Assessing the impact of human mobility to predict regional excess death in Ecuador.

COVID-19 outbreaks have had high mortality in low- and middle-income countries such as Ecuador. Human mobility is an important factor influencing the spread of diseases possibly leading to a high burden of disease at the country level. Drastic control measures, such as complete lockdown, are effective epidemic controls, yet in practice one hopes that a partial shutdown would suffice. It is an open problem to determine how much mobility can be allowed while controlling an outbreak. In this paper, we use statistical models to relate human mobility to the excess death in Ecuador while controlling for demographic factors. The mobility index provided by GRANDATA, based on mobile phone users, represents the change of number of out-of-home events with respect to a benchmark date (March 2nd, 2020). The study confirms the global trend that more men are dying than expected compared to women, and that people under 30 show less deaths than expected, particularly individuals younger than 20 with a death rate reduction between 22 and 27%. The weekly median mobility time series shows a sharp decrease in human mobility immediately after a national lockdown was declared on March 17, 2020 and a progressive increase towards the pre-lockdown level within two months. Relating median mobility to excess deaths shows a lag in its effect: first, a decrease in mobility in the previous two to three weeks decreases excess death and, more novel, we found an increase of mobility variability four weeks prior increases the number of excess deaths.

The Impact of Strict Public Health Restrictions on Pediatric Critical Illness.

OBJECTIVES: To characterize the impact of public health interventions on the volume and characteristics of admissions to the PICU. DESIGN: Multicenter retrospective cohort study. SETTING: Six U.S. referral PICUs during February 15, 2020-May 14, 2020, compared with the same months during 2017-2019 (baseline). PATIENTS: PICU admissions excluding admissions for illnesses due to severe acute respiratory syndrome coronavirus 2 and readmissions during the same hospitalization. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: Primary outcome was admission volumes during the period of stay-at-home orders (March 15, 2020-May 14, 2020) compared with baseline. Secondary outcomes were hospitalization characteristics including advanced support (e.g., invasive mechanical ventilation), PICU and hospital lengths of stay, and mortality. We used generalized linear mixed modeling to compare patient and admission characteristics during the stay-at-home orders period to baseline. We evaluated 7,960 admissions including 1,327 during March 15, 2020-May 14, 2020. Daily admissions and patients days were lower during the period of stay-at-home orders compared with baseline: median admissions 21 (interquartile range, 17-25) versus 36 (interquartile range, 30-42) (p < 0.001) and median patient days 93.0 (interquartile range, 55.9-136.7) versus 143.6 (interquartile range, 108.5-189.2) (p < 0.001). Admissions during the period of stay-at-home orders were less common in young children and for respiratory and infectious illnesses and more common for poisonings, endocrinopathies and for children with race/ethnicity categorized as other/unspecified. There were no differences in hospitalization characteristics except fewer patients received noninvasive ventilation during the period of stay-at-home orders. CONCLUSIONS: Reductions in PICU admissions suggest that much of pediatric critical illness in younger children and for respiratory and infectious illnesses may be preventable through targeted public health strategies.

Estimating the effect of social inequalities on the mitigation of COVID-19 across communities in Santiago de Chile.

We study the spatio-temporal spread of SARS-CoV-2 in Santiago de Chile using anonymized mobile phone data from 1.4 million users, 22% of the whole population in the area, characterizing the effects of non-pharmaceutical interventions (NPIs) on the epidemic dynamics. We integrate these data into a mechanistic epidemic model calibrated on surveillance data. As of August 1, 2020, we estimate a detection rate of 102 cases per 1000 infections (90% CI: [95-112 per 1000]). We show that the introduction of a full lockdown on May 15, 2020, while causing a modest additional decrease in mobility and contacts with respect to previous NPIs, was decisive in bringing the epidemic under control, highlighting the importance of a timely governmental response to COVID-19 outbreaks. We find that the impact of NPIs on individuals' mobility correlates with the Human Development Index of comunas in the city. Indeed, more developed and wealthier areas became more isolated after government interventions and experienced a significantly lower burden of the pandemic. The heterogeneity of COVID-19 impact raises important issues in the implementation of NPIs and highlights the challenges that communities affected by systemic health and social inequalities face adapting their behaviors during an epidemic.

