1. Models of host-parasite regulation D. Gurarie

2. I. Macro-parasites (helminth) regulation Macro parasites can regulate the host reproduction and growth (Anderson-May 1978) ; Contribute to host birth/death rates (additive or multiplicative)

3. Single host models Inf+L system: Burden strata

4. Reduced (closure) models Fix-k model (k – aggregation index; w=P/H –mean burden) For negative binomial with aggregation k

5. Reduced ‘predator-prey’ For quasi-equilibrated larvae: H1H1 H0H0 f=0 g=0 H

6. Two-host models (schisto) Life Cycle of Schistosomiasis

7. Human ‘burden’ strata + snail ‘prevalence’+ 2 larvae => Reduced 6D, 4D, 3D models. Differs from standard Ross-Macdonald -“Mean burden” + “infected prevalence” -(for const N)

8. Applications Regulation and stability of host–parasite populations (Anderson-May 1978) Aggregation for single parasite species and multi-strain competition, coexistence, invasion (Dobson-Roberts 1994; Pugliese 2000, Rosa- Pugliese 2002) Parasite (schisto) diversity and drug resistance (Feng et al 2001) Goal: application to schisto control

9. II. Micro-parasite regulation (malaria) Intra-host P. regulation by host immunity Community transmission modulated by immune regulation Goal: improved SIR (for control, drug resistance, et al)!

10. Life cycle More details

11. RBC cycle and immune response Merozoites: 48 hr replication cycle in RBC with replicating factor: Fever suppression at pyrogenic level: Immunity (transient, lost in the absence of reinfection). 3 forms: fever control; species transcending (ST); species specific (SS)

12. Parasitemia (Parasites/μl) Temp. (°F) 105 - 103 - 101 - 99 - 96 - 10 100 1,000 10,000 Inoculation by 15 P. falciparum (black line; gametocytes – black dots) + P. vivax (red line) infected A. quadrimaculatus Day #1Day #25 Day #50 Day #75 TxTx Day #86 TxTx Zimmerman et al. Figure 1A Natural infection histories

13. Zimmerman et al. Figure 1B Parasitemia (Parasites/μl) Temp. (°F) 105 - 10 100 1,000 10,000 P. vivax Inoculation by 12 P. falciparum + P. vivax infected A. quadrimaculatus Day #1 TxTx Day #20Day #40Day #60Day #80Day #100Day #120Day #140 99 - 101 - 103 -

14. Continuous regulation models Feedback circuits: Stimulation/growth Inhibition/loss u gMgM b  x LL  fMfM b1b1  u b2b2 x LL  y LL  g,N h,Nh,N c1c1 c2c2  w  v gMgM b1b1  u b2b2 x LL  y LL  Single P. with fever and ST 2 species with fever and ST 2 species with fever, ST and SS

15. DDE models Single w. ST: 2 species w. ST: 2 species w. ST and SS (5D system)

16. Results: single species

17. 2 species: SS/ST

18. Future plans Deterministic and stochastic growth/removal models w. discrete time step Estimation, validation Applications to community transmission ???