Effects of treatment and prevalence-dependent recruitment on the dynamics of a fatal disease

Abstract

This paper studies models for the sexual transmission of IllV f AIDS that incorporate changes in behavior as well as the effects associated with IDV treatment. The recruitment rate into the core is assumed to be a function of the prevalence of the disease within the core and it may trigger the existence of periodic solutions through Hopf bifurcations, provided that there is at least a weak demographic interaction with the non-core. The recruitment function is set up for two cases: dependence on the total proportion of infectious individuals and dependence only on the proportion of treated infectious indi~duals. In the general model, numerical evidence suggests that both cases may produce periodic solutions when the perception of risk of joining the core group is sufficiently high. Two limiting cases are also studied: when the growth rate of the core and non core groups are essentially the same, and when treatment has no effect on the transmission rate of infected individuals.

Statistical physics of vaccination

“…As noted in [80] "the combination of a long incubation period, with difficult and costly treatment, and the lack of a vaccine, have made instilling preventive behavior through the dissemination of information on risky behavior with respect to sexual or intra-venous drug use the main control strategy, especially in poor resource settings." In this situation, where reliable data on individuals' responses to the spread of epidemics were mostly missing, mathematical modeling played a pioneering role in the understanding of the effects of behavior change on HIV dynamics, including the effect of prevalence-dependent switching to lower risk groups, reducing contact rates after screening or treatment, prevalence-dependent sexual mixing patterns, including the warning that availability of effective therapies and protective vaccine might increases disease severity by raising at-risk behavior [111,[482][483][484][485][486][487]. Though most among the cited papers, which were pioneers in an endless list, considered phenomenological models, there have been also instances of more structured approaches to behavior, such as [488,489].…”

Mathematical models for the study of HIV spread and control amongst men who have sex with men

“…The combined effects on epidemic projections of ART and education [75], or host genetic differences [18], or both [76] have also been explored. The impact of an increase in unprotected sex as a consequence of ART has been repeatedly highlighted since early in the epidemic [32,[77][78][79]. New technologies for HIV prevention and control have been hypothetically evaluated before they even become available [21,22,65,[80][81][82][83].…”

SIS and SIR Epidemic Models Under Virtual Dispersal

“…Specifically, the study of the impact of patch residence times (modeled by a matrix of constants) on disease dynamics within a Susceptible-Infected-Susceptible ( SIS ) framework is carried out first, under the philosophy found in [10, 11, 13, 15, 17, 21, 34, 48]. Individuals move across patches as a function of their assessment of relative levels of infection in each area (studies using alternative classical approaches are found in [15, 16, 35, 69]). The concept of modeling disease dynamics where the population is structured into several communities goes back to Rushton and Mautner [63].…”