In this paper, we report an application for the mathematical theory of dynamic optimization for design of optimal strategies that account for daily commuting of human residents, aiming to reduce vector-borne infections (dengue) among human populations. Our analysis is based on a two-patch dengue transmission model amended with control variables that represent personal protection measures aimed at reduction of the number of contacts between mosquitoes and human hosts (e.g., the use of repellents, mosquito nets, or insecticide-treated clothing). As a result, we have proposed and numerically solved an optimal control problem to minimize the costs associated with the application of control measures, while also minimizing the total number of dengue-infected people in both residential areas. Our principal goal was to identify an optimal strategy for personal protection that renders the maximal number of averted human infections per unit of invested cost, and this goal has been accomplished on the grounds of cost-effectiveness analysis.

Despite the ongoing preventive measures of vector control, dengue fever still presents outbreaks, and daily commuting of people also facilitates its propagation. To contain the disease spread after an outbreak has already occurred, the local healthcare authorities are compelled to perform insecticide spraying as a corrective measure of vector control, thus trying to avoid massive human infections. Several issues concerned with the practical implementation of such corrective measures can be solved from a mathematical standpoint, and the purpose of this study is to contribute to this strand of research. Using as a basis a two-patch dengue transmission ODE model, we designed the patch-dependent optimal strategies for the insecticide spraying with the optimal control approach. We also analyzed the response of the optimal strategies to three alternative modes of budget cuts under different intensities of daily commuting. Our approach illustrated that trying “to save money” by reducing the budget for corrective control is completely unwise, and the anticipated “savings” will actually turn into considerable additional public spending for treating human infections, which could have been averted by a timely corrective intervention.

In this paper, we propose and justify a synthesized version of the tuberculosis transmission model featuring treatment abandonment. In contrast to other models that account for the treatment abandonment, our model has only four state variables or classes (susceptible, latent, infectious, and treated), while people abandoning treatment are not gathered into an additional class. The proposed model retains the core properties that are highly desirable in epidemiological modeling. Namely, the disease transmission dynamics is characterized by the basic reproduction number $ \mathscr{R}_0 $, a threshold value that determines the number of possible steady states and their stability properties. It is shown that the disease-free equilibrium is globally asymptotically stable (GAS) only if $ \mathscr{R}_0 < 1 $, while a strictly positive endemic equilibrium exists and is GAS only if $ \mathscr{R}_0 > 1. $ Analysis of the dependence of $ \mathscr{R}_0 $ on the treatment abandonment rate shows that a reduction of the treatment abandonment rate has a positive effect on the disease incidence and results in avoiding disease-related fatalities.

This study presents a mathematical modeling framework to analyze the impact of integrating sterilizing treatment into tuberculosis (TB) control strategies, particularly in resource-limited settings. Our findings highlight that while sterilizing treatment alone is highly effective in reducing TB incidence and mortality, its widespread implementation requires significant financial investment. The optimal control approach demonstrates that a mixed strategy, combining sterilizing and non-sterilizing treatments, can achieve comparable public health benefits at a lower cost, especially in the medium-term planning. From a long-term perspective, however, our results suggest that exclusively sterilizing treatment ultimately leads to greater reductions in TB incidence, prevalence, and mortality, justifying its higher initial cost. This is primarily due to the ability of sterilizing drugs to eliminate latent TB infections, prevent future active infections and disease-induced deaths, and avoid a considerable number of treatments. Additionally, under scenarios where the cost of sterilizing drugs decreases over time, a swift transition to a solely sterilizing treatment could result in both epidemiological and economic advantages for healthcare systems.

This study presents a mathematical modeling framework to analyze the impact of integrating sterilizing treatment into tuberculosis (TB) control strategies, particularly in resource-limited settings. The numerical analysis of the proposed mathematical framework indicates that while sterilizing treatment alone is highly effective in reducing TB incidence and mortality, its widespread implementation requires significant financial investment. The optimal control approach demonstrates that a mixed strategy, combining sterilizing and non-sterilizing treatments, can achieve comparable public health benefits at a lower cost, especially in medium-term planning. From a long-term perspective, however, our results suggest that exclusively sterilizing treatment ultimately leads to greater reductions in TB incidence, prevalence, and mortality, justifying its higher initial cost. This is primarily due to the ability of sterilizing drugs to eliminate latent TB infections, prevent future active infections and disease-induced deaths, and avoid a considerable number of treatments. Additionally, under scenarios where the cost of sterilizing drugs decreases over time, a swift transition to a solely sterilizing treatment could result in both epidemiological and economic advantages for healthcare systems.