THE COMPUTATION OF REPRODUCTION NUMBERS FOR THE ENVIRONMENT-HOST-ENVIRONMENT CHOLERA TRANSMISSION DYNAMICS

This study presents a new model for the environment-host-environment transmission dynamics of V. cholerae in a community with an interconnected aquatic pond–river water network. For the case when the human host is the sole target of anti-cholera control and the volume of water in the pond is maximum, the disease-free equilibrium of the model is shown to be globally asymptotically stable whenever a certain epidemiological threshold, known as the basic reproduction number [Formula: see text], is less than unity. The epidemiological implication of this result is that cholera can be eliminated from the community if the control strategies implemented can bring (and maintain) [Formula: see text] to a value less than unity. Four scenarios, that represent different interpretations of the role of the V. cholerea pathogen within the environment, were studied. The corresponding basic reproduction numbers were shown to exhibit the same threshold property with respect to the value unity (i.e., if one is less (equal, greater) than unity, then the three others are also less (equal, greater) than unity. Further, it was shown that for the case where anti-cholera control is focused on the human host population, the associated type reproduction number of the model (corresponding to each of the four transmission scenarios considered) is unique. The implication of this result is that the estimate of the effort needed for disease elimination (i.e., the required herd immunity threshold) is unique, regardless of which of the four transmission scenarios is considered. However, when any of the other two bacterial population types in the aquatic environment (i.e., bacterial in the pond or river) is the focus of the control efforts, this study shows that the associated type reproduction number is not unique. Extensive numerical simulations of the model, using a realistic set of parameters from the published literature, show that the community-wide implementation of a strategy that focus on improved water quality, sanitation, and hygiene (known as WASH-only strategy), using the current estimated coverage of 50% and efficacy of 60%, is unable to lead to the elimination of the disease. Such elimination is attainable if the coverage and efficacy are increased (e.g., to 80% and 90%, respectively). Further, elimination can be achieved using a strategy that focuses on oral rehydration therapy and the use of antibiotics to treat the infected humans (i.e., treatment-only strategy) for moderate effectiveness and coverage levels. The combined hybrid WASH-treatment strategy provides far better population-level impact vis a vis disease elimination. This study ranks the three interventions in the following order of population-level effectiveness: combined WASH-treatment, followed by treatment-only and then WASH-only strategy.

The type-reproduction number of sexually transmitted infections through heterosexual and vertical transmission

Multiple sexually transmitted infections (STIs) have threatened human health for centuries. Most STIs spread not only through sexual (horizontal) transmission but also through mother-to-child (vertical) transmission. In a previous work (Ito et al. 2019), we studied a simple model including heterosexual and mother-to-child transmission and proposed a formulation of the basic reproduction number over generations. In the present study, we improved the model to take into account some factors neglected in the previous work: adult mortality from infection, infant mortality caused by mother-to-child transmission, infertility or stillbirth caused by infection, and recovery with treatment. We showed that the addition of these factors has no essential effect on the theoretical formulation. To study the characteristics of the epidemic threshold, we derived analytical formulas for three type-reproduction numbers for adult men, adult women and juveniles. Our result indicates that if an efficient vaccine exists for a prevalent STI, vaccination of females is more effective for containment of the STI than vaccination of males, because the type-reproduction number for adult men is larger than that for adult women when they are larger than one.