A probabilistic approach for the study of epidemiological dynamics of infectious diseases: Basic model and properties.

The dynamics of epidemiological phenomena associated to infectious diseases have long been modelled taking different approaches. However, recent pandemic events exposed many areas of opportunity to improve the existing models. We develop a stochastic model based on the idea that transitions between epidemiological stages are alike sampling processes that may involve more than one subset of the population or may be mostly dependent on time intervals defined by pathological or clinical criteria. We apply the model to simulate epidemics, analyse the final distribution of the case fatality ratio, and define a basic reproductive number to determine the existence of a probabilistic phase transition for the dynamics. The resulting modelling scheme is robust, easy to implement, and can readily lend itself for extensions aimed at answering questions that emerge from close examination of data trends, such as those emerging from the COVID-19 pandemic, and other infectious diseases.

Collateral Effects of Insecticide-Treated Nets on Human and Environmental Safety in an Epidemiological Model for Malaria with Human Risk Perception.

Malaria remains a major health problem in many parts of the world, including Sub-Saharan Africa. Insecticide-treated nets, in combination with other control measures, have been effective in reducing malaria incidence over the past two decades. Nevertheless, there are concerns about improper handling and misuse of nets, producing possible health effects from intoxication and collateral environmental damage. The latter is caused, for instance, from artisanal fishing. We formulate a model of impulsive differential equations to describe the interplay between malaria dynamics, human intoxication, and ecosystem damage; affected by human awareness to these risks and levels of net usage. Our results show that an increase in mosquito net coverage reduces malaria prevalence and increases human intoxications. In addition, a high net coverage significantly reduces the risk perception to disease, naturally increases the awareness for intoxications from net handling, and scarcely increases the risk perception to collateral damage from net fishing. According to our model, campaigns aiming at reducing disease prevalence or intoxications are much more successful than those creating awareness to ecosystem damage. Furthermore, we can observe from our results that introducing closed fishing periods reduces environmental damage more significantly than strategies directed towards increasing the risk perception for net fishing.

epidWaves: A code for fitting multi-wave epidemic models.

The COVID-19 pandemic has given rise to a great demand for computational models capable of describing and inferring the evolution of an epidemic outbreak in the short term. In this sense, we introduce epidWaves, a package that provides a framework for fitting multi-wave epidemic models to data from actual outbreaks of COVID-19 and other infectious diseases.

ARBO: Arbovirus modeling and uncertainty quantification toolbox.

The ongoing pandemic of COVID-19 has highlighted the importance of mathematical tools to understand and predict outbreaks of severe infectious diseases, including arboviruses such as Zika. To this end, we introduce ARBO, a package for simulation and analysis of arbovirus nonlinear dynamics. The implementation follows a minimalist style, and is intuitive and extensible to many settings of vector-borne disease outbreaks. This paper outlines the main tools that compose ARBO, discusses how recent research works about the Brazilian Zika outbreak have explored the package's capabilities, and describes its potential impact for future works on mathematical epidemiology.

How disease risk awareness modulates transmission: coupling infectious disease models with behavioural dynamics.

Epidemiological models often assume that individuals do not change their behaviour or that those aspects are implicitly incorporated in parameters in the models. Typically, these assumptions are included in the contact rate between infectious and susceptible individuals. However, adaptive behaviours are expected to emerge and play an important role in the transmission dynamics across populations. Here, we propose a theoretical framework to couple transmission dynamics with behavioural dynamics due to infection awareness. We modelled the dynamics of social behaviour using a game theory framework, which is then coupled with an epidemiological model that captures the disease dynamics by assuming that individuals are aware of the actual epidemiological state to reduce their contacts. Results from the mechanistic model show that as individuals increase their awareness, the steady-state value of the final fraction of infected individuals in a susceptible-infected-susceptible (SIS) model decreases. We also incorporate theoretical contact networks, having the awareness parameter dependent on global or local contacts. Results show that even when individuals increase their awareness of the disease, the spatial structure itself defines the steady state.

An epidemic model for COVID-19 transmission in Argentina: Exploration of the alternating quarantine and massive testing strategies.

