics. Our objective is to obtain an estimate of the Ross-Macdonald biting rate from the feeding parameters that reproduce the same dynamics as the model with active and inactive vectors. Two different cases were analyzed: a SIS-SI model and a SIR-SI model with a single epidemic. Different methods to estimate the biting rate in the Ross-Macdonald model were proposed and analyzed. To compare the results of the models, different epidemiological indicators were considered. When the biting rate is estimated considering that both models have the same basic reproduction number, very similar disease dynamics are obtained. This method is a simple way to incorporate the mosquito feeding behavior into the standard Ross-Macdonald model.

Simple epidemic network model for highly heterogeneous populations.

Network models for disease transmission and dynamics are popular because they are among the simplest agent-based models. Highly heterogeneous populations (in the number of contacts) may be modeled by networks with long-tailed degree distributions for which the variance is much greater than the mean degree. An example is given by scale-free networks where the degree distribution follows a power law. In these type of networks there is not a typical degree. Some nodes may have low representation in the population but are key to drive disease transmission. Coarse graining may be used to simplify these complex networks. In this work we present a simple model consisting in of a network where nodes have only two possible degrees, a low degree close to the mean degree and a high degree about ten times the mean degree. We show that in spite of this extreme simplification, main features of disease dynamics in scale-free networks are well captured by our model.

Epidemiological modeling of Trypanosoma cruzi: Low stercorarian transmission and failure of host adaptive immunity explain the frequency of mixed infections in humans.

People living in areas with active vector-borne transmission of Chagas disease have multiple contacts with its causative agent, Trypanosoma cruzi. Reinfections by T. cruzi are possible at least in animal models leading to lower or even hardly detectable parasitaemia. In humans, although reinfections are thought to have major public health implications by increasing the risk of chronic manifestations of the disease, there is little quantitative knowledge about their frequency and the timing of parasite re-inoculation in the course of the disease. Here, we implemented stochastic agent-based models i) to estimate the rate of re-inoculation in humans and ii) to assess how frequent are reinfections during the acute and chronic stages of the disease according to alternative hypotheses on the adaptive immune response following a primary infection. By using a hybrid genetic algorithm, the models were fitted to epidemiological data of Argentinean rural villages where mixed infections by different genotypes of T. cruzi reach 56% in humans. To explain this percentage, the best model predicted 0.032 (0.008-0.042) annual reinfections per individual with 98.4% of them occurring in the chronic phase. In addition, the parasite escapes to the adaptive immune response mounted after the primary infection in at least 20% of the events of re-inoculation. With these low annual rates, the risks of reinfection during the typically long chronic stage of the disease stand around 14% (4%-18%) and 60% (21%-70%) after 5 and 30 years, with most individuals being re-infected 1-3 times overall. These low rates are better explained by the weak efficiency of the stercorarian mode of transmission than a highly efficient adaptive immune response. Those estimates are of particular interest for vaccine development and for our understanding of the higher risk of chronic disease manifestations suffered by infected people living in endemic areas.

Aedes aegypti oviposition dynamics in towns with low human population density in yungas and dry chaco, Salta, Argentina.

We assessed the presence of Aedes aegypti in five ecorregions of Salta province and compared the oviposition activity of Ae. aegypti using ovitraps in towns of two contrasting ecoregions (yungas and Chaco dry forests) in the province of Salta, Argentina, a major contrast in these ecoregions are rain patterns and altitude. Our aim was to estimate how oviposition activities were associated with the ecoregion and site scale local environmental variables. Mosquito oviposition activity was monitored weekly during the summer using ovitraps. Predictor variables were ecoregion, town, and meteorological variables. The effect of the predictor variables was measured on the response variables using multi-model inference. Besides yungas, the presence of Aedes aegypti was confirmed in towns of dry Chaco and High Monte. The only factor that had a significant effect on the presence of eggs in the ovitraps was the ecoregion, with the frequency of positives being higher in yungas. For the number of eggs, the ecoregion, the night temperature of the first week and the NDVI would explain said variable. Overall, results indicate that the variations between towns would be more related with their ecological and climatic characteristics than with the more immediate meteorological variations.

Meteorological indicators of dengue epidemics in non-endemic Northwest Argentina.

In the last two decades dengue cases increased significantly throughout the world, giving place to more frequent outbreaks in Latin America. In the non-endemic city of San Ramón de la Nueva Orán, located in Northwest Argentina, large dengue outbreaks alternate with several years of smaller ones. This pattern, as well as the understanding of the underlying mechanisms, could be essential to design proper strategies to reduce epidemic size. We develop a stochastic model that includes climate variables, social structure, and mobility between a non-endemic city and an endemic area. Climatic variables were input of a mosquito population ecological model, which in turn was coupled to a meta-population, spatially explicit, epidemiological model. Human mobility was included into the model given the high border crossing to the northern country of Bolivia, where dengue transmission is sustained during the whole year. We tested different hypotheses regarding people mobility as well as climate variability by fitting numerical simulations to weekly clinical data reported from 2009 to 2016. After assessing the number of imported cases that triggered the observed outbreaks, our model allows to explain the observed epidemic pattern. We found that the number of vectors per host and the effective reproductive number are proxies for large epidemics. Both proxies are related with climate variability such as rainfall and temperature, opening the possibility to test these meteorological variables for forecast purposes.

Inference in epidemiological agent-based models using ensemble-based data assimilation.

