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This paper is devoted to the study of optimal release strategies to control vector-borne diseases, such as dengue, Zika, chikungunya and malaria. Two techniques are considered: the sterile insect one (SIT), which consists in releasing sterilized males among wild vectors in order to perturb their reproduction, and the Wolbachia one (presently used mainly for mosquitoes), which consists in releasing vectors, that are infected with a bacterium limiting their vectorial capacity, in order to replace the wild population by one with reduced vectorial capacity. In each case, the time dynamics of the vector population is modeled by a system of ordinary differential equations in which the releases are represented by linear combinations of Dirac measures with positive coefficients determining their intensity. We introduce optimal control problems that we solve numerically using ad-hoc algorithms, based on writing first-order optimality conditions characterizing the best combination of Dirac measures. We then discuss the results obtained, focusing in particular on the complexity and efficiency of optimal controls and comparing the strategies obtained. Mathematical modeling can help testing a great number of scenarios that are potentially interesting in future interventions (even those that are orthogonal to the present strategies) but that would be hard, costly or even impossible to test in the field in present conditions., Competing Interests: Declarations Conflict of interest The authors have no conflict of interest to declare that are relevant to the content of this article., (© 2024. The Author(s).)

Setting global strategies and targets for disease prevention and control often involves mathematical models. Model structure is typically subject to intense scrutiny, such as confrontation with empirical data and alternative formulations, while a less frequently challenged aspect is the widely adopted reduction of parameters to their average values. Focusing on endemic diseases, we use a general transmission model to explain how mean field approximations decrease the estimated R0 from prevalence data, while threshold phenomena - such as the epidemic and reinfection thresholds - remain invariant. This results in an underestimation of the effort required to control disease, which may be particularly severe when the approximation inappropriately places transmission estimates below important thresholds. These concepts are widely applicable across endemic pathogen systems., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

The hypothesis that infection prevalence in a population correlates negatively with variance in the susceptibility of its individuals has support from experimental, field, and theoretical studies. However, its generality has never been formally demonstrated. Here we formulate an endemic SIS model with individual susceptibility distributed according to a discrete or continuous probability function to assess the generality of such hypothesis. We introduce an ordering among susceptibility distributions with the same mean, analogous to that considered in Katriel (J Math Biol 65:237-262, 2012) to order the attack rates in an epidemic SIR model with heterogeneity. It turns out that if one distribution dominates another in this order then it has greater variance and corresponds to a lower infection prevalence for R0 varying in a suitable maximal interval of the form ]1, R0*]. We show that in both the discrete and continuous frameworks R0* can be finite, so that the expected correlation among variance and prevalence does not always hold. For discrete distributions this fact is demonstrated analytically, and the proof introduces a constructive procedure to find ordered pairs for which R0* is arbitrarily close to 1. For continuous distributions our conclusion is based on numerical studies with the beta distribution. Finally, we present explicit partial orderings among discrete susceptibility distributions and among symmetric beta distributions which guarantee that R0* = +∞.

In this paper we address the persistence of a class of seasonally forced epidemiological models. We use an abstract theorem about persistence by Fonda. Five different examples of application are given.

Heterogeneity in susceptibility and infectivity is inherent to infectious disease transmission in nature. Here we are concerned with the formulation of mathematical models that capture the essence of heterogeneity while keeping a simple structure suitable of analytical treatment. We explore the consequences of host heterogeneity in the susceptibility to infection for epidemiological models for which immunity conferred by infection is partially protective, known as susceptible-infected-recovered-infected (SIRI) models. We analyze the impact of heterogeneity on disease prevalence and contrast the susceptibility profiles of the subpopulations at risk for primary infection and reinfection. We present a systematic study in the case of two frailty groups. We predict that the average rate of reinfection may be higher than the average rate of primary infection, which may seem paradoxical given that primary infection induces life-long partial protection. Infection generates a selection mechanism whereby fit individuals remain in S and frail individuals are transferred to R. If this effect is strong enough we have a scenario where, on average, the rate of reinfection is higher than the rate of primary infection even though each individual has a risk reduction following primary infection. This mechanism may explain high rates of tuberculosis reinfection recently reported. Finally, the enhanced benefits of vaccination strategies that target the high-risk groups are quantified.

In this paper we analyze the dynamics of two families of epidemiological models which correspond to transitions from the SIR (susceptible-infectious-resistant) to the SIS (susceptible-infectious-susceptible) frameworks. In these models we assume that the force of infection is a nonlinear function of density of infectious individuals, I. Conditions for the existence of backwards bifurcations, oscillations and Bogdanov-Takens points are given.