Epidemiological surveillance systems often provide data on specific characteristics of an infected population. For instance, sex, geographical location, socioeconomic level and age of the registered individuals. This allows us to study the population divided into groups. However, information on the dynamics of infected people classified by group is not usually exploited when analyzing the evolution of an epidemic. In this work, we propose a tool to analyze how the spread of an epidemic is heterogeneous among different population groups. Based on records of infected individuals we identify synchronicity and causality interactions among population groups. Describing this dynamics and which population groups are the first focus of infection is essential for decision makers. We represent time series by population group and their degree of similarity using a weighted graph, and we apply a community detection algorithm to partition this graph. Each community is composed of synchronized age groups. The direction of interaction among different communities is identified using sample cross-correlation in a domain that can indicate causality. This is illustrated by considering age groups and using datasets of COVID-19 in Jalisco, Mexico and influenza A(H1N1) in the USA. In both cases, the proposed methodology detected which age groups show synchronized behavior across time, and which age groups influence the subsequent appearance of epidemic outbreaks in other groups.

Epidemic severity indices that incorporate disease information are essential tools for decision-makers, as these indices allow the design and evaluation of possible control strategies in advance of implementation in susceptible populations. In spatially structured settings, indices that consider human mobility provide valuable information on the spread of infectious diseases and the potential impact of mobility restrictions during outbreaks. In this context, the final epidemic size in metapopulation models serves as an effective measure of outbreak severity in geographical terms. However, the existence and uniqueness of the solution to the corresponding equation have only been established in particular cases. In this study, we derived conditions that guarantee the existence and uniqueness of the solution to the final epidemic size equation in a SIR-type metapopulation model. We also conducted a sensitivity analysis in a two-region, unidirectional infection scenario, which allowed us to examine the effects of mobility between an infected region and a susceptible one. Our results indicate that, under relatively simple conditions, restricting mobility can help contain outbreaks. However, we also identified situations in which mobility is not detrimental and may even be beneficial. These findings provide a preliminary framework for assessing the appropriateness of mobility restrictions during infectious disease outbreaks in spatially structured regions.

This study presents a mathematical model of the transmission and spread of the Echinococcus granulosus parasite. The model incorporates host mobility, laws governing the dynamics of Echinococcosis transmission between hosts, and control and prevention measures. The basic reproductive number of the proposed model is calculated, and a sensitivity analysis is performed to identify the parameters that most influence the dynamics of transmission and spread of the disease among its hosts. The study evaluates two control strategies—dog deworming and sheep vaccination—based on their respective target reproductive numbers. The impact of these control and prevention measures is investigated through numerical simulations, which reveal that the dog deworming strategy consistently reduces infections in humans. In contrast, the sheep vaccination strategy demonstrates a more favorable scenario for disease eradication in both hosts. In addition, simulations show a close relationship between the early detection of the disease and the recovery of the patient.

Datasets often include geographical locations, making it essential to effectively capture the spatial relationships within such data. In particular, geographical data play a crucial role in studying the spread of epidemics across regions. Applying epidemiological models that account for spatial heterogeneity requires partitioning the study area into meaningful regions. This partition must be appropriately scaled—small enough to capture local dynamics yet large enough to ensure a sufficient population. Additionally, the number of regions should remain manageable to facilitate analysis. To generate partitions with any desired number of regions, we propose a community detection method for networks weighted by a relevant variable. Our approach leverages generalized modularity matrices and leading eigenvectors to create an initial partition. We include two algorithms to refine the partition by identifying sub-communities or forming supra-communities, enabling flexible adjustments to the desired number of regions. Each detected community corresponds to a geographically connected region. A key advantage of our methodology is its ability to capture intra-community heterogeneity by assigning a level of membership to each node, while also recognizing the hierarchical relevance of their connections. We constructed networks for the states of Guanajuato and Jalisco in Mexico, weighted using COVID-19 incidence data. Our method outperforms Leiden, Louvain, Combo, and two variants of Spectral Clustering. For both networks, we identified key nodes within each community based on the level of membership assigned to the municipalities. The geographical regions identified by our method in each state closely align with the official administrative regions defined by the respective governments.

Vaccination and prevention are commonly employed strategies in disease control. However, the influence of sexual preferences on the spread of sexually transmitted infections (STIs) remains underexplored due to the lack of adequate mathematical models. This study addresses this gap by evaluating the impact of sexual preferences on STIs transmission and providing a tool for implementing more effective control policies. We develop two models that describe STIs transmission dynamics in populations with exclusively same-sex or opposite-sex contacts. Later, we introduce a third, more general model that integrates both scenarios. Sensitivity analysis reveals that prevention often outperforms vaccination in effectiveness. Our findings highlight the critical need for tailoring control policies. In the cases of sexual preferences, it is paramount to pay attention to the group with the highest local basic reproduction number, underscoring the importance of customized strategies in disease management.