To represent the complex individual interactions in the dynamics of disease spread informed by data, the coupling of an epidemiological agent-based model with the ensemble Kalman filter is proposed. The statistical inference of the propagation of a disease by means of ensemble-based data assimilation systems has been studied in previous works. The models used are mostly compartmental models representing the mean field evolution through ordinary differential equations. These techniques allow to monitor the propagation of the infections from data and to estimate several parameters of epidemiological interest. However, there are many important features which are based on the individual interactions that cannot be represented in the mean field equations, such as social network and bubbles, contact tracing, isolating individuals in risk, and social network-based distancing strategies. Agent-based models can describe contact networks at an individual level, including demographic attributes such as age, neighborhood, household, workplaces, schools, entertainment places, among others. Nevertheless, these models have several unknown parameters which are thus difficult to prescribe. In this work, we propose the use of ensemble-based data assimilation techniques to calibrate an agent-based model using daily epidemiological data. This raises the challenge of having to adapt the agent populations to incorporate the information provided by the coarse-grained data. To do this, two stochastic strategies to correct the model predictions are developed. The ensemble Kalman filter with perturbed observations is used for the joint estimation of the state and some key epidemiological parameters. We conduct experiments with an agent based-model designed for COVID-19 and assess the proposed methodology on synthetic data and on COVID-19 daily reports from Ciudad Autónoma de Buenos Aires, Argentina.

Ross-Macdonald models: Which one should we use?

Ross-Macdonald models are the building blocks of most vector-borne disease models. Even for the same disease, different authors use different model formulations, but a study of the dynamical consequences of assuming different hypotheses is missing. In this work we present different formulations of the basic Ross-Macdonald model together with a careful discussion of the assumptions behind each model. The most general model presented is an agent based model for which arbitrary distributions for latency and infectious periods for both, host and vectors, is considered. At population level we also developed a deterministic Volterra integral equations model for which also arbitrary distributions in the waiting times are included. We compare the model solutions using different distributions for the infectious and latency periods using statistics, like the epidemic peak, or epidemic final size, to characterize the epidemic curves. The basic reproduction number (R0) for each formulation is computed and compared with empirical estimations obtained with the agent based models. The importance of considering realistic distributions for the latent and infectious periods is highlighted and discussed. We also show that seasonality is a key driver of vector-borne disease dynamics shaping the epidemic curve and its duration.

Building epidemiological models from R0: an implicit treatment of transmission in networks.

Simple deterministic models are still at the core of theoretical epidemiology despite the increasing evidence for the importance of contact networks underlying transmission at the individual level. These mean-field or 'compartmental' models based on homogeneous mixing have made, and continue to make, important contributions to the epidemiology and the ecology of infectious diseases but fail to reproduce many of the features observed for disease spread in contact networks. In this work, we show that it is possible to incorporate the important effects of network structure on disease spread with a mean-field model derived from individual level considerations. We propose that the fundamental number known as the basic reproductive number of the disease, R0, which is typically derived as a threshold quantity, be used instead as a central parameter to construct the model from. We show that reliable estimates of individual level parameters can replace a detailed knowledge of network structure, which in general may be difficult to obtain. We illustrate the proposed model with small world networks and the classical example of susceptible-infected-recovered (SIR) epidemics.

Tuberculosis models with fast and slow dynamics: the role of close and casual contacts.

Models that incorporate local and individual interactions are introduced in the context of the transmission dynamics of tuberculosis (TB). The multi-level contact structure implicitly assumes that individuals are at risk of infection from close contacts in generalized household (clusters) as well as from casual (random) contacts in the general population. Epidemiological time scales are used to reduce the dimensionality of the model and singular perturbation methods are used to corroborate the results of time-scale approximations. The concept and impact of optimal average cluster or generalized household size on TB dynamics is discussed. We also discuss the potential impact of our results on the spread of TB.

Life history traits of Sirex noctilio F. (Hymenoptera: Siricidae) can explain outbreaks independently of environmental factors.

The woodwasp Sirex noctilio is a major pest of pine plantations worldwide. Economically significant damage is however limited to outbreak populations. To understand what determines outbreaks dynamics in this species, we developed an individual based model for a wasp population developing within a pine plantation. We show that outbreaks may be the result of the insect's life history. Specifically we show that limited dispersal may not only increase population persistence but also create the conditions for eruptive dynamics. When the probability of long distance dispersal is greater than zero, but relatively small (P(LDD) = 0.1) large outbreaks are the norm, with all of the suitable trees dead at the end of the simulation. For P(LDD) = 0 (only local dispersal allowed) outbreaks are smaller in size, and in some cases not well defined and spread over longer periods. For P(LDD) = 1 (only long distance dispersal allowed), the frequency of local population extinction (without outbreaks) increases significantly. Aggregated attacks may induce physiological changes in the trees which could allow other wasps to detect them. These changes may in turn trigger an outbreak. In contrast, healthy, vigorous trees are not suitable for wasp oviposition. In our model the density of suitable trees (healthy trees but yet suitable for oviposition) are a key factor determining population persistence before outbreaks. From an applied perspective, our results emphasize the importance of adequate plantation management in preventing woodwasp infestation.

Mathematical modelling of tuberculosis epidemics.

The strengths and limitations of using homogeneous mixing and heterogeneous mixing epidemic models are explored in the context of the transmission dynamics of tuberculosis. The focus is on three types of models: a standard incidence homogeneous mixing model, a non-homogeneous mixing model that incorporates 'household' contacts, and an age-structured model. The models are parameterized using demographic and epidemiological data and the patterns generated from these models are compared. Furthermore, the effects of population growth, stochasticity, clustering of contacts, and age structure on disease dynamics are explored. This framework is used to asses the possible causes for the observed historical decline of tuberculosis notifications.