Individuals in this phase are called exposed, that is, MTB-positive persons
Individuals in this phase are called exposed, that is, MTB-positive persons. The transmission coefficientdepends among a multitude of factors on the contacts with infectious particles and duration of contact. immunodeficiency virus). They can also be transmitted indirectly by vectors (as in dengue) and intermediate hosts (as in schistosomiasis). According to the natural history of diseases, an incubation period followed by an infectious period has to be considered a common characteristic. Numerous viral infections confer long-lasting immunity after their infectious periods, mainly because of immunological memory [1]. However, in many bacterial infections, antigenically more complex than viruses, the acquisition of acquired immunity following infection is neither so complete nor confers long-lasting immunity. Hence, in most viral infections, a single infection is sufficient to stimulate the immune system and elicit a lifelong response, while multiple infections can occur in diseases caused by bacteria. The simplest quantitative description of the transmission of infections is the mass action law; that is, the likelihood of an infectious event (infection) is proportional to the densities of Rabbit polyclonal to LDLRAD3 susceptible and infectious individuals. Essentially, this law oversimplifies the Pamapimod (R-1503) acquisition of infection by susceptibles from micro-organisms excreted by infectious individuals into the environment (aerial transmission), or present in the epithelia (infection by physical contact) or the blood (transmission by sexual contact or transfusion) of infectious individuals. In this paper we deal with the transmission dynamics of tuberculosis. Tuberculosis (TB) is caused byMycobacterium tuberculosis(MTB), which is transmitted by respiratory contact. This presents two routes for the progression to Pamapimod (R-1503) disease: primary progression (the disease develops soon after infection) or endogenous reactivation (the disease can develop many years after infection). After primary infection, progressive TB may develop either as a continuation of primary infection (fast TB) or as endogenous reactivation (slow TB) of a latent focus. In some patients, however, disease may also result from exogenous reinfection by a second strain of MTB. There are reports of exogenous reinfection in the literature in both immunosuppressed and immunocompetent individuals [2]. Martcheva and Thieme [3] called the exogenous reinfection ‘super-infection’. To what extent simultaneous infections or reinfections with MTB are responsible for primary, reactivation or relapse TB has been the subject of controversy. However, cases of reinfection by a second MTB strain and occasional infection with more than one strain have been documented. Shamputaet al.[4] and Bradenet al.[5] investigated that in areas where the incidence of TB is high Pamapimod (R-1503) and exposures to multiple strains may occur. Although the degree of immunity to a second MTB infection is not known, simultaneous infection by multiple strains or reinfection by a second MTB strain may be responsible for a portion of TB cases. A very special feature of TB is that the natural history of the disease encompasses a long and variable period of incubation. This is why a super-infection can occur during this period, overcoming the immune response and resulting in the onset of disease. When mathematical modelling encompasses the natural history of disease (the onset of disease after a long period since the first infection) together with multiple infections during the incubation period to promote a ‘short-cut’ to disease onset, a so-called ‘backward’ bifurcation appears (see Castillo-Chavez and Song [6] for a review of the literature Pamapimod (R-1503) associated with TB models). Another possible ‘fast’ route is due to acquired immunodeficiency syndrome (AIDS) [7-9]. Our aim is to understand the interplay between multiple infections and long latency in the overall transmission of TB. Another goal is to assess how they act on immunosuppressed individuals. Since the backward bifurcation is well documented in the literature, we focus on the contributions of the model’s parameters to the appearance of this kind of bifurcation. This paper is structured as follows. In the following section we present a model that describes the dynamics of the TB infection, which is analyzed in the steady state with respect to the trivial and non-trivial equilibrium points (Appendix B). In the third section we assess the effects of super-infection and latent period in TB transmission. This is followed by a discussion and our conclusions. == Model for TB transmission == Here we present a mathematical model of MTB transmission. In Appendix A, we briefly present some aspects of the biology of TB that substantiate the hypotheses assumed in the formulation of our model. There are many similarities between the ways by which different infectious diseases progress over time. Taking into account the natural history of infectious disease, in.