Modeling the transmission dynamics and the impact of the control interventions for the COVID-19 epidemic outbreak.

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.

Modeling Public Health Campaigns for Sexually Transmitted Infections via Optimal and Feedback Control.

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.

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.

The role of behavioral changes and prompt treatment in the control of STIs.

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.

Vector Preference Annihilates Backward Bifurcation and Reduces Endemicity.

We propose and analyze a mathematical model of a vector-borne disease that includes vector feeding preference for carrier hosts and intrinsic incubation in hosts. Analysis of the model reveals the following novel results. We show theoretically and numerically that vector feeding preference for carrier hosts plays an important role for the existence of both the endemic equilibria and backward bifurcation when the basic reproduction number [Formula: see text] is less than one. Moreover, by increasing the vector feeding preference value, backward bifurcation is eliminated and endemic equilibria for hosts and vectors are diminished. Therefore, the vector protects itself and this benefits the host. As an example of these phenomena, we present a case of Andean cutaneous leishmaniasis in Peru. We use parameter values from previous studies, primarily from Peru to introduce bifurcation diagrams and compute global sensitivity of [Formula: see text] in order to quantify and understand the effects of the important parameters of our model. Global sensitivity analysis via partial rank correlation coefficient shows that [Formula: see text] is highly sensitive to both sandflies feeding preference and mortality rate of sandflies.

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.

Deceptive pollination and insects' learning: a delicate balance.

In this paper we propose and discuss a simple two-dimensional model describing the interaction between two species: a plant population that gets pollinated by an insect population. The plants attract the insects deceiving them and not delivering any reward. We are interested in analysing the effect of learning by the insect population due to unsuccessfully visiting the deceiving plants. We are especially interested in three elements: conditions for the simultaneous coexistence of both species, their extinction as a function of the biological cost of the deceptiveness for the pollinator, and the appearance of oscillations in the dynamics. We also look for conditions under which plants would be better off by switching to different strategies, in particular, we look for conditions for the existence and stability of the equilibria of the corresponding differential equations system, and the conditions for the existence of periodic solutions.

Variation in the outcome of population interactions: bifurcations and catastrophes.

The nature of the association between two species may vary depending on population abundances, age or size of individuals, or environmental conditions. Interactions may switch between beneficial and detrimental depending on the net balance of costs and benefits involved for each species. We study the repercussion of the ecological setting on the outcomes of conditional or variable interactions by means of a model that incorporates density-dependent interaction coefficients; that is, interaction alpha-functions. These characterize the responsiveness and sensitivity of the association to changes in partner's abundance, and can take positive and negative values. Variable outcomes - and transitions between them - are categorized as homeo- or allo-environmental, that is, occurring under the same ecological setting, or not, respectively. Bifurcation analyses show that these dynamics are moulded by ecological factors that are: intrinsic to the nature of the association (concerning the sensitivity of the interaction), and extrinsic to the association itself (the quality of the environment referred to each species alone). The influence of these factors may be conflicting; consequently, the dynamics involve catastrophic events. In a facultative variable association, stable coexistence is expected when environmental conditions are adverse; otherwise, the exclusion of one species is the likely outcome. Remarkable situations as the switching of victim-exploiter roles illustrate the theoretical perspective.