Structural and Practical Identifiability Issues of Immuno-Epidemiological Vector–Host Models with Application to Rift Valley Fever

Abstract

In this article, we discuss the structural and practical identifiability of a nested immuno-epidemiological model of arbovirus diseases, where host-vector transmission rate, host recovery, and disease-induced death rates are governed by the within-host immune system. We incorporate the newest ideas and the most up-to-date features of numerical methods to fit multi-scale models to multi-scale data. For an immunological model, we use Rift Valley Fever Virus (RVFV) time-series data obtained from livestock under laboratory experiments, and for an epidemiological model we incorporate a human compartment to the nested model and use the number of human RVFV cases reported by the CDC during the 2006-2007 Kenya outbreak. We show that the immunological model is not structurally identifiable for the measurements of time-series viremia concentrations in the host. Thus, we study the non-dimensionalized and scaled versions of the immunological model and prove that both are structurally globally identifiable. After fixing estimated parameter values for the immunological model derived from the scaled model, we develop a numerical method to fit observable RVFV epidemiological data to the nested model for the remaining parameter values of the multi-scale system. For the given (CDC) data set, Monte Carlo simulations indicate that only three parameters of the epidemiological model are practically identifiable when the immune model parameters are fixed. Alternatively, we fit the multi-scale data to the multi-scale model simultaneously. Monte Carlo simulations for the simultaneous fitting suggest that the parameters of the immunological model and the parameters of the immuno-epidemiological model are practically identifiable. We suggest that analytic approaches for studying the structural identifiability of nested models are a necessity, so that identifiable parameter combinations can be derived to reparameterize the nested model to obtain an identifiable one. This is a crucial step in developing multi-scale models which explain multi-scale data.

Infection severity across scales in multi-strain immuno-epidemiological Dengue model structured by host antibody level

“…Observe that recovered individuals at the lower bound of antibody level satisfiesr k (y c ) = 0 when µ > ξ (natural death rate greater than waning rate), andr k (y c ) = +∞ when µ < ξ, however the total amount of recovered individuals stays finite by (36). Furthermore, as mentioned previously, primary Dengue infection induces a period of temporary cross-immunity.…”

“…The controversy surrounding apparent rise in DHF among certain vaccinated individuals after a vaccination campaign [4,40] and questions into how to safely vaccinate Dengue-at-risk populations, motivates the need for predictive modeling frameworks including effects of targeted vaccination on population antibody levels. Such a model would also require robust parameter estimation and identifiability analysis extending prior work in multi-scale data fitting [36]. Ideally, the model may suggest whom to target for vaccination dependent on cross-reactive antibody level measured by blood samples, in order to prevent DHF incidence and ultimately eradicate the disease.…”

Practical unidentifiability of a simple vector-borne disease model: Implications for parameter estimation and intervention assessment

“…However, relatively few efforts have been made to formally examine questions of parameter identifiability in these models (Mendes Luz et al, 2003; Laneri et al, 2010; Bhadra et al, 2011; Moulay et al, 2012b; Pandey et al, 2013; Reiner et al, 2014; Zhu et al, 2015; Tuncer et al, 2016; Shutt et al, 2017). Two studies that directly evaluated identifiability issues include: Denis-Vidal, Verdière, and colleagues assessed the structural (theoretical) identifiability of a chikungunya transmission model assuming all the states in human population and mosquito larva are observable (Moulay et al, 2012b; Zhu et al, 2015); Tuncer et al (2016) examined both structural and practical identifiability of a within-to-between host model of Rift Valley fever, addressing how the multi-scale nature of such immuno-epidemiological problems affects model identifiability. Building on these results, we examine the identifiability of a simple compartmental model based on the Ross-Macdonald framework with various scenarios of measurement assumption (Newton and Reiter, 1992).…”

Practical unidentifiability of a simple vector-borne disease model: implications for parameter estimation and intervention assessment

“…(theoretical) identifiability of a chikungunya transmission model assuming all the states in human 40 population and mosquito larva are observable [46,49]; Tuncer et al [50] examined both structural 41 and practical identifiability of a within-to-between host model of Rift Valley fever, addressing how 42 the multi-scale nature of such immuno-epidemiological problems affects model identifiability. 43 Building on these results, we examine the identifiability of a simple compartmental model based 44 on the Ross-Macdonald framework with various scenarios of measurement assumption [51].…”

“…However, in spite of the abundance of transmission models in mosquito-borne diseases and the 36 common use of parameter estimation in fitting these models to data, relatively few efforts have been 37 made to examine questions of parameter identifiability in these models. [43][44][45][46][47][48][49][50]. Two studies that 38 directly evaluated the issues include: Denis-Vidal, Verdière, and colleagues assessed the structural 39…”