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. 2024 May 31;10(11):e32012.
doi: 10.1016/j.heliyon.2024.e32012. eCollection 2024 Jun 15.

Mathematical model to assess the impact of contact rate and environment factor on transmission dynamics of rabies in humans and dogs

Mfano Charles  1   2 , Verdiana G Masanja  1 , Delfim F M Torres  3 , Sayoki G Mfinanga  4 , G A Lyakurwa  1
Affiliations

Mathematical model to assess the impact of contact rate and environment factor on transmission dynamics of rabies in humans and dogs

Mfano Charles et al. Heliyon. .

Abstract

This paper presents a mathematical model to understand how rabies spreads among humans, free-range, and domestic dogs. By analyzing the model, we discovered that there are equilibrium points representing both disease-free and endemic states. We calculated the basic reproduction number, R 0 using the next generation matrix method. When R 0 < 1 , the disease-free equilibrium is globally stable, whereas when R 0 ≥ 1 , the endemic equilibrium is globally stable. To identify the most influential parameters in disease transmission, we used the normalized forward sensitivity index. The simulations revealed that the contact rates between the infectious agent and humans, free-range dogs, and domestic dogs, have the most significant impact on rabies transmission. The study also examines how periodic changes in transmission rates affect the disease dynamics, emphasizing the importance of transmission frequency and amplitude on the patterns observed in rabies spread. To reduce disease sensitivity, one should prioritize effective disease control measures that focus on keeping both free-range and domestic dogs indoors. This is a crucial factor in preventing the spread of disease and should be implemented as a primary disease control measure.

Keywords: Contact rate; Environment; Mathematical model; Periodic transmission; Rabies disease.

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Conflict of interest statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Figures

Figure 1
Figure 1
Flow diagram for rabies transmission among human, free range and domestic dogs with parameters.
Figure 2
Figure 2
Scatter estimated with standard deviation of 0.05 and numerical simulation (sold) with confidence interval of 95%.
Figure 3
Figure 3
The impact of human population bite incidence on the occurrence of periodic rabies outbreaks.
Figure 4
Figure 4
The impact of free range dogs bite incidence on the occurrence of periodic rabies outbreaks.
Figure 5
Figure 5
The impact of domestic dogs bite incidence on the occurrence of periodic rabies outbreaks.
Figure 6
Figure 6
The impact of environment shedding incidence on the occurrence of periodic rabies outbreaks.
Figure 7
Figure 7
Effect of R0 with respect to κ1, κ2, ψ1, and ψ2.
Figure 8
Figure 8
Simulation results of model (5) for IH with respect to τ1, τ2, and τ3.
Figure 9
Figure 9
Simulation results of model (5) for ID with respect to ψ1, ψ2, and ψ3.
Figure 10
Figure 10
Simulation results of model (5) for IF with respect to τ1, τ2, and τ3.
See this image and copyright information in PMC

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