Silvia Martorano Raimundo

A Comparative Analysis of the Relative Efficacy of Vector-Control Strategies Against Dengue Fever

Dengue is considered one of the most important vector-borne infection, affecting almost half of the world population with 50 to 100 million cases every year. In this paper, we present one of the simplest models that can encapsulate all the important variables related to vector control of dengue fever. The model considers the human population, the adult mosquito population and the population of immature stages, which includes eggs, larvae and pupae. The model also considers the vertical transmission of dengue in the mosquitoes and the seasonal variation in the mosquito population. From this basic model describing the dynamics of dengue infection, we deduce thresholds for avoiding the introduction of the disease and for the elimination of the disease. In particular, we deduce a Basic Reproduction Number for dengue that includes parameters related to the immature stages of the mosquito. By neglecting seasonal variation, we calculate the equilibrium values of the model’s variables. We also present a sensitivity analysis of the impact of four vector-control strategies on the Basic Reproduction Number, on the Force of Infection and on the human prevalence of dengue. Each of the strategies was studied separately from the others. The analysis presented allows us to conclude that of the available vector control strategies, adulticide application is the most effective, followed by the reduction of the exposure to mosquito bites, locating and destroying breeding places and, finally, larvicides. Current vector-control methods are concentrated on mechanical destruction of mosquitoes’ breeding places. Our results suggest that reducing the contact between vector and hosts (biting rates) is as efficient as the logistically difficult but very efficient adult mosquito’s control.

An approach to estimating the transmission coefficients for AIDS and for tuberculosis using mathematical models

A mathematical model is presented to simulate the interaction between Human Immunodeficiency Virus (HIV) and Mycobacterium tuberculosis (MTB) infections in a closed environment. The dynamics is formulated through a compartmental system of non-linear ordinary differential equations. The stability of the trivial equilibrium point or absence of infections and the endemic basins are analyzed based on the threshold values for the HIV and MTB transmission coefficients. In order to deal with the estimation of the transmission coefficients of HIV and MTB infections we consider the incarcerated individuals in the Female Penitentiary of São Paulo State, Brazil.

Modeling the interaction between aids and tuberculosis

A deterministic model is proposed for the study of the dynamics of acquired immunodeficiency syndrome (AIDS) and tuberculosis (TB) co-infection. The model is comprised by a set of sixteen ordinary differential equations representing different states of both diseases, and it is intended to provide a theretical framework for the study of the interaction between both infections. Numerical simulations of the model resulted in three striking outcomes: first, the pathogenicity of Human Immunodeficiency Virus (HIV) is enhanced by the presence of TB, and vice-versa; second, the prevalence of AIDS is higher in the presence of TB; and third, relative risk analysis demonstrated a much stronger influence of AIDS on TB than the other way around.

THE ATTRACTING BASINS AND THE ASSESSMENT OF THE TRANSMISSION COEFFICIENTS FOR HIV AND M. TUBERCULOSIS INFECTIONS AMONG WOMEN INMATES

It has been observed that in many cases one infection can partially protect against another infection or it may lead to a co-infection. For instance, the interaction between infections with different strains, like dengue and malaria or tuberculosis and lepra, induces cross immunity. On the other hand, individuals infected with HIV are much more susceptible to other infections, for instance, tuberculosis. We propose a compartmental model to describe the transmission of AIDS and tuberculosis in a closed community as an example of one infection activating the other one. When studying the dynamics of the interactions we obtain basins of attraction where one infection prevails over the other one and where both infections coalesce. Furthermore, we are taking into account an adaptation of the model in order to assess the transmission coefficients for HIV and Mycobacterium tuberculosis infections among women inmates.

Transmission of Tuberculosis with Exogenous Re-infection and Endogenous Reactivation

A theoretical framework to assess the transmission dynamics of Tuberculosis (TB) is developed. Once infected with Mycobacterium tuberculosis, individuals can either develop active TB or remain infected for the rest of their life unless endogenous reactivation or exogenous re-infection occurs. The effects of vaccination and treatment of active TB cases suggest that even if these control strategies could have a significant effect on reducing TB incidence, the exogenous re-infection and the endogenous reactivation, mainly due to HIV infection, will still increase the incidence of TB.

