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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