The COVID-19 pandemic has challenged authorities at different levels of government administration around the globe. When faced with diseases of this severity, it is useful for the authorities to have prediction tools to estimate in advance the impact on the health system as well as the human, material, and economic resources that will be necessary. In this paper, we construct an extended Susceptible-Exposed-Infected-Recovered model that incorporates the social structure of Mar del Plata, the 4°most inhabited city in Argentina and head of the Municipality of General Pueyrredón. Moreover, we consider detailed partitions of infected individuals according to the illness severity, as well as data of local health resources, to bring predictions closer to the local reality. Tuning the corresponding epidemic parameters for COVID-19, we study an alternating quarantine strategy: a part of the population can circulate without restrictions at any time, while the rest is equally divided into two groups and goes on successive periods of normal activity and lockdown, each one with a duration of τ days. We also implement a random testing strategy with a threshold over the population. We found that τ=7 is a good choice for the quarantine strategy since it reduces the infected population and, conveniently, it suits a weekly schedule. Focusing on the health system, projecting from the situation as of September 30, we foresee a difficulty to avoid saturation of the available ICU, given the extremely low levels of mobility that would be required. In the worst case, our model estimates that four thousand deaths would occur, of which 30% could be avoided with proper medical attention. Nonetheless, we found that aggressive testing would allow an increase in the percentage of people that can circulate without restrictions, and the medical facilities to deal with the additional critical patients would be relatively low.

Assessing the effects of diagnostic sensitivity on schistosomiasis dynamics.

Schistosomiasis is a parasite infection that affects millions of people around the world. It is endemic in 13 different states in Brazil and responsible for increasing morbidity in the population. One of its main characteristics is a heterogeneous distribution of worm burden in the human population, which makes the diagnosis difficult. We aimed to investigate how the sensitivity of the diagnostic method may contribute to successful control interventions against infections in a population. In order to do that, we present an ordinary differential equations model that considers three levels of worm burden in the human population, a snail population, and a miracidium reservoir. Through a steady-state analysis and its local stability, we show how this worm-burden heterogeneity can be responsible for the persistence of infection, especially due to reinfection in the highest level of worm burden. The analysis highlights sensitive diagnosis, besides treatment and sanitary improvements, as a key factor for schistosomiasis transmission control.

Lessons from being challenged by COVID-19.

We present results of different approaches to model the evolution of the COVID-19 epidemic in Argentina, with a special focus on the megacity conformed by the city of Buenos Aires and its metropolitan area, including a total of 41 districts with over 13 million inhabitants. We first highlight the relevance of interpreting the early stage of the epidemic in light of incoming infectious travelers from abroad. Next, we critically evaluate certain proposed solutions to contain the epidemic based on instantaneous modifications of the reproductive number. Finally, we build increasingly complex and realistic models, ranging from simple homogeneous models used to estimate local reproduction numbers, to fully coupled inhomogeneous (deterministic or stochastic) models incorporating mobility estimates from cell phone location data. The models are capable of producing forecasts highly consistent with the official number of cases with minimal parameter fitting and fine-tuning. We discuss the strengths and limitations of the proposed models, focusing on the validity of different necessary first approximations, and caution future modeling efforts to exercise great care in the interpretation of long-term forecasts, and in the adoption of non-pharmaceutical interventions backed by numerical simulations.

Individual-based modelling and control of bovine brucellosis.

We present a theoretical approach to control bovine brucellosis. We have used individual-based modelling, which is a network-type alternative to compartmental models. Our model thus considers heterogeneous populations, and spatial aspects such as migration among herds and control actions described as pulse interventions are also easily implemented. We show that individual-based modelling reproduces the mean field behaviour of an equivalent compartmental model. Details of this process, as well as flowcharts, are provided to facilitate the reproduction of the presented results. We further investigate three numerical examples using real parameters of herds in the São Paulo state of Brazil, in scenarios which explore eradication, continuous and pulsed vaccination and meta-population effects. The obtained results are in good agreement with the expected behaviour of this disease, which ultimately showcases the effectiveness of our theory.

Modeling the epidemiological impact of a preventive behavioral group. / Modelización del impacto epidemiológico de la existencia de un grupo conductual preventivo.

Concerning health, experience indicates that in all human groups a percentage of individuals behave conscientiously when facing contagious diseases. This aware group responds with activities to prevent disease transmission and to minimize risk. In contrast, other individuals tend to behave with less engagement except in catastrophic cases. Assuming the theoretical and methodological framework provided by mathematical epidemiology, and based on a Susceptible – Infectious - Recovered (SIR) model, we evaluated the factors of size and intensity of the behaviours in the aware group to determine the basic reproduction number. This number is the reduction in the number of secondary cases that would be produced by a first infectious individual. Additionally, we calculated the total and individual prevented prevalence for each aware individual for different parametric scenarios. Lastly, we suggest that distance and interpersonal contact should be included as factors associated to the potential of transmission.

