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Transcript
7/28/10 This presentation is made available through a Creative Commons AttributionNoncommercial license. Details of the license and permitted uses are available at http://creativecommons.org/licenses/by-nc/3.0/ Dynamics of vector-borne pathogens © 2010 Dr. Juliet Pulliam Title: Dynamics of Vector-Borne Pathogens Attribution: Dr. Juliet Pulliam, Topics in Biomedical Sciences Source URL: http://lalashan.mcmaster.ca/theobio/mmed/index.php/Honours Course For further information please contact Dr. Juliet Pulliam ([email protected]). Dr. Juliet Pulliam RAPIDD Program Division of International Epidemiology Fogarty International Center National Institutes of Health (USA) Topics in Biomedical Sciences BSc Honours Course in Biomathematics African Institute for the Mathematical Sciences Muizenberg, South Africa 20 May 2010 Infectious diseases Infectious diseases Transmission Transmission Mode of transmission Mode of transmission Direct transmission Direct transmission Direct contact Droplet spread Direct contact Droplet spread Indirect transmission Indirect transmission Airborne Vehicle-borne (fomites) Vector-borne (mechanical or biological) Airborne Vehicle-borne (fomites) Vector-borne (mechanical or biological) Portal of entry Portal of entry Portal of exit Portal of exit Mosquitoes Ticks Sandflies Tsetse flies Reduviid bugs 1 7/28/10 Vector-borne pathogens Vector-borne pathogens “Typical” natural history “Typical” natural history HOST Infection Onset of symptoms Infection VECTOR Onset of symptoms Infection Incubation Latent period Clinical disease Incubation Infectious period Onset of shedding Clinical disease Latent period Infectious period Onset of shedding Vector-borne pathogens Vector-borne pathogens “Typical” natural history Examples Often acute: timecourse of infection << normal lifespan of host Death Latent Infectious Onset of shedding Mosquitoes Anopheles spp., malaria vectors Culex spp., West Nile vectors BUT timecourse of infection ~ normal lifespan of vector Other biting flies Phlebotomus papatasi, Leishmania vector Sometimes immunizing: infection may stimulate antibody production, preventing future infection… or may not… or somewhere in between Glossina spp., African trypanosomiasis vectors True bugs Triatoma infestans, Chagas vector Ticks Amblyomma spp., heartwater vectors 2 7/28/10 not so Vector-borne pathogens A^simple view of the world HOST Infection Vector-borne pathogens not so A^simple view of the world Don’t worry about symptoms and disease! Onset of symptoms Infectivity < 1 Infectivity < 1 Exposed & Infected Exposed & Infected Incubation Infectious Latent period Clinical disease Infection HOST Infectious period Latent period Diseased Onset of shedding not so Infectious period Infectious Vector-borne pathogens A^simple view of the world Onset of shedding A^simple view of the world βH = infectivity to humans x per capita (vector) biting rate Infectivity < 1 Vector-borne pathogens not so HOST Susceptible Infection HOST Exposed & Infected Latent period Infectious period Infectious Onset of shedding Exposed & infected (not infectious) Infectious Recovered 3 7/28/10 Vector-borne pathogens not so not so A^simple view of the world Vector-borne pathogens A^simple view of the world VECTOR βV = infectivity to vectors x per capita (vector) biting rate VECTOR Infectivity < 1 Infection SV HOST Death SH IV EV Exposed & Infected EH Latent InfectiousInfectious period IH Infectious RH Onset of shedding not so Vector-borne pathogens not so A^simple view of the world VECTOR A^simple view of the world SV HOST Vector-borne pathogens birth rate per capita mortality rate SH IV EV per capita birth rate EH per capita mortality rate IH 1/latent period RH 1/infectious period 4 7/28/10 not so Vector-borne pathogens not so A^simple view of the world VECTOR A^simple view of the world SV HOST SH IV EH Vector-borne pathogens EV β = infectivity x per capita contact rate β = infectivity x per capita (vector) biting rate infectivity = proportion of susceptible individuals that become infected, given exposure IH HOST exposure = bite by IV VECTOR exposure = bite on IH per capita (vector) biting rate = bites by one individual vector per time unit RH not so Vector-borne pathogens A^simple view of the world HOST β = infectivity x per capita contact rate β = infectivity x per capita biting rate infectivity = proportion of susceptible individuals that become infected, given exposure per capita (vector) biting rate = bites by one individual vector per unit time exposure = bite by IV infectivity to host = host infections produced per bite by IV on SH βH = bites (potentially infectious to host) by one individual vector per unit time βHIV = bites (potentially infectious to host) per unit time βHIV/NH = bites (potentially infectious to host) per host per unit time βHSHIV/NH = infectious bites per unit time not so Vector-borne pathogens A^simple view of the world VECTOR β = infectivity x per capita contact rate β = infectivity x per capita biting rate infectivity = proportion of susceptible individuals that become infected, given exposure per capita (vector) biting rate = bites by one individual vector per unit time exposure = bites on IH infectivity to vector = vector infections produced per bite by SV on IH βV = bites (potentially infectious to vector) by one individual vector per unit time βVSV = bites (potentially infectious to vector) per unit time βVSV/NH = bites (potentially infectious to vector) per host per unit time βVSVIH/NH = infectious bites per unit time 5 7/28/10 not so Vector-borne pathogens not so A^simple view of the world VECTOR A^simple view of the world SV HOST HOST SH IV EH Vector-borne pathogens VECTOR EV IH RH Vector-borne pathogens Vector-borne pathogens A^simple view of the world A simple method for complex models not so HOST VECTOR FV-1 = is the “next generation matrix” For all compartments xi containing infected individuals (ie, EH , IH, EV, IV), the time derivative can be rewritten as where = the rate of appearance of new infections in compartment xi = the rate of transfer out of compartment xi = the rate of transfer of individuals into compartment xi, other than new infections 6 7/28/10 Vector-borne pathogens A simple method for complex models not so Vector-borne pathogens A^simple view of the world For our system, we have FV-1 = is the “next generation matrix” F and V are then the square matrices defined by and where not so Vector-borne pathogens A^simple view of the world not so Vector-borne pathogens A^simple view of the world For our system, we have For our system, we have and we find which gives 7 7/28/10 not so Vector-borne pathogens A^simple view of the world not so Vector-borne pathogens A^simple view of the world For our system, we have For our system, we have “next generation matrix” and 8
