Modeling the Impact of Alternative Immunization Strategies: Using Matrices as Memory Lanes

<div><p>Existing modeling approaches are divided between a focus on the constitutive (micro) elements of systems or on higher (macro) organization levels. Micro-level models enable consideration of individual histories and interactions, but can be unstable and subject to cumulative errors. Macro-level models focus on average population properties, but may hide relevant heterogeneity at the micro-scale. We present a framework that integrates both approaches through the use of temporally structured matrices that can take large numbers of variables into account. Matrices are composed of several bidimensional (time×age) grids, each representing a state (e.g. physiological, immunological, socio-demographic). Time and age are primary indices linking grids. These matrices preserve the entire history of all population strata and enable the use of historical events, parameters and states dynamically in the modeling process. This framework is applicable across fields, but particularly suitable to simulate the impact of alternative immunization policies. We demonstrate the framework by examining alternative strategies to accelerate measles elimination in 15 developing countries. The model recaptured long-endorsed policies in measles control, showing that where a single routine measles-containing vaccine is employed with low coverage, any improvement in coverage is more effective than a second dose. It also identified an opportunity to save thousands of lives in India at attractively low costs through the implementation of supplementary immunization campaigns. The flexibility of the approach presented enables estimating the effectiveness of different immunization policies in highly complex contexts involving multiple and historical influences from different hierarchical levels.</p></div

Measles immunization scenarios (Status quo, S2, S3, S4) simulated up to 2050.

<p>Vertical bars are proportional to coverage levels. First (MCV1) and second (MCV2) routine doses and supplementary immunization campaigns (SIAs) are represented in green, blue, and grey, respectively. Scenarios were selected by the WHO Strategic Advisory Group of Experts (SAGE). Dependence between MCV1 and MCV2 indicates the % of unvaccinated individuals targeted to receive MCV2. <u>Indian States</u>: Status quo: MCV1 dose at 9 months at current coverage (46%, 90%, 74%, 86%, and 95% in Bihar, Karnataka, Maharashtra, Orissa, and Tamil Nadu, respectively); S2: MCV1 coverage improved to 90% over 5 years; S3: status quo plus inclusion of MCV2 at 18 months, improving from 50% to 97% of MCV1 over 5 years (dependence between doses = 25%); S4: inclusion of SIAs from 2009 onwards targeted at ages 9 months to 5 years with 90% coverage. <u>Africa and Cambodia</u>: Status quo: MCV1 (coverages of 73%, 73%, 51%, 85%, 95%, and 79% in Cameroon, Democratic Republic of Congo, Equatorial Guinea, Ghana, Rwanda, and Cambodia, respectively) and SIAs every 2–4 years (target age: 9 months to 5 years, 90% coverage); S2: status quo and MCV2 at 18 months with coverage improving from 50% to 100% of MCV1 over 5 years (dependence between doses = 25%); S3: status quo and routine MCV2 to 7 year olds, MCV2 coverage improving from 50% to 100% of MCV1 over 5 years (dependence between doses = 25%). <u>Latin America</u>: Status quo: MCV1 (at 15 months) MCV2 (to 7, 4, 4, and 6 year olds in Costa Rica, El Salvador, Paraguay, and Mexico, respectively) at existing coverage (MCV1 and MCV2 coverage in Costa Rica, El Salvador, Paraguay, and Mexico, respectively: 89% and 94% of MCV1; 98% and 94% of MCV1; 88% and 66% of MCV1; 96% and 58% of MCV1) and SIAs implemented every 4 years (target age: 9 months to 5 years, 85% coverage in Costa Rica and 92% in remaining countries); S2: status quo and 100% dependence between MCV1 and MCV2; S3: status quo and elimination of SIAs; S4: status quo elimination of SIAs and 100% dependence between MCV1 and MCV2.</p

Diagram summarizing the events each age cohort can experience in an annual cycle (it can be also understood as the outcomes an individual may experience each year).

<p>The cycle starts (left) and ends (right) with the proportions of susceptible and immune individuals. Events (vaccinations, infections, mortality) during the cycle change the proportions exported for the next cycle and generate intermediate outcomes of interest (proportions of cases and deaths). Each box represents a matrix of 104 age-groups × 71 years. Probabilities are depicted in the small white boxes: C: Vaccine coverage, E: Vaccine efficiency, F: Force of infection, D: Case fatality ratios, and W: waning Immunity probability. The large colored boxes are compartments, and sequences of letters represent sequences of events (e.g. SVSFI blue box: proportion of susceptible individuals S who were vaccinated–SV–but remained susceptible–SVS–were next infected–SVSF–and became immune SVSFI). N stands for non-vaccinated.</p

Cost-effectiveness (panels on the left represent incremental cost-effectiveness ratios (ICERs) in US$ per DALY averted) and percent change in mortality (panels on right) of alternative immunization strategy (S2, S3, S4) relative to baseline status quo immunization scenarios (S2/S3/S4 are described in Fig 2).

<p>For Latin America, ICERs represent the cost saved per DALY averted and mortality change as percent increases in mortality. For the other regions, mortality change represents the percent reduction in mortality. Bars are ordered according to MCV1 coverage.</p