The great crime recovery: Crimes against women during, and after, the COVID-19 lockdown in Mexico.

This paper considers whether the COVID-19 stay-at-home order affected crimes targeting women. To answer this question, we use national municipal-level crime data from Mexico's National Public Security System. The NPSS reports sexual crimes, lapses in alimony, domestic violence, and femicides. Using the NPSS, we track monthly changes in crimes targeting women using an event-study design. Our results show that lapses in alimony, sexual crimes, and domestic violence follow a U-shaped trend. Each crime declined during the stay-at-home order, and then rose back to pre-COVID levels by October. Then, we analyze potential mechanisms for the reduction in crimes against women. We find that infection risk, victim-criminal match, and banning the sale of alcohol are related to higher declines in crime.

Coronavirus disease 2019, food security and maternal mental health in Ceará, Brazil: a repeated cross-sectional survey.

OBJECTIVE: To quantify the change in the risk of food insecurity and maternal mental disorder (MMD) before and during the coronavirus disease 2019 (COVID-19) pandemic. DESIGN: Repeated cross-sectional survey. Between 17 July and 10 September 2020, mother-child pairs who were enrolled in a population-based survey in 2017 were re-contacted by telephone for consent and to complete a telephonic COVID-19 survey. We used the Brazilian Food Insecurity Scale to assess food security and the Self Reporting Questionnaire-20 to assess MMD. McNemar's test for paired data that also accounted for clustering was used. Logistic regression was used to assess the relationship of unemployment and receipt of government assistance with food insecurity and MMD in 2020. SETTING: Ceará, Brazil. PARTICIPANTS: Five hundred and seventy-seven mother-child pairs completed the 2017 and 2020 surveys. At the time of the 2020 interview, the child cohort was 36-108 months of age. RESULTS: The proportion of mothers reporting food insecurity was 15·5 % higher (95 % CI 5·9, 25·1, P value < 0·001) during the pandemic in July-August 2020 as compared with November 2017, while the prevalence of MMD was 40·2 % higher during the pandemic (95 % CI 32·6, 47·8, P value < 0·001). Loss of formal employment was associated with increased risk of food insecurity, but not with the risk of MMD. CONCLUSIONS: The risk of food insecurity and MMD in Ceará increased during the COVID-19 pandemic. These findings highlight the need for policies and interventions to reduce the impact of the COVID-19 pandemic on maternal and child health, nutrition and well-being in Brazil.

Modeling the transmission of the new coronavirus in São Paulo State, Brazil-assessing the epidemiological impacts of isolating young and elder persons.

We developed a mathematical model to describe the new coronavirus transmission in São Paulo State, Brazil. The model divided a community into subpopulations composed of young and elder persons considering a higher risk of fatality among elder persons with severe CoViD-19. From the data collected in São Paulo State, we estimated the transmission and additional mortality rates. Based on the estimated model parameters, we calculated the basic reproduction number $R_{0}$, and we retrieved the number of deaths due to CoViD-19, which was three times lower than those found in the literature. Considering isolation as a control mechanism, we varied the isolation rates in the young and elder subpopulations to assess the epidemiological impacts. The epidemiological scenarios focused mainly on evaluating the reduction in the number of severe CoViD-19 cases and deaths due to this disease when isolation is introduced in a population.

On the effectiveness of the search and find method to suppress spread of SARS-CoV-2.

