1. Disease emergence in immunocompromised populations Jamie Lloyd-Smith Penn State University

2. HIV prevalence in adult populations Africa: a changing immune landscape How might this influence disease emergence?

3. Heterogeneous immunity and disease emergence Individual-level effects of compromised immunity can include: greater susceptibility to infection higher pathogen loads disseminated infection and death longer duration of infection What are the population-level effects of immunocompromised groups on pathogen emergence? In addition to HIV, many other factors affect the host immune response to a given pathogen: Host genetics Nutrition Co-infections Age Immunosuppressive drugs Vaccination and previous exposure

5. Modelling pathogen emergence Linearized birth-and-death process in continuous time. Population is structured into groups according to immunocompetence. Each group has characteristic susceptibility and infectiousness, which can vary independently or co-vary. Stochastic model for disease invasion into a large population. Pathogen is structured into strains representing stages of adaptation to a novel host species. Emergence = introduction + adaptation + invasion Building on work by Antia et al (2003), Andre & Day (2005), and Yates et al (2006). A simple model for pathogen invasion

6. Between-host transmission bottleneck causes founder effect Model assumes: Occurs with fixed probability per transmission event. Occurs at a constant rate within each infected host. Within-host mutation arises during infection and goes to fixation within host A simple model for pathogen adaptation Emergence = introduction + adaptation + invasion  a probability over an average duration of infection.

7. Initial strain Intermediate strain Adapted strain 0 0.5 1 1.5 Pathogen fitness landscapes adaptation One-step adaptation R 0 in healthy population adaptation R 0 in healthy population Initial strain Adapted strain 0 0.5 1 1.5 Two-step adaptation

8. Model assumptions Invasion model (epidemiology) Susceptible pool is large compared to outbreak size. Per capita rates of recovery and transmission are constant. Type of index case is determined by group size weighted by susceptibility: Pr(index case in group i) = (Size of group i) × (Susc. of group i).  j (Size of group j) × (Susc. of group j) Adaptation model (evolution) Parameters describing relative susceptibility and infectiousness don’t depend on pathogen strain. Evolutionary and epidemiological parameters are independent of one another.

9. Model equations: 1 group, 1 strain where, because of the large-population assumption:

10. Model equations: 1 group, 2 strains

11. Model equations: 2 groups, 2 strains

12. Divide population into two groups, healthy and immunocompromised, which mix at random. Consider different epidemiological effects of immune compromise: NO EFFECT (0), S , I , I , S  I , S  I  (assume 10-fold changes) Infectiousness can vary via either the rate or duration of transmission. 20% immuno- compromised 80% healthy  t Normal t  I  rate t  I  duration

13. Covariation of epidemiological parameters When susceptibility and infectiousness co-vary, R 0 for the heterogeneous population  R 0 in a healthy population. R 0 = 1 in healthy population

14. 0246 0 0.2 0.4 0.6 0.8 1 R 0 in healthy population Probability of invasion Pathogen invasion, without evolution SS 0 SS 0246 0 0.2 0.4 0.6 0.8 1 R 0 in heterogeneous population Probability of invasion SS 0 SS Heterogeneous susceptibility only See Becker & Marschner, 1990.

15. 0246 0 0.2 0.4 0.6 0.8 1 R 0 in healthy population Probability of invasion II 0 II 0246 0 0.2 0.4 0.6 0.8 1 R 0 in heterogeneous population Probability of invasion II 0 II Pathogen invasion, without evolution Heterogeneous infectiousness only See Lloyd-Smith et al, 2005.

16. 0246 0 0.2 0.4 0.6 0.8 1 R 0 in healthy population Probability of invasion 0246 0 0.2 0.4 0.6 0.8 1 R 0 in heterogeneous population Probability of invasion SISI SS II 0 SISI SISI SS II, 0 Solid lines: infectiousness varies in transmission rate SISI Pathogen invasion: co-varying parameters

17. Dashed lines: infectiousness varies in duration SISI SS II 0 SISI SISI SS II, 0 SISI 0246 0 0.2 0.4 0.6 0.8 1 R 0 in healthy population Probability of invasion 0246 0 0.2 0.4 0.6 0.8 1 R 0 in heterogeneous population Probability of invasion Pathogen invasion: co-varying parameters

18. Population with heterogeneous infectiousness, I  Pathogen invasion: co-varying parameters Prob. of invasion R 0 when cov(inf, susc) = 0

19. 0 0.511.5 10 -6 10 -5 10 -4 10 -3 10 -2 10 10 0 R 0 in healthy population Probability of adaptation within = between One-step adaptation 0 Pr(between)Pr(within) w = b 1×10 -3 w >> b 1×10 -6 2×10 -3 w << b 2×10 -3 1×10 -6 Pathogen evolution: probability of adaptation R0R0 Initial Adapted 0 1 within >> between within << between

20. SISI SS II 0 SISI SISI SS 0 SISI II Assuming P(within) = P(between) = 1×10 -3 Dashed lines: infectiousness varies in duration Solid lines: infectiousness varies in transmission rate Pathogen evolution: probability of adaptation

21. 00.511.5 10 -6 10 -5 10 -4 10 -3 10 -2 10 10 0 R 0 in healthy population Probability of adaptation 00.511.5 10 -6 10 -5 10 -4 10 -3 10 -2 10 10 0 R 0 in heterogeneous population Probability of adaptation SISI SS II 0 SISI SISI SS 0 SISI II Assuming P(within) = P(between) = 1×10 -3 Solid lines: infectiousness varies in transmission rate Pathogen evolution: probability of adaptation

