Mathematical Models of Some Parasitic Diseases Involving An Intermediate Host

Cover Mathematical Models of Some Parasitic Diseases Involving An Intermediate Host
Mathematical Models of Some Parasitic Diseases Involving An Intermediate Host
Ingemar Nasell
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2 The Prevalence In this section we study the prevalence of the disease in the case where T, T„ > 1 and u 7^ . The 12 o 97 - prevalence is measured by the proportion of definitive hosts that contain at least one parasite In their bodies, i. E. By P{5(t) > 0}. We assume that a sufficiently long time has elapsed so that the prevalence is close to its asymptotic or steady-state value. Prom ( 3, 5 . 3 ) we find that -3 V, Y r/\-i °° loo Pi5(t) > 0} -^ 1 - e as t -^ *=», where 3 = — ' — is given ^ '... CO II *-• ^1 in (3. 5. 1), and Y^ is the limiting value of the function Y(t) as t -> °°. Now Y(t) = N y(t), and, by Theorem 6 . 2 . I| . 1, y(t) -* 1 - „ m as t ^

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