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In this study, we apply optimal control theory to an immuno-epidemiological model of HIV and opioid epidemics. For the multi-scale model, we used four controls: treating the opioid use, reducing HIV risk behaviour among opioid users, entry inhibiting antiviral therapy, and antiviral therapy which blocks the viral production. Two population-level controls are combined with two within-host-level controls. We prove the existence and uniqueness of an optimal control quadruple. Comparing the two population-level controls, we find that reducing the HIV risk of opioid users has a stronger impact on the population who is both HIV-infected and opioid-dependent than treating the opioid disorder. The within-host-level antiviral treatment has an effect not only on the co-affected population but also on the HIV-only infected population. Our findings suggest that the most effective strategy for managing the HIV and opioid epidemics is combining all controls at both within-host and between-host scales. [ABSTRACT FROM AUTHOR]

Sensitivity Analysis (SA) is a useful tool to measure the impact of changes in model parameters on the infection dynamics, particularly to quantify the expected efficacy of disease control strategies. SA has only been applied to epidemic models at the population level, ignoring the effect of within-host virus-with-immune-system interactions on the disease spread. Connecting the scales from individual to population can help inform drug and vaccine development. Thus the value of understanding the impact of immunological parameters on epidemiological quantities. Here we consider an age-since-infection structured vector-host model, in which epidemiological parameters are formulated as functions of within-host virus and antibody densities, governed by an ODE system. We then use SA for these immuno-epidemiological models to investigate the impact of immunological parameters on population-level disease dynamics such as basic reproduction number, final size of the epidemic or the infectiousness at different phases of an outbreak. As a case study, we consider Rift Valley Fever Disease utilizing parameter estimations from prior studies. SA indicates that 1 % increase in within-host pathogen growth rate can lead up to 8 % increase in R 0 , up to 1 % increase in steady-state infected host abundance, and up to 4 % increase in infectiousness of hosts when the reproduction number R 0 is larger than one. These significant increases in population-scale disease quantities suggest that control strategies that reduce the within-host pathogen growth can be important in reducing disease prevalence. [ABSTRACT FROM AUTHOR]

In this paper we the study of dynamics of time since infection structured vector born model with the direct transmission. We use standard incidence term to model the new infections. We analyze the corresponding system of partial differential equation and obtain an explicit formula for the basic reproduction number ℜ0. The diseases-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number is less than one, ℜ0 < 1. Endemic equilibrium exists and is locally asymptotically stable when ℜ0 > 1. The disease will persist at the endemic equilibrium whenever the basic reproduction number is greater than one. [ABSTRACT FROM AUTHOR]

In this paper we formulate a multi-scale nested immuno-epidemiological model of HIV on complex networks. The system is described by ordinary differential equations coupled with a partial differential equation. First, we prove the existence and uniqueness of the immunological model and then establish the well-posedness of the multi-scale model. We derive an explicit expression of the basic reproduction number R 0 of the immuno-epidemiological model. The system has a disease-free equilibrium and an endemic equilibrium. The disease-free equilibrium is globally stable when R 0 < 1 and unstable when R 0 > 1 . Numerical simulations suggest that R 0 increases as the number of nodes in the network increases. Further, we find that for a scale-free network the number of infected individuals at equilibrium is a hump-like function of the within-host reproduction number; however, the dependence becomes monotone if the network has predominantly low connectivity nodes or high connectivity nodes. [ABSTRACT FROM AUTHOR]

Malaria is one of the most common mosquito-borne diseases widespread in the tropical and subtropical regions. Few models coupling the within-host malaria dynamics with the between-host mosquito-human dynamics have been developed. In this paper, by adopting the nested approach, a malaria transmission model with immune response of the host is formulated. Applying age-structured partial differential equations for the between-host dynamics, we describe the asymptomatic and symptomatic infectious host population for malaria transmission. The basic reproduction numbers for the within-host model and for the coupled system are derived, respectively. The existence and stability of the equilibria of the coupled model are analyzed. We show numerically that the within-host model can exhibit complex dynamical behavior, possibly even chaos. In contrast, equilibria in the immuno-epidemiological model are globally stable and their stabilities are determined by the reproduction number. Increasing the activation rate of the within-host immune response 'dampens' the sensitivity of the population level reproduction number and prevalence to the increase of the within-host reproduction of the pathogen. From public health perspective this means that treatment in a population with higher immunity has less impact on the population-level reproduction number and prevalence than in a population with less immunity. [ABSTRACT FROM AUTHOR]