Abstract
A pathogen can infect multiple hosts. For example, zoonotic diseases like rabies often colonize both humans and animals. Meanwhile, a single host can sometimes be infected with many pathogens, such as malaria and meningitis. Therefore, we studied two susceptible classes and , each of which can be infected when interacting with two different infectious groups and . The stochastic models were formulated through the continuous time Markov chain (CTMC) along with their deterministic analogues. The statistics for the developed model were studied using the multi-type branching process. Since each epidemic class was assumed to transmit only its own type of pathogen, two reproduction numbers were obtained, in addition to the probability-generating functions of offspring. Thus, these, together with the mean number of infections, were used to estimate the probability of extinction. The initial population of infectious classes can influence their probability of extinction. Understanding the disease extinctions and outbreaks could result in rapid intervention by the management for effective control measures.
Highlights
Animal diseases such as rabies and hantavirus can be transmitted to humans
Though any other suitable values can be used to test the dynamics of the two infectious classes, the infection rates β 11, β 12, β 21, andβ 22 were held constant to allow us to examine the changes in I1 (t) and I2 (t) when varying the initial conditions of the two host communities
Since the transition probabilities for our continuous time Markov chain (CTMC) model (Table 1) were used when formulating the probability-generating functions of the offspring for the multi-type branching process, our study reported the emergence of two basic reproduction numbers, R01 and R02, for the two infectious classes I1 (t) and I2 (t), respectively
Summary
Animal diseases such as rabies and hantavirus can be transmitted to humans. Since two or more hosts are included in the process, the spread of diseases is sometimes called a multi-host epidemic [2]. The co-infection of two different pathogens in a single host is common [4]. This can be seen when a host is simultaneously infected by HIV and malaria [5] or by cholera and typhoid [6], for example. Even though many mathematical models describing the dynamics of this process were previously studied [7,8,9], models involving co-transmission and co-infection in multiple hosts are lacking. The probabilities of disease extinction associated with such models are not well-studied
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