Transmission dynamics of cryptosporidiosis in humans and cattle: A CTMC stochastic model integrating the role of human immune status

Cryptosporidiosis is a zoonotic disease that affects humans and animals globally, posing a significant public health and veterinary concern. It is mainly transmitted through the faecal-oral route. To capture the inherent variability in the dynamics of cryptosporidiosis, a continuous-time Markov chain (CTMC) stochastic model is developed and analysed, based on an analogous deterministic model. The aim is to investigate the probability of disease persistence in cattle, immunocompetent humans, and immunocompromised humans. The stochastic threshold in the CTMC stochastic model is computed using the multitype branching process. The probability of disease extinction, as determined through the multitype branching process, demonstrates a good match with the probability approximated through numerical simulations. Cryptosporidiosis is more likely to extinct if it emerges from infected immunocompetent human compartments than from infected immunocompromised human compartments. However, a major disease outbreak is probable if the disease originates from either infected cattle compartments or Cryptosporidium oocysts in the environment compartment. The finite time to cryptosporidiosis extinction is shorter when the disease is introduced by an infected human or cattle compared to exposed individuals. This suggests that the incubation period prolongs the extinction time. The results of the sensitivity analysis show that a 90% reduction in human shedding rates of Cryptosporidium oocysts into the environment carries the highest probability of disease extinction, provided that the disease originates from an infected human. Therefore, reducing the shedding rates of Cryptosporidium oocysts into the environment by infectious humans is critical for the control and prevention of cryptosporidiosis in susceptible populations. This underscores the importance of measures such as proper sanitation practices, environmental decontamination, and effective cattle farm management to eliminate Cryptosporidium oocysts, thereby facilitating effective control and prevention of the disease.