Multiscale model within-host and between-host for viral infectious diseases

Abstract

Multiscale models possess the potential to uncover new insights into infectious diseases. Here, a rigorous stability analysis of a multiscale model within-host and between-host is presented. The within-host model describes viral replication and the respective immune response while disease transmission is represented by a susceptible-infected model. The bridging of scales from within- to between-host considered transmission as a function of the viral load. Consequently, stability and bifurcation analyses were developed coupling the two basic reproduction numbers [Formula: see text] and [Formula: see text] for the within- and the between-host subsystems, respectively. Local stability results for each subsystem, including a unique stable equilibrium point, recapitulate classical approaches to infection and epidemic control. Using a Lyapunov function, global stability of the between-host system was obtained. Our main result was the derivation of the [Formula: see text] as an increasing function of [Formula: see text]. Numerical analyses reveal that a Michaelis-Menten form based on the virus is more likely to recapitulate the behavior between the scales than a form directly proportional to the virus. Our work contributes basic understandings of the two models and casts light on the potential effects of the coupling function on linking the two scales.

Stability analysis in COVID-19 within-host model with immune response

“…Our main result is comparable to previous in-host infectious disease modeling [30] . In short, our model yields a unique locally asymptotically stable equilibrium point which is for ( Theorem 1 ) and the positive viral load for ( Theorems 2 and 3 ).…”

“…Regulatory components of the immune system may be important for considering how T cells clear a limited portion of the pathogen [33] . Finally, we may employ a multiscale modeling framework to evaluate how the severity of in-host infection can determine effective between-host transmission [30] .…”

High-resolution epidemic simulation using within-host infection and contact data

“… The transmission potential was assumed as directly related to viral load. While this is reasonable, non-linear relationships might exist [ 16 , 28 ]. Dedicated animal experiments to define the exact relationship between the viral load and the ability to transmit the virus are needed.…”

“…The interplays between within-host infection and between hosts transmission led to arising attempts connecting the two levels [ 4 , 17 , 18 , 24 – 28 ], but the approach is still at its infancy [ 16 ]. On one hand, most of these models were conceptual and theoretical [ 16 , 28 ] or relied on assumptive and previously obtained parameter estimates [ 10 , 11 , 29 ]. We propose that this limitation can be overcomed by using explicitly within-host infection model as a unit in epidemic simulations.…”

Optimal control of acute myeloid leukaemia

“…Michaelis-Menten terms are commonly used to incorporate immune responses in other biologically motivated models [2,24,38]. However, it is unclear, simply by inspection, what parameter values are required to obtain two stable steady states: one coexisting and one healthy.…”