Mathematical modelling of the dynamics of human schistosomiasis with time-discrete delays

Autor: Jean Jules Tewa, I. V. Yatat-Djeumen, I. Ngningone Eya, R. M. Etoua
Rok vydání: 2021
Předmět:
Zdroj: Boletín de la Sociedad Matemática Mexicana. 27
ISSN: 2296-4495
1405-213X
DOI: 10.1007/s40590-021-00376-6
Popis: In this paper, we study a schistosomiasis model incorporating the miracidia and cercariae dynamics, discrete-time delays as well as control measures like water treatment. Modelling the dynamics of schistosomiasis infectious disease is quite challenging because of the different larval forms assumed by the parasite and the requirement of two hosts during the life cycle. Our model is generic in the sense that it considers both situations where particle depletion by hosts or snails could have or not a negligible impact on particle dynamics. Precisely, we introduce two parameters u and v such that when $$u=v=0$$ , then particle depletion by hosts or snails is not considered; when $$u=v=1$$ , then particle depletion by hosts and snails is considered. The model is analyzed to gain insights into the qualitative features of the disease-free equilibrium which allows the determination of the basic reproductive number $${\mathcal {R}}_{u,v}$$ . The Center Manifold Theory is used to discuss existence and local stability of an endemic equilibrium. Global sensitivity analysis (SA) of the schistosomiasis model and the basic reproduction number are carried out. SA results of the model point out the leading role of $$\eta $$ , the parameter that shapes infection-induced death rate in humans, on the dynamics of humans (susceptible and infected), miracidia, cercariae and infected snails. They also reveal the pervasive role of $$\theta $$ , the water treatment-induced death rate of snails, on the dynamics of infected humans, miracidia, snails (susceptible and infected) and cercariae. SA results of the basic reproduction number highlight the role of $$\eta $$ , $$\theta $$ , $$\lambda $$ (the contact rate of transmission of miracidia to susceptible snails), $$\varpi $$ (production rate of miracidia from feces of infected humans) and $$\gamma $$ (the transmission rate of cercariae to susceptible humans). Therefore, a possible way to control the disease could rely on the intensification of sanitization campaigns that will result in an increase of $$\theta $$ together with sensitization about the necessity to have a treatment once you are infected to reduce $$\eta $$ .
Databáze: OpenAIRE