Abstract
This paper proposes a model for brucellosis transmission. The model takes into account the age of infection and waning immunity, that is, the progressive loss of immunity after recovery. Three routes of transmissions are considered: vertical transmission, and both direct and indirect routes of horizontal transmission. According to the well-posedness results, we provide explicit formulas for the equilibria. Next, we derive the basic reproduction number R0 and prove some stability results depending on the basic reproductive number. Finally, we perform numerical simulations using model parameters estimated from biological data to confirm our theoretical results. The results of these simulations suggest that for certain values of parameters, there will be periodic outbreaks of epidemics, and the disease will not be eradicated from the population. Our results also highlight the fact that the birth rate of cattle significantly influences the dynamics of the disease. The proposed model can be of a good use in studying the effects of vaccination on the cattle population.
Highlights
Brucellosis is a zoonotic disease, mainly caused by Brucella abortus
This paper proposes a mathematical model of brucellosis with age of infection and time since recovery to describe the dynamics of brucellosis in a given population under the assumption that immune protection may wane over time
We proposed a new model of brucellosis occurring in cattle populations
Summary
Brucellosis is a zoonotic disease, mainly caused by Brucella abortus. It is transmitted to people from animal species such as cattle, swine, goats, and sheep [1,2]. Several mathematical models of brucellosis have been developed by researchers Their authors have used various mathematical approaches: ordinary differential equations with waning of immunity [9,10,11,12,13,14,15,16], culling [17,18,19], treatment and vaccination [18,20], seasonality [21], and partial differential equations with age of infection [22] and seasonality [23]. This paper proposes a mathematical model of brucellosis with age of infection and time since recovery to describe the dynamics of brucellosis in a given population under the assumption that immune protection may wane over time. Djidjou-Demasse et al [27] considered a model describing the interaction between humans and vectors in malaria Their model incorporated age, time since infection, and waning immunity.
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