Presence and infestation waves of hematophagous arthropod species.

The invasion of hematophagous arthropod species in human settlements represents a threat, not only to the economy but also to the health system in general. Recent examples of this phenomenon were seen in Paris and Mexico City, evidencing the importance of understanding these dynamics. In this work, we present a reaction-diffusion model to describe the invasion dynamics of hematophagous arthropod species. The proposed model considers a denso-dependent growth rate and parameters related to the control of the invasive species. Our results illustrate the existence of two invasion levels (presence and infestation) within a region, depending on control parameter values. We also prove analytically the existence of the presence and infestation waves and show different theoretical types of invasion waves that result from varying control parameters. In addition, we present a condition threshold that determines whether or not an infestation occurs. Finally, we illustrate some results when considering the case of bedbugs and brown dog ticks as invasion species.

Ex Vivo Experiments Shed Light on the Innate Immune Response from Influenza Virus.

The innate immune response is recognized as a key driver in controlling an influenza virus infection in a host. However, the mechanistic action of such innate response is not fully understood. Infection experiments on ex vivo explants from swine trachea represent an efficient alternative to animal experiments, as the explants conserved key characteristics of an organ from an animal. In the present work we compare three cellular automata models of influenza virus dynamics. The models are fitted to free virus and infected cells data from ex vivo swine trachea experiments. Our findings suggest that the presence of an immune response is necessary to explain the observed dynamics in ex vivo organ culture. Moreover, such immune response should include a refractory state for epithelial cells, and not just a reduced infection rate. Our results may shed light on how the immune system responds to an infection event.

COVID-19 optimal vaccination policies: A modeling study on efficacy, natural and vaccine-induced immunity responses.

About a year into the pandemic, COVID-19 accumulates more than two million deaths worldwide. Despite non-pharmaceutical interventions such as social distance, mask-wearing, and restrictive lockdown, the daily confirmed cases remain growing. Vaccine developments from Pfizer, Moderna, and Gamaleya Institute reach more than 90% efficacy and sustain the vaccination campaigns in multiple countries. However, natural and vaccine-induced immunity responses remain poorly understood. There are great expectations, but the new SARS-CoV-2 variants demand to inquire if the vaccines will be highly protective or induce permanent immunity. Further, in the first quarter of 2021, vaccine supply is scarce. Consequently, some countries that are applying the Pfizer vaccine will delay its second required dose. Likewise, logistic supply, economic and political implications impose a set of grand challenges to develop vaccination policies. Therefore, health decision-makers require tools to evaluate hypothetical scenarios and evaluate admissible responses. Following some of the WHO-SAGE recommendations, we formulate an optimal control problem with mixed constraints to describe vaccination schedules. Our solution identifies vaccination policies that minimize the burden of COVID-19 quantified by the number of disability-adjusted years of life lost. These optimal policies ensure the vaccination coverage of a prescribed population fraction in a given time horizon and preserve hospitalization occupancy below a risk level. We explore "via simulation" plausible scenarios regarding efficacy, coverage, vaccine-induced, and natural immunity. Our simulations suggest that response regarding vaccine-induced immunity and reinfection periods would play a dominant role in mitigating COVID-19.

Effect of daily human movement on some characteristics of dengue dynamics.

Human movement is a key factor in infectious diseases spread such as dengue. Here, we explore a mathematical modeling approach based on a system of ordinary differential equations to study the effect of human movement on characteristics of dengue dynamics such as the existence of endemic equilibria, and the start, duration, and amplitude of the outbreak. The model considers that every day is divided into two periods: high-activity and low-activity. Periodic human movement between patches occurs in discrete times. Based on numerical simulations, we show unexpected scenarios such as the disease extinction in regions where the local basic reproductive number is greater than 1. In the same way, we obtain scenarios where outbreaks appear despite the fact that the local basic reproductive numbers in these regions are less than 1 and the outbreak size depends on the length of high-activity and low-activity periods.

Lockdown, relaxation, and acme period in COVID-19: A study of disease dynamics in Hermosillo, Sonora, Mexico.

Lockdown and social distancing measures have been implemented for many countries to mitigate the impacts of the COVID-19 pandemic and prevent overwhelming of health services. However, success on this strategy depends not only on the timing of its implementation, but also on the relaxation measures adopted within each community. We developed a mathematical model to evaluate the impacts of the lockdown implemented in Hermosillo, Mexico. We compared this intervention with some hypothetical ones, varying the starting date and also the population proportion that is released, breaking the confinement. A Monte Carlo study was performed by considering three scenarios to define our baseline dynamics. Results showed that a hypothetical delay of two weeks, on the lockdown measures, would result in an early acme around May 9 for hospitalization prevalence and an increase on cumulative deaths, 42 times higher by May 31, when compared to baseline. On the other hand, results concerning relaxation dynamics showed that the acme levels depend on the proportion of people who gets back to daily activities as well as the individual behavior with respect to prevention measures. Analysis regarding different relaxing mitigation measures were provided to the Sonoran Health Ministry, as requested. It is important to stress that, according to information provided by health authorities, the acme occurring time was closed to the one given by our model. Hence, we considered that our model resulted useful for the decision-making assessment, and that an extension of it can be used for the study of a potential second wave.

The role of animal grazing in the spread of Chagas disease.

Chagas disease is an important neglected tropical disease which causes on average about 7000 deaths per year, and an estimated 25 million people risk of acquiring it. This illness is often found in rural areas, which are usually characterized by poverty and presence of animals which act as reservoirs of the disease. Our main objective is to study the effect of animal grazing on the disease levels of the human population. For this purpose, we consider two environments (domestic and wild) where each one has permanent residents, and there is a proportion of animals that move between both environments due to grazing. This movement is modeled through the residence time in each environment. We analyze the proposed model and finally, we discuss the influence of domestic animals residence time on the disease level of human population.