Search and find methods*) such as cluster tracing1)-6) or large-scale PCR testing**) of those who exhibit no symptoms or only mild symptoms of COVID-19 is shown by data analysis to be a powerful means to suppress the spread of COVID-19 instead of, or in addition to, lockdown of the entire population. Here we investigate this issue by analyzing the data from some cities and countries and we establish that search and find method is as powerful as lockdown of a city or a country. Moreover, in contrast to lockdown, it neither causes inconvenience to citizens nor does it disrupt the economy. Generally speaking, it is advisable that both social distancing and increased test numbers be employed to suppress spread of the virus. The product of the total test number with the rate of positive cases is the crucial index.

High prevalence of food insecurity, the adverse impact of COVID-19 in Brazilian favela.

OBJECTIVE: To investigate food insecurity (FI) prevalence in two favelas in Brazil in the early weeks of the social distancing policy, from 27 March 2020 to 1 June 2020. DESIGN: A cross-sectional study using an online questionnaire to elicit information on socio-economic and demographic characteristics, the types of stores visited to buy food, and FI screening. The FI experience was evaluated according to the Brazilian Food Insecurity Scale. Factors associated with moderate or severe FI were investigated using the logistic regression model. SETTING: São Paulo city, Brazil. PARTICIPANTS: Totally, 909 householders. RESULTS: Eighty-eight per cent of the households included young women working as cleaners or kitchen assistants and in sales services. One-fifth of the participants were involved in the federal cash transfer programme, called Bolsa Família. There were 92 % households with children. The most frequent experience reported was uncertainty about food acquisition or receiving more (89 %), eating less than one should (64 %), not being able to eat healthy and nutritious food (46 %), and skipping a meal (39 %). Forty-seven per cent of the participants experienced moderate or severe FI. Factors associated with moderate and severe FI were low income, being a Bolsa Família recipient, having a low level of education and living in a household without children. CONCLUSIONS: Half of the participants experienced moderate or severe FI, and almost 10 % experienced hunger. Our data suggest that families with children were at a lower risk of moderate to severe FI. It is possible that nationally established social programmes such as Bolsa Família were protecting those families.

Avaliação do acesso ao tratamento de tuberculose sob perspectiva dos usuários na atenção primária / Assessment of access to tuberculosis treatment from the perspective of users in primary care / Evaluación del acceso al tratamiento de tuberculosis desde la perspectiva de los usuarios en la atención primaria

Objetivo: avaliar o acesso ao tratamento em pessoas com Tuberculose na Atenção Primária à Saúde. Métodos: trata-se de uma pesquisa transversal, descritivo e observacional, com abordagem quantitativa, realizada na cidade de Caxias-Maranhão. Obteve-se uma amostra de 133 participantes, porém foram entrevistados 100 pacientes. Resultados: as maiores prevalências ocorreram em homens 55 (55%), com ensino fundamental incompleto 57 (57%). Percebeu-se também, que o acesso ao tratamento é centralizado e os indicadores geográficos foram considerados satisfatórios, como, realização do tratamento na unidade mais próxima 100 (100%), consulta médica em 24 horas 91 (91%), medicamentos 99 (99%), tempo menor de 60 minutos para se consultar 87 (87%). Conclusão: desta forma, este estudo demonstrou associação significativa em relação ao tratamento de tuberculose diante das variáveis de estudo. Portanto, garantir o acesso não é suficiente para o êxito do tratamento, refletindo a necessidade de novas estratégias que visem a promoção da saúde da população

Objective: to evaluate access to treatment in people with Tuberculosis in Primary Health Care. Methods: this is a cross-sectional, descriptive and observational study, with a quantitative approach, carried out in the city of Caxias-Maranhão. A sample of 133 participants was obtained, but 100 patients were interviewed. Results: the highest prevalence occurred in men 55 (55%), with incomplete primary education 57 (57%). It was also noticed that access to treatment is centralized and geographic indicators were considered satisfactory, such as treatment at the nearest unit 100 (100%), medical consultation in 24 hours 91 (91%), medicines 99 (99 %), less than 60 minutes to consult 87 (87%). Conclusion: thus, this study demonstrated a significant association in relation to the treatment of tuberculosis in view of the study variables. Therefore, ensuring access is not sufficient for the success of treatment, reflecting the need for new strategies aimed at promoting the population's health