Many infections are transmitted by direct contacts. Usually, one single direct contact is needed to transmit the required minimum infectious load. Most models describe contagions by single contacts using a term of the type mass action law. However, modelling infections that are transmitted after the susceptible individual had contact with several sources of infection requires more than mass action law terms. We call additive multiple contacts those that do not produce infection by themselves, but can produce infection if they happen simultaneously. We are interested in understanding the role played by R0 missing the mark in infections in which the minimum infectious load is reached not only by single contacts but also by additive multiple contacts. We propose different mathematical models describing not only infections by one single contact but also by additive multiple contacts. We show that all models have the same value of R0, but correspond to different epidemiological mechanisms. Two models show contagions by additive multiple contacts and a third one shows reduction of infections by some saturation process which is not captured by R0. This shows that trying to control the epidemics by controlling R0 could be unsufficient or, in some cases, waste resources.

An epidemiological model is proposed to analyze the COVID-19 epidemics when control interventions are being applied to reduce the speed of the disease. The analyzed model includes parameters that describe control strategies such as behavioral changes of susceptible individuals to reduce the transmission of the disease, rates of diagnosis of the infectious individuals, and other control measures as cleaning and disinfection of contaminated environments. The proposed model is calibrated using Bayesian statistics and the official cumulative confirmed cases for COVID-19 in Mexico. We show which public health strategies contribute the most to the variation of $R_0$. A central result is the fact that the peak of the epidemics can drastically be changed depending on the time when the control strategies are introduced

El número básico de reproducción, en la modelización de enfermedades infecciosas es un valor fundamental para diseñar estrategias de control. Calcular el valor de R0 puede ser difícil en algunas situaciones debido a la complejidad del modelo. Esta complejidad a menudo obstaculiza el cálculo explícito de R0 y dificulta la comprensión de cómo diferentes poblaciones y parámetros influyen en su valor. Trabajos recientes han propuesto el número de reproducción objetivo como alternativa al R0 (Shuai et al., 2013). El número de reproducción objetivo muestra cómo, a través del análisis de algunos de los subsistemas que describen el comportamiento de una enfermedad infecciosa, es posible ejercer control sobre todo el sistema. El número de reproducción objetivo puede proporcionar un marco para la toma de decisiones en salud pública. En este trabajo lo aplicamos a dos modelos: un modelo con vacunación incompleta y un modelo para la leptospirosis. Los modelos presentados exhiben dos características fundamentales del número de reproducción objetivo. En primer lugar, la simplicidad de su expresión en comparación con el número de reproducción básico. En segundo lugar, su comportamiento análogo al R0 en 1.

The aim of this paper is to investigate the effect of drastic behavioral changes on the dynamics of infectious diseases. An SIS model with two classes of individuals with different susceptibilities is analyzed. It focuses in a transition function between both classes of susceptible individuals depending on the density of the infected population. A classification of all the possible bifurcation diagrams that the model can present is done. Specifically, some conditions for the simultaneous existence of backward bifurcation and multiple endemic states are shown.

Se presenta un modelo matemático que consiste en un sistema de dos ecuaciones diferenciales ordinarias (EDO), que describen la interacción competición entre cáncer, sistema inmune y una terapia que para el presente artículo se asume como terapia fotodinámica que usa un nanocompuesto a base de TiO2 modificado [Basante et. al. (2016),(2017)]. Se analizan las consecuencias del tratamiento en base al análisis de estabilidad del sistema dinámico, encontrando que es posible encontrar existen condiciones adecuadas para la eliminación del cáncer.

A simple mathematical model is presented that consists of a system of two ordinary differential equations ( ODEs), applicable to the interaction between cancer cells, the immune system and a photodynamic therapy based on the previous observations of the Physicochemical Research Group of Bio and Nanomaterials of the Universidad del Valle (Basante et al., 2016, Basante, 2017) where an exponential effect is assumed. The consequences of the treatment are analyzed based on the stability analysis of the dynamic system, finding that it is possible to find adequate conditions for the elimination of cancer.

Persistent infection with human papillomavirus (HPV) is the main cause of cervical cancer. Current HPV vaccines protect against both HPV‐16 and ‐18, which are known to cause approximately 70% of cervical cancer cases worldwide. These vaccines have shown to be highly effective in preventing infection by their targeted types. However, there is a broad diversity of HPV types not targeted by the vaccines, and there is controversy about a possible increase in the prevalence of these non‐targeted types after a vaccination program. Here, we propose a within‐host metapopulation model to study the possibility of vaccine‐induced type replacement for oncogenic types. It is generally believed that the theoretical possibility of type replacement strongly depends on the existence of natural type competition mechanisms. Nevertheless, our results suggest that type replacement is viable at the within‐host level if the degree of cross‐protection induced by the vaccine is low, even if there is no underlying competition among HPV types. Consequently, the impact of current HPV vaccines at both the immunological and epidemiological levels rely upon the level of cross‐protection.

