4.2 Article

MATHEMATICAL ANALYSIS OF THE TRANSMISSION DYNAMICS OF SCHISTOSOMIASIS IN THE HUMAN-SNAIL HOSTS

Journal

JOURNAL OF BIOLOGICAL SYSTEMS
Volume 17, Issue 3, Pages 397-423

Publisher

WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218339009002910

Keywords

Schistosomiasis; Biomphalaria glabrata; Center Manifold; Mathematical Modeling

Funding

  1. DST/NRF Centre of Excellence in Epidemiological Modeling and Analysis in South Africa (SACEMA)

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The spread and persistence of schistosomiasis are some of the more complex host parasite processes to model mathematically because of the different larval forms assumed by the parasite and the requirement of two hosts during the life cycle. We construct a deterministic mathematical model to study the transmission dynamics of schistosomiasis where the miracidia and cercariae dynamics are incorporated. The model is analyzed to gain insights into the qualitative features of the equilibrium which allows the determination of the basic reproductive number. Conditions for existence of the endemic equilibrium are discussed and its local stability is determined using the Center Manifold Theory. Analytical and numerical techniques are employed to assess the conditions of containment and persistence of schistosomiasis. Our results show that control strategies that target the transmission of the disease from the snail to man will be more effective in the control of the disease than those that block the transmission from man to snail.

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