Objetivo: evaluar el acceso al tratamiento en personas con tuberculosis en Atención Primaria de Salud. Método: estudio transversal, descriptivo y observacional, con enfoque cuantitativo, realizado en la ciudad de Caxias-Maranhão. Se obtuvo una muestra de 133 participantes, pero se entrevistó a 100 pacientes. Resultados: la prevalencia más alta ocurrió en hombres 55 (55%), con educación primaria incompleta 57 (57%). También se observó que el acceso al tratamiento está centralizado y los indicadores geográficos se consideraron satisfactorios, como el tratamiento en la unidad más cercana 100 (100%), consulta médica en 24 horas 91 (91%), medicamentos 99 (99%), menor 60 minutos para consultar 87 (87%). Conclusión: por lo tanto, este estudio demostró una asociación significativa en relación con el tratamiento de la tuberculosis debido a las variables del estudio. Por lo tanto, garantizar el acceso no es suficiente para el éxito del tratamiento, lo que refleja la necesidad de nuevas estrategias destinadas a promover la salud de la población

Medidas de contenção de tipo lockdown para prevenção e controle da COVID-19: estudo ecológico descritivo, com dados da África do Sul, Alemanha, Brasil, Espanha, Estados Unidos, Itália e Nova Zelândia, fevereiro a agosto de 2020 / Medidas de contención tipo lockdown para prevención y control del COVID-19: estudio ecológico descriptivo con datos de febrero a agosto de 2020 en Sudáfrica, Alemania, Brasil, España, Estados Unidos, Italia y Nueva Zelanda / Lockdown-type containment measures for COVID-19 prevention and control: a descriptive ecological study with data from South Africa, Germany, Brazil, Spain, United States, Italy and New Zealand, February - August 2020

Objetivo: Descrever as medidas de contenção de tipo lockdown e a incidência da COVID-19 em sete países: África do Sul, Alemanha, Brasil, Espanha, Estados Unidos, Itália e Nova Zelândia. Métodos: Estudo ecológico descritivo, com dados da incidência diária dos casos confirmados de COVID-19 entre 22 de fevereiro e 31 de agosto de 2020, e informações sobre medidas de lockdown implementadas pelo governo de cada país. Resultados: Os países que implementaram lockdown tiveram diminuição da incidência diária de COVID-19 (casos por milhão de habitantes) no período de três semanas, a contar do início da medida: África do Sul (3,7 a 1,7), Alemanha (37,5 a 33,7), Espanha (176,3 a 82,0), Itália (92,0 a 52,1) e Nova Zelândia (7,5 a 1,7). O Brasil e os Estados Unidos, que não implementaram lockdown, não apresentaram uma diminuição considerável. Conclusão: Após a implementação de lockdown, houve uma diminuição considerável do número de casos confirmados.

Objetivo: Describir las medidas de contención tipo lockdown y la incidencia de COVID-19 en los países de Sudáfrica, Alemania, Brasil, España, Estados Unidos, Italia y Nueva Zelanda. Métodos: Estudio ecológico descriptivo con datos de la incidencia diaria de los casos confirmados de COVID-19, del 22 de febrero al 31 de agosto de 2020 e informaciones sobre medidas de contención lockdown implementadas por los gobiernos de cada uno de los países. Resultados: Los países que implementaron lockdown, desde el inicio de su implementación hasta tres semanas después, tuvieron una disminución en la incidencia diaria (casos por millón de habitantes): Sudáfrica (3,7 a 1,7), Alemania (37,5 a 33,7), España (176,3 a 82,0), Italia (92,0 a 52,1) y Nueva Zelanda (7,5 a 1,7). Brasil y Estados Unidos, que no implementaron lockdown, no tuvieron una disminución considerable Conclusión: Luego de la implementación del lockdown, hubo una disminución considerable en el número de casos confirmados.

