Compartmental modelling for the transmission dynamics of ringworm disease in humans and pets with bifurcation analysis

Abstract

Ringworm disease is a fungal infection caused by $$ {Trichophyton}, {Microsporum}$$ and $$ {Epidermophyton}$$ with humans, pets and environment as the key drivers of the infection in Sub-Sahara Africa. The effect of this on the infection transmissibility can be better understood when these transmission pathways are been considered. In this study, a novel mathematical model is formulated using a system of non-linear differential equations to represent and determine the impact of transmission routes on the disease progression through seven interconnected compartments: susceptible humans, infected humans, recovered humans, susceptible pets, infected pets, recovered pets and dermatophytosis fungi populations. The positivity and boundedness of the solution was investigated. We calculated the basic reproduction number, $$R_0$$ using next generation matrix which can be employed to study the asymptotic stability of disease-free and diseased equilibrium points. Applying geometric approach, Routh-Hurwitz and Castillo-Chavez criteria, we examine qualitatively the local and global asymptotic behaviour of these equilibrium points. Furthermore, we explore under certain conditions the possibility of forward bifurcation using the theory of center manifold. Partial Rank Correlation Coefficients (PRCCs) plots, heat maps and phase portraits prioritize main factors for controlling ringworm infections. Numerical results of the model inform that two or more sources of infection promotes the disease spread with pets as the most harmful source of ringworm infection to humans than any other factors. Our findings further suggests that to avoid dermatophytic fungi dominance within the environment, control health policies for ringworm disease should be deployed in the first $$0-5$$ days of the epidemic outbreak. Hence, we recommend that multidisciplinary control approaches be adopted by health policy makers in order to mitigate this infection since its transmission is multifaceted, and keeping of pets among families or communities should be practised with optimum health tips since pets are the major drivers of ringworm disease among humans. Lastly, the study advocates for proper hygiene practices and sanitization of dirty surfaces in order to control the effects of shedding of dermatophytosis fungi into the environment.