En lo que concierne a salud, la experiencia indica que en toda población humana existe un porcentaje de individuos que se comporta en forma consciente ante la presencia de enfermedades infectocontagiosas. Esto implica que existen grupos con una orientación hacia la prevención en sus actividades para atenuar el riego, mientras que en general la mayoría lo hace distraídamente. La excepción la constituyen los casos de orden catastrófico. Asumiendo el marco teórico y metodológico que otorga la epidemiología matemática, se evaluaron los factores tamaño e intensidad de la conducta del grupo cuidadoso en la determinación del número reproductivo básico, basándose en un modelo tipo SIR (susceptibles - infecciosos - recuperados). Es decir, se midió la reducción en la cantidad de casos secundarios que produciría un primer caso infeccioso. Junto con estos indicadores, se procedió a evaluar la prevalencia evitada total e individual por cada sujeto cuidadoso en diferentes escenarios paramétricos. Finalmente, se plantea la necesidad de integrar en futuros estudios la variable distancia y el contacto interpersonal como factores asociados al potencial de transmisión.

Modelización del impacto epidemiológico de la existencia de un grupo conductual preventivo / Modeling the epidemiological impact of a preventive behavioral group

En lo que concierne a salud, la experiencia indica que en toda población humana existe un porcentaje de individuos que se comporta en forma consciente ante la presencia de enfermedades infectocontagiosas. Esto implica que existen grupos con una orientación hacia la prevención en sus actividades para atenuar el riego, mientras que en general la mayoría lo hace distraídamente. La excepción la constituyen los casos de orden catastrófico. Asumiendo el marco teórico y metodológico que otorga la epidemiología matemática, se evaluaron los factores tamaño e intensidad de la conducta del grupo cuidadoso en la determinación del número reproductivo básico, basándose en un modelo tipo SIR (susceptibles - infecciosos - recuperados). Es decir, se midió la reducción en la cantidad de casos secundarios que produciría un primer caso infeccioso. Junto con estos indicadores, se procedió a evaluar la prevalencia evitada total e individual por cada sujeto cuidadoso en diferentes escenarios paramétricos. Finalmente, se plantea la necesidad de integrar en futuros estudios la variable distancia y el contacto interpersonal como factores asociados al potencial de transmisión.

Concerning health, experience indicates that in all human groups a percentage of individuals behave conscientiously when facing contagious diseases. This aware group responds with activities to prevent disease transmission and to minimize risk. In contrast, other individuals tend to behave with less engagement except in catastrophic cases. Assuming the theoretical and methodological framework provided by mathematical epidemiology, and based on a Susceptible ­ Infectious - Recovered (SIR) model, we evaluated the factors of size and intensity of the behaviours in the aware group to determine the basic reproduction number. This number is the reduction in the number of secondary cases that would be produced by a first infectious individual. Additionally, we calculated the total and individual prevented prevalence for each aware individual for different parametric scenarios. Lastly, we suggest that distance and interpersonal contact should be included as factors associated to the potential of transmission.

Simultaneous reconstruction of evolutionary history and epidemiological dynamics from viral sequences with the birth-death SIR model.

The evolution of RNA viruses, such as human immunodeficiency virus (HIV), hepatitis C virus and influenza virus, occurs so rapidly that the viruses' genomes contain information on past ecological dynamics. Hence, we develop a phylodynamic method that enables the joint estimation of epidemiological parameters and phylogenetic history. Based on a compartmental susceptible-infected-removed (SIR) model, this method provides separate information on incidence and prevalence of infections. Detailed information on the interaction of host population dynamics and evolutionary history can inform decisions on how to contain or entirely avoid disease outbreaks. We apply our birth-death SIR method to two viral datasets. First, five HIV type 1 clusters sampled in the UK between 1999 and 2003 are analysed. The estimated basic reproduction ratios range from 1.9 to 3.2 among the clusters. All clusters show a decline in the growth rate of the local epidemic in the middle or end of the 1990s. The analysis of a hepatitis C virus genotype 2c dataset shows that the local epidemic in the Córdoban city Cruz del Eje originated around 1906 (median), coinciding with an immigration wave from Europe to central Argentina that dates from 1880 to 1920. The estimated time of epidemic peak is around 1970.