In this paper we develop a compartmental epidemic model to study the transmission dynamics of the COVID-19 epidemic outbreak, with Mexico as a practical example. In particular, we evaluate the theoretical impact of plausible control interventions such as home quarantine, social distancing, cautious behavior and other self-imposed measures. We also investigate the impact of environmental cleaning and disinfection, and government-imposed isolation of infected individuals. We use a Bayesian approach and officially published data to estimate some of the model parameters, including the basic reproduction number. Our findings suggest that social distancing and quarantine are the winning strategies to reduce the impact of the outbreak. Environmental cleaning can also be relevant, but its cost and effort required to bring the maximum of the outbreak under control indicate that its cost-efficacy is low.

This paper aims to evaluate the potential cost-effectiveness of healthcare interventions against human papillomavirus (HPV). For this, we consider a two-sex epidemic model for the transmission dynamics of HPV which includes screening, vaccination of adolescent boys and girls, and vaccination of sexually active adults. We first propose public health policies using constant control parameters and develop a cost-effectiveness analysis (CEA) to identify which intervention delivers the best effectiveness for the money invested. Secondly, we consider time-dependent control parameters and formulate an optimal control problem to obtain time-dependent versions of the interventions. As in the case of constant control parameters, we perform a CEA to investigate the cost-effectiveness of the time-dependent control interventions. Our findings suggest that females' vaccination, including adolescent girls and adult women, is the most cost-effective strategy. We also compare constant against the time-dependent healthcare interventions which are optimal in the sense that they minimize the objective functional of the optimal control problem. The results indicate that time-dependent controls are not always more cost-effective than constant controls.

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.

In this paper, we study general recovery functions and treatment in the dynamics of an S I S model for sexually transmitted infections with nonzero partnership length. It is shown how partnership dynamics influences the predicted prevalence at the steady state and the basic reproduction number. Sobol's indices are used to evaluate the contribution of model parameters to the overall variance of R 0 . The recovery functions studied here take into account that society's capacity to provide treatment is limited when the number of infected individuals is large. Bifurcation analysis is used to establish a relationship between an alert level of prevalence and the minimum recovery time that guarantees the eradication of the disease. We also show that a backward bifurcation can occur when there are delays in the treatment of infected individuals.

We investigate the optimal vaccination and screening strategies to minimize human papillomavirus (HPV) associated morbidity and the interventions cost. We propose a two-sex compartmental model of HPV-infection with time-dependent controls (vaccination of adolescents, adults, and screening) which can act simultaneously. We formulate optimal control problems complementing our model with two different objective functionals. The first functional corresponds to the protection of the vulnerable group and the control problem consists of minimizing the cumulative level of infected females over a fixed time interval. The second functional aims to eliminate the infection, and, thus, the control problem consists of minimizing the total prevalence at the end of the time interval. We prove the existence of solutions for the control problems, characterize the optimal controls, and carry out numerical simulations using various initial conditions. The results and properties and drawbacks of the model are discussed.

Control of sexually transmitted infections (STIs) poses important challenges to public health authorities. Obstacles for STIs’ control include low priority in public health programs and disease transmission mechanisms. This work uses a compartmental pair model to explore different public health strategies on the evolution of STIs. Optimal control and feedback control are used to model realistic strategies for reducing the prevalence of these infections. Feedback control is proposed to model the reaction of public health authorities relative to an alert level. Optimal control is used to model the optimization of available resources for implementing strategies. Numerical simulations are performed using trichomoniasis, gonorrhea, chlamydia and human papillomavirus (HPV) as study cases. HPV is non-curable, and it is analyzed only under transmission control such as condom promotion campaigns. Trichomoniasis, gonorrhea and chlamydia are curable STIs that are modeled here additionally under treatment control. Increased cost-effectiveness ratio is employed as a criterion to measure control strategies performance. The features and drawbacks of control strategies under the pair formation process are discussed.

In this work we introduce a family of operators called discrete advection–reaction operators. These operators are important on their own right and can be used to efficiently analyze the asymptotic behavior of a finite differences discretization of variable coefficient advection–reaction–diffusion partial differential equations. They consists of linear bidimensional discrete dynamical systems defined in the space of real sequences. We calculate explicitly their asymptotic evolution by means of a matrix representation. Finally, we include the special case of matrices with different eigenvalues to show the connection between the operators evolution and interpolation theory.

In this paper, we propose a model describing the interaction between two species: a plant population that gets pollinated by an insect population. We assume the plant population is divided into two groups: the first group in mutualistic relationship with the insect and the second group attracting the insects while deceiving them and not delivering any reward. In addition, we assume that the insect population reduces the number of visits to the plants after several unsuccessful visits. We are interested in the conditions for the coexistence of both species, especially in the appearance of damped or sustained oscillations. We focus the analysis on the parameters that measure the balance among deceit, the benefit that the insect gets from the plant, and the learning by the pollinators. We are especially interested in analyzing the effect of learning by the insect population due to unsuccessfully visiting the deceiving plants.