The impact of density-dependent processes on the eradicability of parasitic diseases

Transcription

1 The impact of density-dependent processes on the eradicability of parasitic diseases Hans Peter Duerr Martin Eichner Klaus Dietz Department of Medical Biometry University of Tübingen Oberwolfach /12

2 Introduction Onchocerciasis: Vectorcontrol until 2002, successor program: mass drug administration of ivermectin Onchocerciasis Control Programme African Programme for Onchocerciasis Control (APOC) Global Program to Eliminate lymphatic filariasis (GPELF) Lymphatic filariasis: Elimination intended by mass drug administration of ivermectin / DEC... 2/12

3 Density-dependent regulation in a host-parasite relationship n 1 n 2 No. of parasites in the human host n 3 n x+i Facilitation (positive feedback) No regulation n 6 No. of parasites in the vector n 4 Limitation (negative feedback) n 5 Number of parasites of stage x n x 3/12

4 Comparing processes of density-dependent regulation n 2 No. of parasites in the human host n x+i n 1 n 3 n 6 No. of parasites in the vector n 4 Common equilibrium parasite burden n 5 n x 4/12

5 Equilibrium under limitation h No. of parasites in the human host h v v(h) h(v) v No. of parasites in the vector v Unstable zero h v(h) h(v) v h Equilibrium parasite density 5/12

6 Equilibrium under limitation + intervention h No. of parasites in the human host h v(h) h(v) No. of parasites in the vector v v 6/12

7 Basics of persistence and eradicability Transmission thresholds... refer to a vector density below which the infection cannot persist Threshold Biting Rate (TBR): "If there are too few vector-host contacts, then, a parasite in the human host will die before the next one can establish" Parasite burden TBR Force of infection 7/12

8 Equilibria under facilitation h h h(v) No. of parasites in the human host v v(h) v h No. of parasites in the vector h v(h) h(v) Stable equilibrium v Stable zero Unstable equilibrium v 8/12

9 Mating probability of dioceous parasites P ( 2sex) = 1 P( only male worms) P( only female worms) = = males W females // males == females = W ϕ W ~ NBD( w, k) : ( ) ( W 1 w = ) W = 1 = 1+ k k + w k NBD( w, k) 2 k + 1 k 2k + w k 1 ϕ (w) w May, R. M. (1977). Togetherness among schistosomes... Math Biosci 35, model 9/12

10 Basics of persistence and eradicability Transmission thresholds... refer to a vector density below which the infection cannot persist Threshold Biting Rate (TBR): "If there are too few vector-host contacts, then, a parasite in the human host will die before the next one can establish" Breakpoints... refer to a parasite density below which the infection cannot persist Mating process: "If there are too few parasites in a host, then, mating is not possible and reproduction cannot occur" Parasite burden TBR Force of infection Offspring parasites Reproductive parasites 10/12

11 Persistence graph of a filarial infection infection cannot persist infection can persist, elimination is possible infection persists, elimination is difficult parasites Parasite density [ ] host A C2 C1 bloodmeals Annual Biting Rate (ABR) [ year host ] B 11/12

12 Model (filarial parasites) Acquisition & survival of adult parasites: dw = λ ( w, ATP ) ( σ w + µ )w dt Acquisition rate Mortality of adult worms + humans w Definite host Vector l m Production & survival of microfilariae: dm = ϕ ( w) β ( w) ( σ m + µ )m dt Larval development in flies (assumed to be at equilibirum): ( m) = c m ( c m) l Annual Transmission Potential: ATP Mating probability = ε ABR Rate of microfilarial production l l * Mortality of adult worms + humans Annual Biting Rate Adjustment to provide comparable equilibriae 12/12

13 (a) "How many adult parasites result from a certain number of L3 transmitted?" (b) "How many microfilariae in the skin result from adult female parasites?" Adult female O.v. per person limitation Adult parasite Microfilariae per mg skin snip ATP [L3 per person and year] Adult female O.v. per person L4 Definite host Microfilariae L3 Vector Densitydependent processes: Limitation & Facilitation L3 per fly (c) L2 L1 "How many L3 per fly result from microfilariae ingested during a bloodmeal?" Microfilariae per mg skin snip 13/12

14 Density-dependent processes modifying eradicability ATP: Adult: MF: L3: limitation facilitation no regulation no regulation no regulation limitation no regulation limitation no regulation limitation no regulation no regulation limitation limitation facilitation limitation limitation 30 Adult female parasites per host ABR ABR ABR ABR Facilitation "facilitates" the eradicability of an infection, whereas limitation "limits" the prospects of eradication 14/12

15 % reduction of the microfilarial density by microfilaricide Adult female parasites per host Persistence-shifting interventions ivermectinfacilitated immunity Microfilarial density no densitydependent effect Microfilarial density disadvantageous densitydependence Microfilarial density Annual Biting Rate Annual Biting Rate Annual Biting Rate 15/12

16 Conclusions The eradicability of a filarial infection is to a large extent determined by density-dependent processes. Facilitation processes "facilitate" the elimination of a parasite, whereas limitation processes "limit" the prospects of its elimination. Predictions of the success of intervention programs will be over-optimistic - if the degree of facilitation is overestimated or - if the degree of limitation is underestimated... and vice versa. The eradicability of a parasitic infection is not only determined by "biological density-dependence", but also by "intervention-specific" forms of density-dependence. Further to be investigated: effects in a stochastic model 16/12

17 Schedule Filarial diseases & control programs The role of the vectors Theoretical basis of persistence and eradicability: Transmission thresholds & breakpoints Density-dependent processes: Limitation & Facilitation The persistence graph How density-dependent processes influence the eradicability of an infection Persistence-shifting interventions Uncertainties 17/12

18 Life-cycle of a filarial parasite Adult parasite L4 Microfilariae ATP Annual Transmission Potential ( ) L3 L2 Definite host Vector L1 Larvae 18/12

19 Elimination of lymphatic filariasis YES: 1977: Polynesia (Anophelestransmitted W. bancrofti disappeared as a side effect of a malaria control campaign based on DDT house spraying ) 1991: China (DEC distribution eliminated Anopheles-transmitted Brugia malayi infection) NO: 1977: Polynesia (Aedestransmitted W. bancrofti infection could not be eliminated despite 50 years of DEC distribution, partly even involving vector control ) Limitation Anopheles L3 / fly Facilitation Culex MF-density in human hosts 19/12

20 ABR - ATP relationship 62 pre-control villages from 9 OCP-countries: ATP ABR Breakpoint-ATP? Mean(ATP) Mean(ABR) Transmission threshold? 20/12

21 Uncertainties: degree of limitation in ATP Adult female parasites per host α=0.02 α=0.06 α=0.1 ATP ATP ATP Adult female parasites per host ABR ABR ABR 21/12

22 "How many adult parasites result from a certain number of L3 transmitted?" Adult female O.v. per person limitation ATP [L3 per person and year] model cycle 22/12

23 "How many microfilariae in the skin result from adult female parasites?" Microfilariae per mg skin snip f ( w) b wσ m = 1 + s w m Adult female O.v. per person * Duerr HP et al, (2004). The relationships between the burden of adult parasites, host age and the microfilarial density in human onchocerciasis. Int J Parasitol 34: model cycle 23/12

24 "How many L3 per fly result from microfilariae ingested during a bloodmeal?" L3 per fly Microfilariae per mg skin snip model cycle Basáñez MG & Boussinesq M. (1999). Philos Trans R Soc Lond B Biol Sci 354, : l ( m) m = m 24/12

25 Hans-Peter Duerr Universität Tübingen Institut für Medizinische Biometrie