22. 00.511.5 10 -6 10 -5 10 -4 10 -3 10 -2 10 10 0 R 0 in healthy population Probability of emergence 00.511.5 10 -6 10 -5 10 -4 10 -3 10 -2 10 10 0 R 0 in heterogeneous population Probability of emergence SISI SS II 0 SISI SISI SS 0 SISI II Assuming P(within) = P(between) = 1×10 -3 Dashed lines: infectiousness varies in duration Pathogen evolution: probability of adaptation

23. Where does adaptation occur? Dashed lines: infectiousness varies in duration Solid lines: infectiousness varies in transmission rate Assuming P(within) = P(between) = 1×10 -3 00.20.40.60.81 0 0.2 0.4 0.6 0.8 1 R 0 in heterogeneous population Proportion of evolution within host SISI SS II, 0 SISI

24. Where does adaptation occur? Dashed lines: infectiousness varies in duration Solid lines: infectiousness varies in transmission rate Assuming P(within) = P(between) = 1×10 -3 00.20.40.60.81 0 0.2 0.4 0.6 0.8 1 R 0 in heterogeneous population Proportion of evolution within host SISI SS II, 0 SISI

25. 00.511.5 10 -6 10 -4 10 -2 10 0 R 0 in healthy population Probability of adaptation 00.511.5 10 -6 10 -4 10 -2 10 0 R 0 in heterogeneous population Probability of adaptation Two-step adaptation Initial strain Intermediate strain Adapted strain 0 1 R 0 in healthy population adaptation Dashed lines: 1-step adaptationSolid lines: 2-step adaptation Jackpot model

26. Two-step adaptation Initial strain Intermediate strain Adapted strain 0 1 R 0 in healthy population Jackpot model Initial strain Intermediate strain Adapted strain 0 1 R 0 in healthy population Fitness valley model adaptation

27. Two-step adaptation: crossing valleys 10 -6 10 -4 10 -2 10 0 -10 10 -8 10 -6 10 -4 10 -2 R 0 of intermediate strain Probability of adaptation within = between Initial strain Intermediate strain Adapted strain 0 1 R0R0 within >> between II 0 Pr(between)Pr(within) w = b 1×10 -3 w >> b 1×10 -6 2×10 -3 w << b 2×10 -3 1×10 -6 within << between

28. HIV and acute respiratory infections Studies from Chris Hari-Baragwanath Hospital in Soweto. Bacterial respiratory tract infections (Madhi et al, 2000, Clin Inf Dis): Viral respiratory tract infections (Madhi et al, 2000, J. Ped.):

29. Evans et al, 1995 HIV and acute respiratory infections Alagiriswami & Cheeseman, 2001 Couch et al, 1997

30. Illustration: HIV prevalence and influenza emergence 0% 00.511.5 10 -9 10 -6 10 -3 1 R 0 in healthy population Probability of emergence HIV prevalence Assuming: Susceptibility is 8  higher in HIV+ group, and infections last 3  longer. P(within) = 1×10 -3 Two-step jackpot adaptation P(between) = 1×10 -6 R 0 = 2 for adapted strain 20% 10% 5% 1%

31. Summary and future directions Invasion An immunocompromised group can provide a toe-hold for emergence of an unadapted pathogen. Positive covariance between susceptibility and infectiousness can greatly amplify this effect. Adaptation Within-host evolution is crucial at low R 0, and when pathogen must cross fitness valleys to adapt. Prolonged duration of infection has greater influence on emergence than faster rate of transmission. Next steps Link epi and evolution: incorporate effect of pathogen load? Data!! On susceptibility and infectiousness as a function of immune status, and on pathogen fitness landscapes. HIV: more data needed at individual and population levels

32. Acknowledgements Ideas and insights Bryan Grenfell, Mary Poss, Peter Hudson, and many other colleagues at CIDD (Penn State) Wayne Getz (UC Berkeley) Brian Williams (WHO) Sebastian Schreiber (UC Davis) Funding CIDD Fellowship for research DIMACS and NSF for travel

33. Additional material

34. Pathogen evolution – approximate calculations Can distinguish between mechanisms of evolution by considering the total ‘opportunity’ for each to work.  Total infectious duration = L  Total number of transmission events = B Andre & Day (2005) showed, for a homogeneous population, that P(one-step adaptation) ~  L + u B This argument can be generalized to the multi-group setting, using the theory of absorbing Markov processes.  In addition to the approximate P(adaptation), can derive the approximate proportion of emergence events due to within-host vs between-host adaptation

35. Influence of covariation when overall R 0 is fixed II

36. Overall R 0 = 3 10 -2 10 10 0 1 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Relative susceptibility of group 2 P(emergence) P(em if index in group 1) P(em if index in group 2) P(index in group 1) Probability II Influence of covariation when overall R 0 is fixed

37. Overall R 0 = 3 P(emergence) P(em if index in group 1) P(em if index in group 2) P(index in group 1) SS Influence of covariation when overall R 0 is fixed 10 -2 10 10 0 1 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Relative infectiousness of group 2 Probability

38. Previous work on modelling emergence Antia et al, 2003 (between-host evolution, homogeneous population)  If introduced strain has R 0 < 1, ultimate emergence is more likely as R 0 approaches 1. Andre & Day, 2005 (within- and between-host, homogeneous pop.)  Duration of infection can be as important as R 0. Yates et al, 2006 (between-host only, heterogeneous population without covariation between parameters)  Host heterogeneity in susceptibility or infectiousness alone has little effect on emergence. Present goal: analyze disease emergence in a population with heterogeneous immunocompetence so that parameters may co-vary, with both within- and between-host evolution.

39. But CD4 count isn’t the whole story… HIV’s impact on invasive bacterial infection is thought to be mediated by mononuclear innate immune cells (macrophages, dendritic cells, etc) Results are indicating that HAART (and resulting elevated CD4 counts) do not reduce risk of bacterial infections. (Noursadeghi et al, Lancet Inf Dis 2006)