About a year into the pandemic, COVID-19 accumulates more than two million deaths worldwide. Despite non-pharmaceutical interventions 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.

At the date, Europe and part of North America face the second wave of COVID-19, causing more than 1 300 000 deaths worldwide. Humanity lacks successful treatments, and a sustainable solution is an effective vaccine. Pfizer and the Russian Gamaleya Institute report that its vaccines reach more than 90 % efficacy in a recent press release. If third stage trial results favorable, pharmaceutical firms estimate big scale production of its vaccine candidates around the first 2021 quarter and the World Health organization fix as objective, vaccinate 20 % of the whole population at the final of 2021. However, since COVID-19 is new to our knowledge, vaccine efficacy and induced-immunity responses remain poorly understood. There are great expectations, but few think the first vaccines will be fully protective. Instead, they may reduce the severity of illness, reducing hospitalization and death cases.Further, logistic supply, economic and political implications impose a set of grand challenges to develop vaccination policies. For this reason, health decision-makers require tools to evaluate hypothetical scenarios and evaluate admissible responses.Our contribution answers questions in this direction. According to the WHO Strategic Advisory Group of Experts on Immunization Working Group on COVID-19 Vaccines, we formulate an optimal controlled model to describe vaccination policies that minimize the burden of COVID-19 quantified by the number of disability-adjusted years of life lost. Additionally, we analyze the reproductive vaccination number according to vaccination profiles depending on coverage, efficacy, horizon time, and vaccination rate. We explore scenarios regarding efficacy, coverage, vaccine-induced immunity, and natural immunity via numerical simulation. Our results suggest that response regarding vaccine-induced immunity and natural immunity would play a dominant role in the vaccination policy design. Likewise, the vaccine efficacy would influence the time of intensifying the number of doses in the vaccination policy.

Record-breaking and devastating rainfall events have occurred in the past decade. Rain and floods are considered the main risk factors for leptospirosis and several outbreaks have been reported following extreme weather events. In such situations, one possible intervention to prevent leptospirosis cases in high-risk groups is the use of chemoprophylaxis. However, not enough evidence of its effect is available. The objectives of this study were to review the literature on the current practices of chemoprophylaxis for leptospirosis and to explore, using a mathematical model, how various chemoprophylaxis scenarios may affect the progression of a leptospirosis outbreak. Twenty-six peer-reviewed publications were selected (10 quantitative studies, two systematic reviews and 14 articles of other types). Oral doxycycline was the most used antibiotic for chemoprophylaxis of leptospirosis. Post-exposure prophylaxis was assessed in four studies following a natural disaster. Although evidence of the effectiveness of post-exposure prophylaxis is inconsistent, the direction of association supported a protective effect for morbidity and mortality. The theoretical model showed how the assumed benefit of chemoprophylaxis was influenced by the time and rate of administration. Future models should consider the heterogeneity of affected communities, improved estimates of the effect of chemoprophylaxis on leptospirosis infection and disease, as well as potential detrimental impacts. Additional research is critical to provide clear evidence-based recommendations for leptospirosis control during an outbreak. The results of this study suggest that chemoprophylaxis may provide some protection in reducing the number of leptospirosis cases after a high-risk exposure; however, the effective benefit may depend on a variety of factors such as the timing and coverage of prophylaxis. The information summarized can be used to support decision-making during a high-risk event.

Since the first major outbreak reported on the island Yap in 2007, the Zika virus spread has alerted the scientific community worldwide. Zika is an arbovirus transmitted by Aedes mosquitoes; particularly in Central and South America, the main vector is the same mosquito that transmits dengue and chikungunya, Aedes aegypti. Seeking to understand the dynamics of spread of the Zika, in this paper, three mathematical models are presented, in which vector transmission of the virus, sexual contact transmission and migration are considered. Numerical analysis of these models allows us to have a clear view of the effects of sexual transmission and migration in the spread of the virus, showing that sexual transmission influences the magnitude of the outbreaks and migration generates outbreaks over time, each of lower intensity than the previous.

In this paper, we propose a SI model for the study of human and animal leptospirosis. Unlike other models for leptospirosis which consider only rodents as infection vectors, we consider that humans can be infected not only through contact with rodents, but also through any other animal that serves as a reservoir for the bacteria, and through contact with bacteria that are free in the environment. We calculate the basic reproductive number for this model, which is given in terms of the basic reproductive numbers of simpler subsystems of the original model, and propose some intervention techniques for controlling the disease based on our results.