Objective: To describe lockdown-type containment measures and COVID-19 incidence in South Africa, Germany, Brazil, Spain, United States, Italy and New Zealand. Methods: This is a descriptive ecological study with data on daily incidence of confirmed COVID-19 cases from February 22 to August 31 2020, as well as information on lockdown measures implemented by the governments of each country. Results: Daily COVID-19 incidence (cases per 1 million inhabitants) decreased within three weeks after lockdown started in the countries that implemented it: South Africa (3.7 to 1.7), Germany (37.5 to 33.7) Spain (176.3 to 82.0), Italy (92.0 to 52.1) and New Zealand (7.5 to 1.7). As for Brazil and the United States, which did not implement lockdown, there was no considerable decrease. Conclusion: After lockdown implementation, there was a considerable decrease in the number of confirmed cases.

Confidence in social institutions, perceived vulnerability and the adoption of recommended protective behaviors in Brazil during the COVID-19 pandemic.

The current worldwide COVID19 pandemic has required the rapid and drastic adoption of social distancing and protective measures as the leading method for reducing the spread of the disease and death. The purpose of this study is to investigate the factors associated with the adoption of such measures in a large sample of the Brazilian population. We relied on recreancy theory, which argues that confidence in the ability of social institutions and perceived vulnerability to the disease are central factors predicting the adoption of these behaviors. Our results, drawn from 7554 respondents, indicate that self-confidence in the ability to carry out these behaviors, confidence in the ability of social institutions such as the government, hospitals, health workers and the media to cope with the pandemic crisis, and risk perceptions are associated with the adoption of preventive behaviors. Our results expand the recreancy theory and show that beyond the main effects, the effect of perceived vulnerability depends on the values of self-confidence and confidence in social institutions. The theoretical implications of the findings are discussed.

Assessment of early mitigation measures against COVID-19 in Puerto Rico: March 15-May 15, 2020.

On March 15, 2020 Puerto Rico implemented non-pharmaceutical interventions (NPIs), including a mandatory curfew, as part of a state of emergency declaration to prevent the community transmission of the SARS-CoV-2 virus. The strict enforcement of this curfew was extended through May 25, with a gradual relaxation beginning on May 1. This report summarizes an assessment of these early mitigation measures on the progression of the COVID-19 pandemic in the island. From March 15 to May 15, 2020, 70,656 results of molecular (RT-PCR) tests were reported to the Puerto Rico Department of Health. Of these, 1,704 were positive, corresponding to 1,311 individuals with COVID-19 included in the study. We derived the epidemic growth rates (r) and the corresponding reproductive numbers (R) from the epidemic curve of these 1,311 individuals with laboratory-confirmed diagnosis of COVID-19 using their date of test collection as a proxy for symptoms onset. Through May 31, 2020, there were 143 COVID-19 associated deaths in Puerto Rico, for a case fatality risk of 10.9%. We compared the observed cases and deaths with Gompertz model projections had the mitigation measures not been implemented. The number of daily RT-PCR-confirmed cases peaked on March 30 (85 cases), showing a weekly cyclical trend, with lower counts on weekends and a decreasing secular trend since March 30. The initial exponential growth rate (r) was 15.87% (95% CI: 7.59%, 24.15%), corresponding to R of 1.82 (95% CI:1.37, 2.30). After March 30, the r value reverted to an exponential decay rate (negative) of -2.95% (95% CI: -4.99%, -0.92%), corresponding to R of 0.93 (95% CI: 0.86, 0.98). We estimate that, had the initial growth rate been maintained, a total of 6,155 additional COVID-19 cases would have occurred by May 15, with 211 additional COVID-19 deaths by May 31. These findings are consistent with very effective implementation of early NPIs as mitigation measures in Puerto Rico. These results also provide a baseline to assess the impact of the transition from mitigation to subsequent containment stages in Puerto Rico.

Social distancing patterns in nine municipalities of Rio Grande do Sul, Brazil: the Epicovid19/RS study.

