<abstract> <p>In this paper we develop a compartmental epidemic model to study the transmission dynamics of the COVID-19 epidemic outbreak, with Mexico as a practical example. In particular, we evaluate the theoretical impact of plausible control interventions such as home quarantine, social distancing, cautious behavior and other self-imposed measures. We also investigate the impact of environmental cleaning and disinfection, and government-imposed isolation of infected individuals. We use a Bayesian approach and officially published data to estimate some of the model parameters, including the basic reproduction number. Our findings suggest that social distancing and quarantine are the winning strategies to reduce the impact of the outbreak. Environmental cleaning can also be relevant, but its cost and effort required to bring the maximum of the outbreak under control indicate that its cost-efficacy is low.</p> </abstract>

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This paper aims to evaluate the potential cost-effectiveness of healthcare interventions against human papillomavirus (HPV). For this, we consider a two-sex epidemic model for the transmission dynamics of HPV which includes screening, vaccination of adolescent boys and girls, and vaccination of sexually active adults. We first propose public health policies using constant control parameters and develop a cost-effectiveness analysis (CEA) to identify which intervention delivers the best effectiveness for the money invested. Secondly, we consider time-dependent control parameters and formulate an optimal control problem to obtain time-dependent versions of the interventions. As in the case of constant control parameters, we perform a CEA to investigate the cost-effectiveness of the time-dependent control interventions. Our findings suggest that females' vaccination, including adolescent girls and adult women, is the most cost-effective strategy. We also compare constant against the time-dependent healthcare interventions which are optimal in the sense that they minimize the objective functional of the optimal control problem. The results indicate that time-dependent controls are not always more cost-effective than constant controls.

In applications of the optimal control theory to problems in medicine and biology, the dependency of the objective functional on the control itself is often a matter of controversy. In this paper, we explore the impact of the dependency using reasonably simple SIR and SEIRS epidemic models. To qualitatively compare the outcomes for different objective functionals, we apply the cost-effectiveness analysis. Our result shows that, at least for the comparatively inexpensive controls, the variation of the power at the controls in a biologically feasible range does not significantly affect the forms of the optimal controls and the corresponding optimal state solutions. Moreover, the costs and effectiveness are affected even less. At the same time, the dependency of the cost on the state variables can be very significant.