In-host modeling

Abstract

Understanding the mechanisms governing host-pathogen kinetics is important and can guide human interventions. In-host mathematical models, together with biological data, have been used in this endeavor. In this review, we present basic models used to describe acute and chronic pathogenic infections. We highlight the power of model predictions, the role of drug therapy, and advantage of considering the dynamics of immune responses. We also present the limitations of these models due in part to the trade-off between the complexity of the model and their predictive power, and the challenges a modeler faces in determining the appropriate formulation for a given problem.

Fig. 1

Model diagram for Eq. (1).

Fig. 2

(a)–(b) Virus and cell dynamics for a chronic virus infection given by Eq. (1) for parameters $\left(s,d,\beta ,\delta ,p,c\right)=\left({10}^4,0.01,{10}^{-6},\mathrm{1,1200,23}\right)$ and initial conditions $\left(T,I,V\right)\left(0\right)=\left({10}^6,0,{10}^{-6}\right)$ as in (Stafford et al., 2000); (c)–(d) Virus and cell dynamics for a chronic virus infection given by Eq. (6) for parameters $\left(\beta ,k,\delta ,p,c\right)=\left(3.2\times {10}^{-5},\mathrm{4,5.2},4.6\times {10}^{-2},5.2\right)$ and initial conditions $\left(T,E,I,V\right)\left(0\right)=\left(4\times {10}^8,\mathrm{0,0,7.5}\times {10}^{-2}\right)$ as in (Baccam et al., 2006).

Fig. 3

Virus and cell dynamics for: (a)–(d) innate immune responses to acute virus infection given by Eqs. (6), (7), (8), (9), (10), (11), (12), (13), (14), (15), (16), (17), (18), (19), (20), (21), parameters $\left(\beta ,\delta ,p,c,\alpha ,k,\tau ,d_F,{\mathit{\varepsilon }}_1,{\mathit{\varepsilon }}_2\right)=\left(4.2\times {10}^{-6},\mathrm{7,0.32},13.4,\mathrm{1,26.6},0.5,5.2,3.5\times {10}^{-6},3\times {10}^{-7}\right)$ and initial conditions $\left(T,E,I,V,F\right)\left(0\right)=\left(4\times {10}^8,\mathrm{0,0},{10}^{-2},1\right)$ as in (Baccam et al., 2006, Pawelek et al., 2012); (b)–(e) cellular immune responses to chronic virus infection given by Eq. (23) for parameters $\left(s,d,\beta ,\delta ,p,c,\mu ,d_E\right)=\left({10}^4,0.01,{10}^{-6},\mathrm{1,1200,23}\right)$, $\left(s_E,\alpha ,\mu ,d_E\right)=\left(\mathrm{0,0,0,0}\right)$ (solid lines), $\left(s_E,\alpha ,\mu ,d_E\right)=\left(300,{10}^{-5},\mathrm{1,0.5}\right)$ (dashed lines), and initial conditions $\left(T,I,V,E\right)\left(0\right)=\left({10}^6,\mathrm{0,100,10}\right)$; (c)–(f) humoral immune responses to chronic virus infection given by Eq. (25) for parameters $\left(s,d,\beta ,\delta ,p,c\right)=\left({10}^4,0.01,{10}^{-6},\mathrm{1,1200,23}\right)$, $\left(\alpha ,c_A,d_A,s_A\right)=\left(\mathrm{0,0,0,0}\right)$ (solid lines), $\left(\alpha ,c_A,d_A,s_A\right)=\left({10}^{-6},\mathrm{92,0.07},1\right)$ (dashed lines) and initial conditions $\left(T,I,V,A\right)\left(0\right)=\left({10}^6,\mathrm{0,100,14}\right)$.

Fig. 4

Modeling pathway.

Fig. 5

Tradeoff between the incorporation of biological complexity and the applicability of model results to the biological questions at hand. The goal is to maximize new knowledge from results.