The interplay of isolation from reproduction with demography and sexually transmitted diseases

Daniel Maxin, Purdue University

Abstract

We study the demographic and epidemiological effects of isolation from reproduction in heterogeneous populations. We aim at establishing under what conditions the isolation from reproduction and/or sexual activity can cause the population to go extinct or to reach a disease free steady state while maintaining a stable positive total size. We address the problem from a demographic perspective first using extensions of the classical exponential and logistic equations as well as of a newly introduced logistic gender structured model with non-linear mortality. Based on these models we introduce groups of individuals either abstained from sexual contact and/or sexually active but non-procreating. The infectious disease is assumed to be sexually transmitted, long-lasting and mild, i.e. without recovery or additional mortality. We find that the isolation from sexual activity can induce a locally asymptotically stable disease free steady state in an otherwise endemic situation. Under some conditions on the parameters, we also found that the presence of sexually active and non-procreating groups can extend the domain of existence of the disease free equilibrium. Moreover, the gender structured model predicts that the total final population size may reach a larger limit in the presence of isolation from reproduction than in its absence. While the majority of these results are proved locally via linearization around the relevant critical points, we predict that they also hold globally in a biologically meaningful domain and we managed to prove this under additional technical assumptions. Several simulations are also included to illustrate the most general cases.

Degree

Ph.D.

Advisors

Milner, Purdue University.

Subject Area

Mathematics|Epidemiology

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