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Direct-acting antiviral agents (DAAs) have shown higher cure rates for treating hepatitis C virus (HCV) by directly interfering with different steps of the HCV life cycle. To optimize drug combinations and accurately quantify the antiviral effect of DAAs treatments, mathematical models should include the intracellular virus replication processes. In this study, we develop a two-strain multiscale age-structured model that includes intracellular viral RNA replication and extracellular viral infection. We prove the existence, positivity, and boundedness of the solution, and derive the conditions for the existence and stability of the three steady states (non-infection steady state, boundary steady state, and coexistence steady state). Under certain biologically reasonable assumptions, we obtain the approximate solutions of the viral load decline of the two virus strains (sensitive and drug-resistant virus strains) during treatment, and the long-term approximation is shown to be in good agreement with the solution of the original model. We also carry out numerical simulations using the long-term approximate solution, providing insights into the influence of antiviral effects on the viral load change of the two virus strains during treatment with DAAs. • A multiscale mixed-ODE-PDE model is developed to study HCV infection. • The model includes intracellular RNA replication and extracellular viral infection. • We studied the existence and stability of the three steady states. • The approximate analytical solution is convenient for data comparison. [ABSTRACT FROM AUTHOR]

• A two-strain pairwise epidemic model with non-Markovian recovery process is established. • A hyperbolic system can be transformed into an integral differential system by using the method of characteristic. • We carry out rigorous analysis and obtain the relationship between the reproduction number and the final epidemic size. • Three commonly used recovery time distributions on the reproduction number were compared by numerical simulations. • The mean length of the infectious period affects the final epidemic size, the peak time, and the duration of an epidemic. We present and study a two-strain pairwise epidemic model with non-Markovian recovery process in which the recovery rate depends on infection age. The novel model is a hyperbolic system which can be transformed into a system of integro-differential equations by using the method of characteristics. For the two-strain pairwise model, the reproduction number with arbitrary recovery time distributions is obtained. We carry out rigorous analysis and obtain upper and lower estimates for the final epidemic size. Finally, the effects of three commonly used recovery time distributions on the reproduction number are compared by numerical simulations. We further present how the mean length of the infectious period affects the final epidemic size, the peak time and the duration of an epidemic. [ABSTRACT FROM AUTHOR]

In this paper, an age-structured cholera model with both human-to-human and environment-to-human transmissions and saturation incidence is proposed. In the model, we consider the infection age of infectious individuals and the biological age of pathogen in the environment. It is verified that the global dynamics of the model is completely determined by the basic reproduction number. Asymptotic smoothness is verified as a necessary argument. By analyzing corresponding characteristic equations, we discuss the local stability of each of feasible steady states. Uniform persistence is shown by using the persistence theory for infinite dimensional dynamical system. The global stability of each of feasible steady states is established by using suitable Lyapunov functionals and LaSalle’s invariance principle. Numerical simulations are carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

For the long term population behavior, demography is a very important factor impacting the disease spread. Infection age also helps us better understand the process of the disease transmission. In this paper, we incorporate these two factors in an SIR epidemic model on complex networks. Through mathematical analysis, the basic reproduction number R 0 is shown to be a sharp threshold to determine whether or not the disease spreads. Precisely, if R 0 is less than 1 then the disease-free equilibrium is globally asymptotically stable while if R 0 is larger than 1 then the endemic equilibrium is globally asymptotically stable. Some simulations are carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Epidemic models with infection age have been extensively studied in the recent decades. Unfortunately, the incidence rate used is the bilinear one. As incidence rate plays an important role in disease transmission, in this paper, we study an SIR epidemic model with infection age and saturated incidence. We establish a threshold dynamics by applying the fluctuation lemma and Lyapunov functional. Roughly, if the basic reproduction number is less than 1 , then the disease-free equilibrium is globally asymptotically stable; while if the basic reproduction number is larger than 1 , then the endemic equilibrium is globally asymptotically stable in the set with initial infectivity. [ABSTRACT FROM AUTHOR]