Assessing the effects of multiple infections and long latency in the dynamics of tuberculosis

In order to achieve a better understanding of multiple infections and long latency in the dynamics of Mycobacterium tuberculosis infection, we analyze a simple model. Since backward bifurcation is well documented in the literature with respect to the model we are considering, our aim is to illustrate this behavior in terms of the range of variations of the models parameters. We show that backward bifurcation disappears (and forward bifurcation occurs) if: (a) the latent period is shortened below a critical value; and (b) the rates of super-infection and re-infection are decreased. This result shows that among immunosuppressed individuals, super-infection and/or changes in the latent period could act to facilitate the onset of tuberculosis. When we decrease the incubation period below the critical value, we obtain the curve of the incidence of tuberculosis following forward bifurcation; however, this curve envelops that obtained from the backward bifurcation diagram.

A continuous function model for the age-related force of infection

Serological data of measles and rubella from seven non-vaccinated communities were fitted, as related to age, to a sigmoid model. This provided a continuous function which allowed the estimation of the age-related force of infection function. Epidemiological parameters, such as the average age at infection, the critical proportion to vaccinate in order to eradicate the infection, the basic reproductive rate and the optimum age to vaccinate the susceptible population, were derived from the estimated force of infection. The results were checked through numerical simulation of a compartmental model, applying the parameters estimated from the proposed analysis. The model has shown a good fitting accuracy and a good retrieving capacity of the original data.

Modelling the effects of temporary immune protection and vaccination against infectious diseases

In this paper, we develop a mathematical model to describe the dynamics of reinfection under the assumption that immune protection may wane over time. As a disease control strategy a schedule of primary and secondary (booster) vaccination is studied, with vaccine induced immunity declining over time. A distinction is made between infection in immunological naive individuals (primary infection) and infection in individuals whose immune system has been primed by vaccination or infection (reinfection). Using the model we analyze the association between prevalence of infection and immunity, induced either by infection or by vaccine. The model shows that eradication depends on vaccination coverage as well as on vaccine efficacy.

Modeling the emergence of HIV-1 drug resistance resulting from antiretroviral therapy: Insights from theoretical and numerical studies

The use of antiretroviral therapy has proven to be remarkably effective in controlling the progression of human immunodeficiency virus (HIV) infection and prolonging patients survival. Therapy however may fail and therefore these benefits can be compromised by the emergence of HIV strains that are resistant to the therapy. In view of these facts, the question of finding the reason for which drug-resistant strains emerge during therapy has become a worldwide problem of great interest. This paper presents a deterministic HIV-1 model to examine the mechanisms underlying the emergence of drug-resistance during therapy. The aim of this study is to determine whether, and how fast, antiretroviral therapy may determine the emergence of drug resistance by calculating the basic reproductive numbers. The existence, feasibility and local stability of the equilibriums are also analyzed. By performing numerical simulations we show that Hopf bifurcation may occur. The model suggests that the individuals with drug-resistant infection may play an important role in the epidemic of HIV.

Equilibrium Analysis of a Yellow Fever Dynamical Model with Vaccination

We propose an equilibrium analysis of a dynamical model of yellow fever transmission in the presence of a vaccine. The model considers both human and vector populations. We found thresholds parameters that affect the development of the disease and the infectious status of the human population in the presence of a vaccine whose protection may wane over time. In particular, we derived a threshold vaccination rate, above which the disease would be eradicated from the human population. We show that if the mortality rate of the mosquitoes is greater than a given threshold, then the disease is naturally (without intervention) eradicated from the population. In contrast, if the mortality rate of the mosquitoes is less than that threshold, then the disease is eradicated from the populations only when the growing rate of humans is less than another threshold; otherwise, the disease is eradicated only if the reproduction number of the infection after vaccination is less than 1. When this reproduction number is greater than 1, the disease will be eradicated from the human population if the vaccination rate is greater than a given threshold; otherwise, the disease will establish itself among humans, reaching a stable endemic equilibrium. The analysis presented in this paper can be useful, both to the better understanding of the disease dynamics and also for the planning of vaccination strategies.