OBJECTIVE To describe social distancing practices in nine municipalities of the state of Rio Grande do Sul, Brazil, stratified by gender, age, and educational attainment. METHODS Two sequential cross-sectional studies were conducted in the municipalities of Canoas, Caxias do Sul, Ijuí, Passo Fundo, Pelotas, Porto Alegre, Santa Cruz do Sul, Santa Maria, and Uruguaiana to estimate the population prevalence of COVID-19. The study was designed to be representative of the urban population of these municipalities. A questionnaire including three questions about social distancing was also administered to the participants. Here, we present descriptive analyses of social distancing practices by subgroups and use chi-square tests for comparisons. RESULTS In terms of degree of social distancing, 25.8% of the interviewees reported being essentially isolated and 41.1% reported being quite isolated. 20.1% of respondents reported staying at home all the time, while 44.5% left only for essential activities. More than half of households reported receiving no visits from non-residents. Adults aged 20 to 59 reported the least social distancing, while more than 80% of participants aged 60 years or older reported being essentially isolated or quite isolated. Women reported more stringent distancing than men. Groups with higher educational attainment reported going out for daily activities more frequently. CONCLUSIONS The extremes of age are more protected by social distancing, but some groups remain highly exposed. This can be an important limiting factor in controlling progression of the COVID-19 pandemic.

The Impact of COVID-19 Partial Lockdown on Primary Pollutant Concentrations in the Atmosphere of Rio de Janeiro and São Paulo Megacities (Brazil).

As COVID-19 spread all over the world, most of the countries adopted some kind of restrictions to avoid the collapse of health systems. In Brazil, São Paulo and Rio the Janeiro, the two most populated cities in the country, were the first to determine social distancing. In this study, the impact of the social distancing measures on the concentrations of the three main primary air pollutants (PM10, NO2 and CO) was analyzed. CO levels showed the most significant reductions (up to 100%) since it is related to light-duty vehicular emissions. NO2 also showed reductions (9.1%-41.8%) while PM10 levels were only reduced in the 1st lockdown week. The decrease of pollutants was not directly proportional to the vehicular flux reduction, because it depends on other factors such as the transport of air masses from industrial and rural areas. The differences observed can be explained considering the fleet characteristics in the two cities and the response of the population to the social distancing recommendations.

Social distancing patterns in nine municipalities of Rio Grande do Sul, Brazil: the Epicovid19/RS study / Padrões de distanciamento social em nove cidades gaúchas: estudo Epicovid19/RS

ABSTRACT OBJECTIVE To describe social distancing practices in nine municipalities of the state of Rio Grande do Sul, Brazil, stratified by gender, age, and educational attainment. METHODS Two sequential cross-sectional studies were conducted in the municipalities of Canoas, Caxias do Sul, Ijuí, Passo Fundo, Pelotas, Porto Alegre, Santa Cruz do Sul, Santa Maria, and Uruguaiana to estimate the population prevalence of COVID-19. The study was designed to be representative of the urban population of these municipalities. A questionnaire including three questions about social distancing was also administered to the participants. Here, we present descriptive analyses of social distancing practices by subgroups and use chi-square tests for comparisons. RESULTS In terms of degree of social distancing, 25.8% of the interviewees reported being essentially isolated and 41.1% reported being quite isolated. 20.1% of respondents reported staying at home all the time, while 44.5% left only for essential activities. More than half of households reported receiving no visits from non-residents. Adults aged 20 to 59 reported the least social distancing, while more than 80% of participants aged 60 years or older reported being essentially isolated or quite isolated. Women reported more stringent distancing than men. Groups with higher educational attainment reported going out for daily activities more frequently. CONCLUSIONS The extremes of age are more protected by social distancing, but some groups remain highly exposed. This can be an important limiting factor in controlling progression of the COVID-19 pandemic.

