A model of insect control with imperfect treatment

Congenital transmission of Chagas disease: The role of newborn therapy on the disease's dynamics

Chagas disease, also known as American trypanosomiasis, is caused by a protozoan blood-borne pathogen called Trypanosoma cruzi. The World Health Organization (WHO) has classified Chagas as one of 21 neglected tropical diseases present in the world and estimates that 6-7 million people are currently infected with Chagas. Congenital transmission of Chagas disease contributes to a significant amount of new infections, especially in endemic areas where 22.5% of new infections are due to congenital transmission. In this paper, we investigate congenital transmission's impact on Chagas disease dynamics through a mathematical model. Specifically, we examine how treating a proportion of infants born to infected individuals impacts the progression and spread of Chagas disease. The influence of newborn therapy on the dynamics of the model is thoroughly investigated, both theoretically and numerically. The results illustrate the importance of treating a high proportion of newborns to reduce the number of infected cases of the disease. The findings show that the therapy given to newborns is necessary but not sufficient to curb the transmission of Chagas disease, and a comprehensive approach that includes vector and vertical transmission control strategies is essential for eradicating Chagas disease. We also observed that if vector transmission can be controlled, then at least 55% of the newborns need to be treated to eliminate the disease.

Modeling the impact of non-human host predation on the transmission of Chagas disease

In addition to the traditional transmission route via the biting-and-defecating process, non-human host predation of triatomines is recognized as another significant avenue for Chagas disease transmission. In this paper, we develop an eco-epidemiological model to investigate the impact of predation on the disease's spread. Two critical thresholds, Rvp (the basic reproduction number of triatomines) and R0p (the basic reproduction number of the Chagas parasite), are derived to delineate the model's dynamics. Through the construction of appropriate Lyapunov functions and the application of the Bendixson-Dulac theorem, the global asymptotic stabilities of the equilibria are fully established. The vector-free equilibrium E0 is globally stable when Rvp<1. E1, the disease-free equilibrium, is globally stable when Rvp>1 and R0p<1, while the endemic equilibrium E∗ is globally stable when both Rvp>1 and R0p>1. Numerical simulations highlight that the degree of host predation on triatomines, influenced by non-human hosts activities, can variably increase or decrease the Chagas disease transmission risk. Specifically, low or high levels of host predation can reduce R0p to below unity, while intermediate levels may increase the infected host populations, albeit with a reduction in R0p. These findings highlight the role played by non-human hosts and offer crucial insights for the prevention and control of Chagas disease.

A description of the epidemiological dynamics of Chagas disease via mathematical modeling

Chagas disease is caused by the protozoan Trypanosoma cruzi, which parasitizes many mammals, including humans. Its vectors are blood-feeding hematophagous triatomine insects of different species, which vary according to the geographical area. One of the 17 neglected diseases targeted by the World Health Organization, Chagas disease is endemic to the Americas, but has spread to other countries due to human migratory movements. In this study, we describe the epidemiological dynamics of Chagas disease in an endemic area, considering the main transmission mechanisms and the demographic effects of birth, mortality, and human migration in this phenomenon. We apply mathematical models as a methodological approach to simulate the interactions between reservoirs, vectors, and humans using a system of ordinary differential equations. The results show that the Chagas disease control measures currently in place cannot be relaxed without endangering the progress achieved to date.

COVID-19 intervention models: An initial aggressive treatment strategy for controlling the infection

The novel coronavirus (COVID-19) outbreak emerged in December 2019. The disease has caused loss of many lives and has become an unprecedented threat to public health worldwide. We develop simple COVID-19 epidemic models to study treatment strategies to control the pandemic. The results show that eradication of the disease is possible if the efficacy of treatment is perfect. We also investigate the existence of a dual-rate effect. Conditions under which the effect occurs are derived. When the effect is present, a tactic to control the infection might be to initially treat infected individuals aggressively at a relatively high rate to drive the prevalence to a lower region that can be maintained in the long run at relatively moderate rate and cost.