A compartmental model for Schistosoma japonicum transmission dynamics in the Philippines

Schistosomiasis is a chronic and debilitating neglected tropical disease (NTD), second only to malaria as one of the most devastating parasitic diseases. Caused by a parasitic flatworm of the genus Schistosoma, infection occurs when skin comes in contact with contaminated freshwater that contains schistosome-hosting snails. The disease continues to be endemic in many regions of the Philippines, where it poses a significant public health challenge due to a lack of healthcare resources. In the Philippines, additional mammalian reservoirs for the S. japonicum parasite, especially bovines such as carabaos, also facilitate the spread of schistosomiasis. We extend existing compartment models to include human, snail, bovine, and free-living Schistosoma for a comprehensive look at the transmission dynamics of the disease. Sensitivity analysis of model parameters shows that the carabaos themselves can sustain the endemicity of schistosomiasis. Thus, we consider the control method of farming mechanization to avoid contaminated freshwater sources. We find that a reduction of contaminated water contacts by at least 77% will break the transmission cycle and eliminate the disease. However, reducing the contact by about 70% will still result in decrease of human schistosomiasis prevalence to under 1% in 15 years or less. Achieving such high reduction of contact rates could be a daunting task, especially in rural areas. Still, the potential to eliminate or at least reduce the schistosomiasis prevalence should be considered an additional benefit of mechanization efforts in the Philippines.

A Human-Bovine Schistosomiasis Mathematical Model with Treatment and Mollusciciding

To mitigate the spread of schistosomiasis, a deterministic human-bovine mathematical model of its transmission dynamics accounting for contaminated water reservoirs, including treatment of bovines and humans and mollusciciding is formulated and theoretically analyzed. The disease-free equilibrium is locally and globally asymptotically stable whenever the basic reproduction number [Formula: see text], while global stability of the endemic equilibrium is investigated by constructing a suitable Lyapunov function. To support the analytical results, parameter values from published literature are used for numerical simulations and where applicable, uncertainty analysis on the non-dimensional system parameters is performed using the Latin Hypercube Sampling and Partial Rank Correlation Coefficient techniques. Sensitivity analysis to determine the relative importance of model parameters to disease transmission shows that the environment-related parameters namely, [Formula: see text] (snails shedding rate of cercariae), [Formula: see text] (probability that cercariae shed by snails survive), c (fraction of the contaminated environment sprayed by molluscicides) and [Formula: see text] (mortality rate of cercariae) are the most significant to mitigate the spread of schistosomiasis. Mollusciciding, which directly impacts the contaminated environment as a single control strategy is more effective compared to treatment. However, concurrently applying mollusciciding and treatment will yield a better outcome.

An age-structured epidemic model with boosting and waning of immune status

In this paper, we developed an age-structured epidemic model that takes into account boosting and waning of immune status of host individuals. For many infectious diseases, the immunity of recovered individuals may be waning as time evolves, so reinfection could occur, but also their immune status could be boosted if they have contact with infective agent. According to the idea of the Aron's malaria model, we incorporate a boosting mechanism expressed by reset of recovery-age (immunity clock) into the SIRS epidemic model. We established the mathematical well-posedness of our formulation and showed that the initial invasion condition and the endemicity can be characterized by the basic reproduction number $ R_0 $. Our focus is to investigate the condition to determine the direction of bifurcation of endemic steady states bifurcated from the disease-free steady state, because it is a crucial point for disease prevention strategy whether there exist subcritical endemic steady states. Based on a recent result by Martcheva and Inaba ^[1], we have determined the direction of bifurcation that endemic steady states bifurcate from the disease-free steady state when the basic reproduction number passes through the unity. Finally, we have given a necessary and sufficient condition for backward bifurcation to occur.