RESUMO OBJETIVO Descrever práticas de distanciamento social em nove municípios do Rio Grande do Sul por sexo, idade, escolaridade e cidade. MÉTODOS Foram realizados dois estudos transversais sequenciais representativos da população urbana nos municípios de Canoas, Caxias do Sul, Ijuí, Passo Fundo, Pelotas, Porto Alegre, Santa Cruz do Sul, Santa Maria e Uruguaiana com o intuito de estimar a prevalência populacional de Covid-19. Foi aplicado questionário contendo três perguntas sobre distanciamento social, cujas práticas foram submetidas a análises descritivas por subgrupos. Os dados foram comparados por testes qui-quadrado. RESULTADOS Em termos de grau de distanciamento social, 25,8% dos entrevistados relataram estar praticamente isolados e 41,1% indicam praticar bastante distanciamento. Relataram ficar em casa o tempo todo 20,1% dos entrevistados, e 44,5% informam que saem apenas para atividades essenciais. Mais da metade dos domicílios não recebe visitas de não moradores. O grupo que relatou menos distanciamento social foi o de adultos entre 20 e 59 anos, enquanto mais de 80% dos entrevistados com 60 anos ou mais relataram estar praticamente isolados ou fazendo bastante distanciamento. As mulheres relataram fazer mais distanciamento que os homens, e os grupos de maior escolaridade foram os que relataram sair diariamente para atividades regulares com mais frequência. CONCLUSÕES Os grupos mais jovens e mais idosos estão mais protegidos pelo distanciamento social, mas há grupos bastante expostos, o que pode ser um limitador importante no controle da progressão da epidemia de Covid-19.

Backward Bifurcation as a Desirable Phenomenon: Increased Fecundity Through Infection.

Backward or subcritical bifurcation is usually considered an undesirable phenomenon in epidemiology since control measures require a reduction in R0 not below one but below a much smaller value. However, there are contexts for which a backward or subcritical bifurcation is not a bad thing; it can even be desirable. Such is the case for any characteristic that can be passed to the next generation (genetically fixed or not) and that increases the effective reproductive rate of the host or the total number of individuals. In the present work, we study an epidemiological model consisting of two classes, susceptible and "infected" individuals; the model considers a characteristic that is passed from "infected" to "susceptible" by direct "contact," for instance increased fecundity. We analyze conditions for the appearance of a backward or subcritical bifurcation. We discuss the advantage for the population under infection, since the total number of individuals increases at equilibrium. If one takes that as a proxy for increased fitness, it would increase the species' ecological success. One key element in the model is the fact that "susceptible" individuals have "susceptible" descendants, but "infected" individuals can have "infected" descendants as well as "susceptible" ones. A somehow rare addition for epidemiological models, the fact that "infected" individuals reproduce more rapidly than the susceptible ones, leads to unexpected consequences. Facilitating the "inoculation" increases the total population size, i.e., the backward or subcritical bifurcation appears, with desirable consequences for the population. We show that an increase in the number of susceptible newborns is the main reason for the appearance of a backward or subcritical bifurcation, which induces a bigger population size. We analyze the effect of different combinations of susceptible/infected birth rates. This kind of phenomenon has been observed for bacterial infections in several insects-bacteria and nematodes-bacteria interactions; in particular, it has been intensely studied in interactions of wasps and flies with the genus Wolbachia. It has also been shown in amphibians.

Control Strategies in Multigroup Models: The Case of the Star Network Topology.

In this paper, we propose control strategies for multigroup epidemic models. We use compartmental [Formula: see text] models to study the dynamics of n host groups sharing the same source of infection in addition to the transmission among members of the same group. In particular, we consider a model for infectious diseases with free-living pathogens in the environment and a metapopulation model with a central patch. We give the detailed derivation of the target reproduction number under three public health interventions and provide the corresponding biological insights. Moreover, using the next-generation approach, we calculate the basic reproduction numbers associated with subsystems of our models and determine algebraic connections to the target reproduction number of the complete model. The analysis presented here illustrates that understanding the topological structure of the infection process and partitioning it into simple cycles is useful to design and evaluate the control strategies.