Modelling and optimising healthcare interventions in a model with explicit within- and between-host dynamics

Given an endemic infectious disease and a budget, how do we optimally allocate interventions to control the disease? This paper shows that the optimal strategy varies depending on the budget, the type of intervention, the trajectory of pathogen load, and the objective. Using a model with explicit within- and between-host dynamics, we model isolation, supportive treatment, and specific treatment. Isolation and supportive treatment affect the transmission coefficient and the disease-induced mortality rate, respectively, in the between-host dynamics. Specific treatment affects the clearance rate of pathogens in the within-host dynamics. We study the optimisation of the three interventions for various budget levels via evaluating isolation and supportive treatment at the population level and specific treatment at both the population and individual levels. At the population level, we consider the risk of transmission, the burden of illness, and the survival probability, and to that end, we choose the population-level infection rate, the population density of infected individuals, and the total disease-induced mortality rate as objective functions. At the individual level, we consider the length of infection and the pathogen load, and to that end, we choose the maximum infection-age and the maximum pathogen load as objective functions. The objective is to minimise these functions through varying two variables that refer to when the intervention starts and when it stops for an infected individual and also indicate what kind of individuals can get the intervention from the population perspective. We find that the optimal strategy of isolation is to isolate individuals with a higher pathogen load, given a lower budget. The optimal strategy of supportive treatment can be the same as isolation or simply no treatment. The optimal strategy of specific treatment is complicated, and it can be to treat individuals with pathogen loads above a particular level until they recover or until the pathogens can decrease when treatment stops, or it can be another scenario.